Optimization Software Class Libraries 1st Edition Stefan Voß
- 1. Optimization Software Class Libraries 1st Edition Stefan Voß pdf download https://ebookfinal.com/download/optimization-software-class- libraries-1st-edition-stefan-vos/ Explore and download more ebooks or textbooks at ebookfinal.com
- 2. We have selected some products that you may be interested in Click the link to download now or visit ebookfinal.com for more options!. Pro iOS Apps Performance Optimization 1st Edition Khang Vo (Auth.) https://ebookfinal.com/download/pro-ios-apps-performance- optimization-1st-edition-khang-vo-auth/ Annual Reports on NMR Spectroscopy Volume 83 1st Edition Webb https://ebookfinal.com/download/annual-reports-on-nmr-spectroscopy- volume-83-1st-edition-webb/ The Sniper Play 1 g6 Bg7 and c5 First Edition Charlie Storey https://ebookfinal.com/download/the-sniper-play-1-g6-bg7-and-c5-first- edition-charlie-storey/ Using the TI 83 Plus TI 84 Plus Christopher R. Mitchell https://ebookfinal.com/download/using-the-ti-83-plus-ti-84-plus- christopher-r-mitchell/
- 3. Lithography 1st Edition Stefan Landis https://ebookfinal.com/download/lithography-1st-edition-stefan-landis/ Leviticus Stefan Schorch https://ebookfinal.com/download/leviticus-stefan-schorch/ Software Metrics and Software Metrology 1st Edition Alain Abran https://ebookfinal.com/download/software-metrics-and-software- metrology-1st-edition-alain-abran/ Nanotechnology in Biology and Medicine Methods Devices and Applications 1st Edition Tuan Vo-Dinh https://ebookfinal.com/download/nanotechnology-in-biology-and- medicine-methods-devices-and-applications-1st-edition-tuan-vo-dinh/ Weblogs and Libraries 1st Edition Laurel Clyde (Auth.) https://ebookfinal.com/download/weblogs-and-libraries-1st-edition- laurel-clyde-auth/
- 5. Optimization Software Class Libraries 1st Edition Stefan Voß Digital Instant Download Author(s): Stefan Voß, David L. Woodruff ISBN(s): 9780306481260, 1402070020 Edition: 1 File Details: PDF, 6.35 MB Year: 2002 Language: english
- 7. Optimization Software Class Libraries
- 8. OPERATIONS RESEARCH/COMPUTER SCIENCE INTERFACES SERIES Series Editors Professor Ramesh Sharda Oklahoma State University Prof. Dr. Stefan Voß Technische Universität Braunschweig Other published titles in the series: Greenberg, Harvey J. / A Computer-Assisted Analysis System for Mathematical Programming Models and Solutions: A User’s Guide for ANALYZE Greenberg, Harvey J. / Modeling by Object-Driven Linear Elemental Relations: A Users Guide for MODLER Brown, Donald/Scherer, William T. / Intelligent Scheduling Systems Nash, Stephen G./Sofer, Ariela / The Impact of Emerging Technologies on Computer Science & Operations Research Barth, Peter / Logic-Based 0-1 Constraint Programming Jones, Christopher V. / Visualization and Optimization Barr, Richard S./ Helgason, Richard V./ Kennington, Jeffery L. / Interfaces in Computer Science & Operations Research: Advances in Metaheuristics, Optimization, and Stochastic Modeling Technologies Ellacott, Stephen W./ Mason, John C./ Anderson, Iain J. / Mathematics of Neural Networks: Models, Algorithms & Applications Woodruff, David L. / Advances in Computational & Stochastic Optimization, Logic Programming, and Heuristic Search Klein, Robert / Scheduling of Resource-Constrained Projects Bierwirth, Christian / Adaptive Search and the Management of Logistics Systems Laguna, Manuel / González-Velarde, José Luis / Computing Tools for Modeling, Optimization and Simulation Stilman, Boris / Linguistic Geometry: From Search to Construction Sakawa, Masatoshi / Genetic Algorithms and Fuzzy Multiobjective Optimization Ribeiro, Celso C./ Hansen, Pierre / Essays and Surveys in Metaheuristics Holsapple, Clyde/ Jacob, Varghese / Rao, H. R. / BUSINESS MODELLING: Multidisciplinary Approaches — Economics, Operational and Information Systems Perspectives Sleezer, Catherine M./ Wentling, Tim L./ Cude, Roger L. / HUMAN RESOURCE DEVELOPMENT AND INFORMATION TECHNOLOGY: Making Global Connections
- 9. Optimization Software Class Libraries Edited by Stefan Voß Braunschweig University of Technology, Germany David L. Woodruff University of California, Davis, USA KLUWER ACADEMIC PUBLISHERS NEW YORK, BOSTON, DORDRECHT, LONDON, MOSCOW
- 10. eBook ISBN: 0-306-48126-X Print ISBN: 1-4020-7002-0 ©2003 Kluwer Academic Publishers New York, Boston, Dordrecht, London, Moscow Print ©2002 Kluwer Academic Publishers All rights reserved No part of this eBook may be reproduced or transmitted in any form or by any means, electronic, mechanical, recording, or otherwise, without written consent from the Publisher Created in the United States of America Visit Kluwer Online at: http://kluweronline.com and Kluwer's eBookstore at: http://ebooks.kluweronline.com Dordrecht
- 11. Contents Preface 1 ix 1 2 3 20 23 25 25 26 36 43 49 51 57 59 60 61 65 69 74 77 78 Optimization Software Class Libraries Stefan Voß and David L. Woodruff 1.1 1.2 1.3 1.4 Introduction Component Libraries Callable Packages and Numerical Libraries Conclusions and Outlook 2 Distribution, Cooperation, and Hybridization for Combinatorial Optimization Martin S. Jones, Geoff P. McKeown and Vic J. Rayward-Smith 2.1 2.2 2.3 2.4 2.5 2.6 2.7 Introduction Overview of the Templar Framework Distribution Cooperation Hybridization Cost of Supporting a Framework Summary 3 A Framework for Local Search Heuristics for Combinatorial Optimiza- tion Problems Alexandre A. Andreatta, Sergio E.R. Carvalho and Celso C. Ribeiro 3.1 3.2 3.3 3.4 3.5 3.6 3.7 Introduction Design Patterns The Searcher Framework Using the Design Patterns Implementation Issues Related Work Conclusions and Extensions
- 12. vi OPTIMIZATION SOFTWARE CLASS LIBRARIES 81 81 83 85 103 137 146 153 155 177 177 178 179 180 182 186 190 190 193 193 196 198 202 211 215 219 219 221 225 239 249 250 4 HOTFRAME: A Heuristic Optimization Framework Andreas Fink and Stefan Voß 4.1 4.2 4.3 4.4 4.5 4.6 4.7 Introduction A Brief Overview Analysis Design Implementation Application Conclusions 5 Writing Local Search Algorithms Using EASYLOCAL++ Luca Di Gaspero and Andrea Schaerf 5.1 5.2 5.3 5.4 5.5 5.6 Introduction An Overview of EASYLOCAL++ The COURSE TIMETABLING Problem Solving COURSE TIMETABLING Using EASYLOCAL++ Debugging and Running the Solver DiscussionandConclusions 6 Integrating Heuristic Search and One-Way Constraints in the iOpt Toolkit Christos Voudouris and Raphaël Dorne Introduction One-Way Constraints Constraint Satisfaction Algorithms for One-Way Constraints The Invariant Library of iOpt The Heuristic Search Framework of iOpt Experimentation on the Graph Coloring and the Vehicle Routing Problem Related Work and Discussion Conclusions 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 7 The OptQuest Callable Library Manuel Laguna and Rafael Martí 7.1 7.2 7.3 7.4 7.5 7.6 Introduction ScatterSearch The OCL Optimizer OCL Functionality OCL Application Conclusions 8 A Constraint Programming Toolkit for Local Search Paul Shaw, Vincent Furnon and Bruno De Backer 8.1 8.2 8.3 8.4 8.5 8.6 Introduction Constraint Programming Preliminaries The Local Search Toolkit Industrial Example: Facility Location Extending the Toolkit Specializing the Toolkit: ILOG Dispatcher 155 156 161 162 172 174
- 13. Contents vii 259 260 263 263 265 269 276 279 290 294 295 296 304 317 319 328 331 335 357 8.7 8.8 Related Work Conclusion 9 The Modeling Language OPL – A Short Overview Pascal Van Hentenryck and Laurent Michel 9.1 9.2 9.3 9.4 9.5 9.6 9.7 Introduction Frequency Allocation Sport Scheduling Job-Shop Scheduling The Trolley Application Research Directions Conclusion 10 Genetic Algorithm Optimization Software Class Libraries Andrew R. Pain and Colin R. Reeves 10.1 10.2 10.3 10.4 10.5 Introduction Class Library Software Java Class Library Software Genetic Algorithm Optimization Software Survey Conclusions Abbreviations References Index
- 14. This page intentionally left blank
- 15. Preface Optimization problems in practice are diverse and evolve over time, giving rise to re- quirements both for ready-to-use optimization software packages and for optimization software libraries, which provide more or less adaptable building blocks for appli- cation-specific software systems. In order to apply optimization methods to a new type of problem, corresponding models and algorithms have to be “coded” so that they are accessible to a computer. One way to achieve this step is the use of a model- ing language. Such modeling systems provide an excellent interface between models and solvers, but only for a limited range of model types (in some cases, for example, linear) due, in part, to limitations imposed by the solvers. Furthermore, while mod- eling systems especially for heuristic search are an active research topic, it is still an open question as to whether such an approach may be generally successful. Modeling languages treat the solvers as a “black box” with numerous controls. Due to variations, for example, with respect to the pursued objective or specific problem properties, ad- dressing real-world problems often requires special purpose methods. Thus, we are faced with the difficulty of efficiently adapting and applying appropriate methods to these problems. Optimization software libraries are intended to make it relatively easy and cost effective to incorporate advanced planning methods in application-specific software systems. A general classification provides a distinction between callable packages, numeri- cal libraries, and component libraries. Component libraries provide useful abstractions for manipulating algorithm and problem concepts. Object-oriented software technol- ogy is generally used to build and apply corresponding components. To enable adap- tation, these components are often provided at source code level. Corresponding class libraries support the development of application-specific software systems by provid- ing a collection of adaptable classes intended to be reused. However, the reuse of algorithms may be regarded as “still a challenge to object-oriented programming”. Component libraries are the subject of this edited volume. That is, within a careful collection of chapters written by experts in their fields we aim to discuss all relevant aspects of component libraries. To allow for wider applicability, we restrict the expo- sition to general approaches opposed to problem-specific software.
- 16. x OPTIMIZATION SOFTWARE CLASS LIBRARIES Acknowledgements Of course such an ambitious project like publishing a high quality book would not have been possible without the most valuable input of a large number of individuals. First of all, we wish to thank all the authors for their contributions, their patience and fruitful discussion. We are grateful to the whole team at the University of Technology Braunschweig, who helped in putting this book together, and to Gary Folven at Kluwer Academic Publishers for his help and encouragement. The Editors: Stefan Voß David L. Woodruff
- 17. 1 OPTIMIZATION SOFTWARE CLASS LIBRARIES Stefan Voß1 and David L. Woodruff2 1 Technische Universität Braunschweig Institut für Wirtschaftswissenschaften Abt-Jerusalem-Straße 7, D-38106 Braunschweig, Germany stefan.voss@tu—bs.de 2 Graduate School of Management University of California at Davis Davis, California 95616, USA dlwoodruff@ucdavis.edu Abstract: Many decision problems in business and engineering may be formulated as optimization problems. Optimization problems in practice are diverse, often complex and evolve over time, so one requires both ready-to-use optimization software packages and optimization software libraries, which provide more or less adaptable building blocks for application-specific software systems. To provide a context for the other chapters in the book, it is useful to briefly survey optimization software. A general classification provides a distinction between callable packages, numerical libraries, and component libraries. In this introductory chapter, we discuss some general aspects of corresponding libraries and give an overview of avail- able libraries, which provide reusable functionality with respect to different optimization methodologies. To allow for wider applicability we devote little attention to problem- specific software so we can focus the exposition on general approaches.
- 18. OPTIMIZATION SOFTWARE CLASS LIBRARIES 1.1 INTRODUCTION New information technologies continuously transform decision processes for man- agers and engineers. This book is the result of the confluence of recent developments in optimization techniques for complicated problems and developments in software development technologies. The confluence of these technologies is making it possible for optimization methods to be embedded in a host of applications. Many decision problems in business and engineering may be formulated as opti- mization problems. Optimization problems in practice are diverse, often complex and evolve over time, so one requires both ready-to-use optimization software packages and optimization software libraries, which provide more or less adaptable building blocks for application-specific software systems. To provide a context for the other chapters in the book, it is useful to briefly survey optimization software. In order to apply optimization methods to a new type of problem, corresponding models and algorithms have to be “coded” so that they are accessible to a computer program that can search for a solution. Software that can take a problem in canonical form and find optimal or near optimal solutions is referred to as a solver. The transla- tion of the problem from its physical or managerial form into a form usable by a solver is a critical step. One way to achieve this step is the use of a modeling language. Such modeling systems provide an excellent interface between models and solvers, but only for a limited range of model types (in some extreme cases, e.g., linear). This is partly due to limitations imposed by the solvers. Furthermore, while modeling systems are an active research topic, it is still an open question whether such an approach may be successful for complex problems. Modeling languages treat the solvers as a “black box” with numerous controls. Due to variations, for example, with respect to the pursued objective or specific problem properties, addressing real-world problems often requires special purpose methods. Thus, we are faced with the difficulty of efficiently adapting and applying appropriate methods to these problems. Optimization software libraries are intended to make it relatively easy and cost effective to incorporate advanced planning methods in application-specific software systems. Callablepackages allow users to embed optimization functionality in applications, and are designed primarily to allow the user’s software to prepare the model and feed it to the package. Such systems typically also include routines that allow manipulation of the model and access to the solver’s parameters. As with the modeling language approach, the solver is treated essentially as an opaque object, which provides a clas- sical functional interface, using procedural programming languages such as C. While there are only restricted means to adapt the corresponding coarse-grained functional- ity, the packages do often offer callbacks that facilitate execution of user code during the solution process. Numerical libraries provide similar functionality, except that the model data is treated using lower levels of abstraction. For example, while modeling languages and callable packages may allow the user to provide names for sets of variables and indexes into the sets, numerical libraries facilitate only the manipulation of vectors and matrices as numerical entities. Well-known solution techniques can be called as 2
- 19. OPTIMIZATION SOFTWARE CLASS LIBRARIES 3 subroutines, or can be built from primitive operations on vectors and matrices. These libraries provide support for linear algebra, numerical computation of gradients, and support for other operations of value, particularly for continuous optimization. Component libraries provide useful abstractions for manipulating algorithm and problem concepts. Object-oriented software technology is generally used to build and deploy components. To enable adaptation these components are often provided at source code level. Class libraries support the development of application-specific software systems by providing a collection of adaptable classes intended to be reused. Nevertheless, the reuse of algorithms may be regarded as “still a challenge to object- oriented programming” (Weihe (1997)). As we point out later, there is no clear di- viding line between class libraries and frameworks. Whereas class libraries may be more flexible, frameworks often impose a broader structure on the whole system. Here we use the term component library or componentware that should embrace both class libraries and frameworks, but also other concepts that build on the idea of creating software systems by selecting, possibly adapting, and combining appropriate modules from a huge set of existing modules. In the following sections we provide a briefsurvey on callable packages and numer- ical libraries (Section 1.3) as well as component libraries (Section 1.2). Our survey in this chapter must necessarily be cursory and incomplete; it is not intended to be judgmental and in some cases one has to rely on descriptions provided by software vendors. Therefore, we include several references (literature and WWW) that provide further information; cf. Fink et al. (2001). As our main interest lies in optimization software class libraries and frameworks for heuristic search, we provide a somewhat more in depth treatment of heuristics and metaheuristics within the section on component libraries to let the reader visualize the preliminaries of this rapidly evolving area; cf. Voß (2001). 1.2 COMPONENT LIBRARIES Class libraries support the development of application-specific software systems by providing a collection of (possibly semi-finished) classes intended to be reused. The approach to build software by using class libraries corresponds to the basic idea of object-oriented software construction, which may be defined as building software sys- tems as “structured collections of possibly partial abstract data type implementations” (Meyer (1997)). The basic object-oriented paradigm is to encapsulate abstractions of all relevant concepts ofthe considered domain in classes. To be truly reusable, all these classes have to be applicable in different settings. This requires them to be polymor- phic to a certain degree, i.e., to behave in an adaptable way. Accordingly, there have to be mechanisms to adapt these classes to the specific application. Class libraries are mostly based on dynamic polymorphism by factoring out common behavior in general classes and providing the specialized functionality needed by subclassing (in- heritance). Genericity, which enables one to leave certain types and values unspecified until the code is actually instantiated and used (compiled) is another way - applicable orthogonal to inheritance - to define polymorphic classes. One approach primarily devoted to the goal to achieve a higher degree of reuse is the framework approach; see, e.g., Bosch et al. (1999), Fayad and Schmidt (1997b)
- 20. Most discrete optimization problems are nearly impossible to solve to optimality. Many can be formally classified as (Garey and Johnson (1979)). Moreover, the modeling of the problem is often an approximate one, and the data are often impre- cise. Consequently, heuristics are a primary way to tackle these problems. The use of appropriate metaheuristics generally meets the needs of decision makers to efficiently generate solutions that are satisfactory, although perhaps not optimal. The common incorporation of advanced metaheuristics in application systems requires a way to reuse much of such software and to redo as little as possible each time. However, in 1.2.1 Libraries for Heuristic Optimization and Johnson and Foote (1988). Taking into account that for the development of ap- plication systems for given domains quite similar software is needed, it is reasonable to implement such common aspects by a generic design and embedded reusable soft- ware components. Here, one assumes that reuse on a large scale cannot only be based on individual components, but there has to be to a certain extent a reuse of design. Thus, the components have to be embedded in a corresponding architecture, which defines the collaboration between the components. Such a framework may be defined as a set of classes that embody an abstract design for solutions to a family of related problems (e.g., heuristics for discrete optimization problems), and thus provides us with abstract applications in a particular domain, which may be tailored for individual applications. A framework defines in some way a definition ofa reference application architecture (“skeleton”), providing not only reusable software elements but also some type of reuse of architecture and design patterns (Buschmann et al. (1996b), Gamma et al. (1995)), which may simplify software development considerably. (Patterns, such as frameworks and components, may be classified as object-oriented reuse techniques. Simply put a pattern describes a problem to be solved, a solution as well as the context in which the solution applies.) Thus, frameworks represent implementation-oriented generic models for specific domains. There is no clear dividing line between class libraries and frameworks. Whereas class libraries may be more flexible, frameworks often impose a broader structure on the whole system. Frameworks, sometimes termed as component libraries, may be subtly differentiated from class libraries by the “activeness” of components, i.e., components of the framework define application logic and call application-specific code. This generally results in a bi-directional flow of control. In the following, we will use the term component library or componentware that should embrace both class libraries and frameworks, but also other concepts that build on the idea of creating software systems by selecting, possibly adapting, and com- bining appropriate modules from a large set of existing modules. The flexibility of a component library is dependent on the specific possibilities for adaptation. As cer- tain aspects of the component library application cannot be anticipated, these aspects have to be kept flexible, which implies a deliberate incompleteness of generic software components. Based on these considerations we chose the title optimization software class li- braries. In the sequel we distinguish between libraries for heuristic search (Sec- tion 1.2.1) and constraint programming (Section 1.2.2). OPTIMIZATION SOFTWARE CLASS LIBRARIES 4
- 21. OPTIMIZATION SOFTWARE CLASS LIBRARIES 5 comparison to the exact optimization field, there is less support by corresponding soft- ware libraries that meet practical demands with respect to, for example, robustness and ease-of-use. What are the difficulties in developing reusable and adaptable software components for heuristic search? Compared to the field of mathematical program- ming, which relies on well-defined, problem-independent representation schemes for problems and solutions on which algorithms may operate, metaheuristics are based on abstract definitions of solution spaces and neighborhood structures. Moreover, for example, memory-based tabu search approaches are generally based on abstract problem-specific concepts such as solution and move attributes. The crucial problem of local search based metaheuristics libraries is a generic im- plementation of heuristic approaches as reusable software components, which must operate on arbitrary solution spaces and neighborhood structures. The drawback is that the user must, in general, provide some kind of a problem/solution definition and a neighborhood structure, which is usually done using sophisticated computer lan- guages such as An early class library for heuristic optimization by Woodruff (1997) included both local search based methods and genetic algorithms. This library raised issues that illustrate both the promise and the drawbacks to the adaptable component approach. From a research perspective such libraries can be thought of as providing a concrete taxonomy for heuristic search. So concrete, in fact, that they can be compiled into machine code. This taxonomy sheds some light on the relationships between heuristic search methods for optimization and on ways in which they can be combined. Fur- thermore, the library facilitates such combinations as the classes in the library can be extended and/or combined to produce new search strategies. From a practical and empirical perspective, these types of libraries provide a vehicle for using and testing heuristic search optimization. A user of the library must provide the definition of the problem specific abstractions and may systematically vary and exchange heuristic strategies and corresponding components. In the sequel, we provide a brief survey on the state-of-the-art of heuristic search and metaheuristics before we discuss several heuristic optimization libraries. These libraries differ, e.g., in the design concept, the chosen balance between “ease-of-use” and flexibility and efficiency, and the overall scope. All of these approaches are based on the concepts of object-oriented programming and will be described in much more detail in later chapters of this book. 1.2.1.1 Heuristics: Patient Rules of Thumb and Beyond. Many op- timization problems are too difficult to be solved exactly within a reasonable amount of time and heuristics become the methods of choice. In cases where simply obtaining a feasible solution is not satisfactory, but where the quality of solution is critical, it becomes important to investigate efficient procedures to obtain the best possible so- lutions within time limits deemed practical. Due to the complexity of many of these optimization problems, particularly those of large sizes encountered in most practi- cal settings, exact algorithms often perform very poorly (in some cases taking days or more to find moderately decent, let alone optimal, solutions even to fairly small
- 22. instances). As a result, heuristic algorithms are conspicuously preferable in practical applications. The basic concept of heuristic search as an aid to problem solving was first intro- duced by Polya (1945). A heuristic is a technique (consisting of a rule or a set ofrules) which seeks (and eventually finds) good solutions at a reasonable computational cost. A heuristic is approximate in the sense that it provides (hopefully) a good solution for relatively little effort, but it does not guarantee optimality. Moreover, the usual distinction refers to finding initial feasible solutions and improving them. Heuristics provide simple means of indicating which among several alternatives seems to be the best. And basically they are based on intuition. That is, “heuristics are criteria, methods, orprinciplesfordeciding which among several alternative courses of action promises to be the most effective in order to achieve some goal. They represent compromises between two requirements: the need to make such criteria simple and, at the same time, the desire to see them discriminate correctly between good and bad choices. A heuristic may be a rule ofthumb that is used to guide one’s action.” (Pearl (1984)) Greedy heuristics are simple heuristics available for any kind of combinatorial op- timization problem. They are iterative and a good characterization is their myopic behavior. A greedy heuristic starts with a given feasible or infeasible solution. In each iteration there is a number of alternative choices (moves) that can be made to trans- form the solution. From these alternatives which consist in fixing (or changing) one or more variables, a greedy choice is made, i.e., the best alternative according to a given evaluation measure is chosen until no such transformations are possible any longer. Among the most studied heuristics are those based on applying some sort of greed- iness or applying priority based procedures such as insertion and dispatching rules. As an extension of these, a large number of local search approaches has been developed to improve given feasible solutions. The basic principle of local search is that solutions are successively changed by performing moves which alter solutions locally. Valid transformations are defined by neighborhoods which give all neighboring solutions that can be reached by one move from a given solution. (Formally, we consider an in- stance of a combinatorial optimization problem with a solution space S of feasible (or even infeasible) solutions. To maintain information about solutions, there may be one or more solution information functions I on S, which are termed exact, if I is injec- tive, and approximate otherwise. With this information, one may store a search history (trajectory). For each S there are one or more neighborhood structures N that define for each solution an ordered set of neighbors To each neighbor corresponds a move that captures the transitional in- formation from to For a general survey on local search see the collection of Aarts and Lenstra (1997) and the references in Aarts and Verhoeven (1997). Moves must be evaluated by some heuristic measure to guide the search. Often one uses the implied change of the objective function value, which may provide reason- able information about the (local) advantage of moves. Following a greedy strategy, steepest descent (SD) corresponds to selecting and performing in each iteration the best move until the search stops at a local optimum. 6 OPTIMIZATION SOFTWARE CLASS LIBRARIES
- 23. OPTIMIZATION SOFTWARE CLASS LIBRARIES 7 As the solution quality of the local optima thus encountered may be unsatisfactory, we need mechanisms which guide the search to overcome local optimality. A simple strategy called iterated local search is to iterate/restart the local search process after a local optimum has been obtained, which requires some perturbation scheme to gen- erate a new initial solution (e.g., performing some random moves). Of course, more structured ways to overcome local optimality might be advantageous. Starting with Lin and Kernighan (1973), a variable way of handling neighborhoods is a topic within local search. Consider an arbitrary neighborhood structure N , which defines for any solution a set of neighbor solutions as a neighborhood of depth In a straightforward way, a neighborhood of depth is defined as the set In general, a large might be unreasonable, as the neighborhood size may grow exponentially. However, depths of two or three may be appropriate. Furthermore, temporarily increasing the neighborhood depth has been found to be a reasonable mechanism to overcome basins of attraction, e.g., when a large number of neighbors with equal quality exist. The main drawback of local search approaches – their inability to continue the search upon becoming trapped in a local optimum – leads to consideration of tech- niques for guiding known heuristics to overcome local optimality. Following this theme, one may investigate the application of intelligent search methods like the tabu search metaheuristic for solving optimization problems. Moreover, the basic concepts of various strategies like simulated annealing, scatter search and genetic algorithms come to mind. This is based on a simplified view of a possible inheritance tree for heuristic search methods, illustrating the relationships between some of the most im- portant methods discussed below, as shown in Figure 1.1. 1.2.1.2 Metaheuristics Concepts. The formal definition of metaheuristics is based on a variety ofdefinitions from different authors going back to Glover (1986). Basically, a metaheuristic is a top-level strategy that guides an underlying heuristic
- 24. Simple Local Search Based Metaheuristics: To improve the efficiency of greedy heuristics, one may apply some generic strategies that may be used alone or in combination with each other, such as dynamically changing or restricting the neigh- borhood, altering the selection mechanism, look ahead evaluation, candidate lists, and randomized selection criteria bound up with repetition, as well as combinations with other methods that are not based on local search. If, instead of making strictly greedy choices, we adopt a random strategy, we can run the algorithm several times and obtain a large number of different solutions. How- ever, purely random choices usually perform very poorly. Thus a combination of best and random choice or else biased random choice seems to be appropriate. For exam- ple, we may define a candidate list consisting of a number of the best alternatives. Out of this list one alternative is chosen randomly. The length of the candidate list is given either as an absolute value, a percentage of all feasible alternatives or implic- itly by defining an allowed quality gap (to the best alternative), which also may be an absolute value or a percentage. Replicating a search procedure to determine a local optimum multiple times with different starting points has been investigated with respect to many different applica- tions; see, e.g., by Feo and Resende (1995). A number of authors have independently noted that this search will find the global optimum in finite time with probability one, solving a given problem. Following Glover it “refers to a master strategy that guides and modifies other heuristics to produce solutions beyond those that are normally gen- erated in a quest for local optimality” (Glover and Laguna (1997)). In that sense we distinguish between a guiding process and an application process. The guiding pro- cess decides upon possible (local) moves and forwards its decision to the application process which then executes the chosen move. In addition, it provides information for the guiding process (depending on the requirements of the respective metaheuristic) like the recomputed set of possible moves. To be more specific, “a meta-heuristic is an iterative master process that guides and modifies the operations of subordinate heuristics to efficiently produce high-quality solutions. It may manipulate a complete (or incomplete) single solution or a collec- tion of solutions at each iteration. The subordinate heuristics may be high (or low) level procedures, or a simple local search, or just a construction method. The fam- ily of meta-heuristics includes, but is not limited to, adaptive memory procedures, tabu search, ant systems, greedy randomized adaptive search, variable neighborhood search, evolutionary methods, genetic algorithms, scatter search, neural networks, simulated annealing, and their hybrids.” (Voß et al. (1999), p. ix) To understand the philosophy of various metaheuristics, it is interesting to note that adaptive processes originating from different settings such as psychology (“learn- ing”), biology (“evolution”), physics (“annealing”), and neurology (“nerve impulses”) have served as a starting point. Applications of metaheuristics are almost uncount- able. Helpful sources for successful applications may be Vidal (1993), Pesch and Voß (1995), Rayward-Smith (1995), Laporte and Osman (1996), Osman and Kelly (1996), Rayward-Smith et al. (1996), Glover (1998a), Voß et al. (1999), Voß (2001), just to mention some. OPTIMIZATION SOFTWARE CLASS LIBRARIES 8
- 25. OPTIMIZATION SOFTWARE CLASS LIBRARIES 9 which is perhaps the strongest convergence result in the heuristic search literature. The mathematics is not considered interesting because it is based on very old and wellknown theory and, like all of the other convergence results in heuristic search, it is not relevant for practical search durations and provides no useful guidance for such searches. When the different initial solutions or starting points are found by a greedy proce dure incorporating a probabilistic component, the method is named greedy random- ized adaptive search procedure (GRASP). Given a candidate list of solutions to choose from, GRASP randomly chooses one of the best candidates from this list with a bias toward the best possible choices. The underlying principle is to investigate many good starting points through the greedy procedure and thereby to increase the possibility of finding a good local optimum on at least one replication. The method is said to be adaptive as the greedy function takes into account previous decisions when perform ing the next choice. It should be noted that GRASP is predated by similar approaches such as Hart and Shogan (1987). Building on simple greedy algorithms such as a construction heuristic the pilot method may be taken as an example of a guiding process based on modified uses of heuristic measure. The pilot method builds primarily on the idea to look ahead for each possible local choice (by computing a socalled “pilot” solution), memorizing the best result, and performing the according move. One may apply this strategy by successively performing a cheapest insertion heuristic for all possible local steps (i.e., starting with all incomplete solutions resulting from adding some not yet included ele ment at some position to the current incomplete solution). The look ahead mechanism of the pilot method is related to increased neighborhood depths as the pilot method exploits the evaluation of neighbors at larger depths to guide the neighbor selection at depth one. Details on the pilot method can be found in Duin and Voß (1999) and Duin and Voß (1994). Similar ideas have been investigated under the name rollout method; see Bertsekas et al. (1997). Hansen and Mladenović (1999) examine the idea of changing the neighborhood during the search in a systematic way. Variable neighborhood search (VNS) explores increasingly distant neighborhoods ofthe current incumbent solution, andjumps from this solution to a new one iff an improvement has been made. In this way often fa vorable characteristics of incumbent solutions, e.g., that many variables are already at their optimal value, will be kept and used to obtain promising neighboring solutions. Moreover, a local search routine is applied repeatedly to get from these neighboring solutions to local optima. This routine may also use several neighborhoods. Therefore, to construct different neighborhood structures and to perform a systematic search, one needs to have a way for finding the distance between any two solutions, i.e., one needs to supply the solution space with some metric (or quasimetric) and then induce neighborhoods from it. Simulated Annealing: Simulated annealing (SA) extends basic local search by allowing moves to inferior solutions; see, e.g., Kirkpatrick et al. (1983). The ba sic algorithm of SA may be described as follows: Successively, a candidate move is randomly selected; this move is accepted if it leads to a solution with a better objec
- 26. Discovering Diverse Content Through Random Scribd Documents
- 27. “I’ll be a regular beacon light, we won’t need the moon coming back,” said Gincy as she flew around to finish her morning’s work. “I’ll put a twist of red ribbon around Abner’s old hat. I’ve a piece that’s almost a match.” When the four girls gathered on the front porch of the Hall, there sat Miss Howard with her folding easel and box of paints. “Girls,” she said, “suppose we change our minds and go to Slate Lick this afternoon, then I can do some sketching.” “Good!” exclaimed Gincy delightedly. “I haven’t been out that way at all.” “It’s mighty pretty, and not so hard walking,” said Kizzie, and the rest seemed equally pleased with the change. “We’ll go down Scafflecane Pike and cut across to the railroad, it’s a good deal shorter.” Miss Howard gathered up her belongings and started off ahead at a brisk pace. At the gate they met Mallie and Nancy Jane, the latter had been crying. “Let’s ask them to go with us,” said Miss Howard, turning suddenly. There was a brief consultation behind the cypresses, then Lalla sped back after the two. “Tell them to come just as they are!” called Urilla. “Thank goodness, they aren’t dressed up.” “What a queer looking bundle,” remarked Mallie as the two joined the waiting group. “Isn’t it?” responded Gincy, patting a bulky parcel. “Shooting irons come handy whar thar air dangerous animals,” relapsing into her former vocabulary. Nancy Jane brightened visibly. “I’m glad some one feels funny; I’ve been too homesick for anything all day. I haven’t had a letter this week.”
- 28. “You’ll get one on the evening mail,” Gincy assured her. “No news, good news. I belong to the Don’t Worry Club; you’d better join.” “Guess I will. I’ve got to scratch around and find out about a lot of new birds before I see Professor Lewis again. I don’t know any, for sure, except robins and buzzards. This will be a good time to get information.” There was a general laugh in which Nancy Jane joined, her sorrows for the moment occupying the background. They filed down the long, straight road and crossed Silver Creek. There was a substantial bridge—built for high water—but Lalla and Mallie preferred the rickety foot-bridge farther down which trembled at every slight bit of weight imposed upon it. Miss Howard watched rather anxiously, but was soon reassured. They reached the farther end safely and started off across the fields toward the railroad. The foothills seemed a vast, undulating semicircle. One bold knob higher than the rest, with precipitous sides patched with pines, stood out with more importance; but it lacked their allurement of tender colouring. Straight into the heart of the range, the railroad cut its way, and a long, creeping freight train trailed by just as they turned to follow the track. A shower of cinders deluged Mallie and Lalla; they wheeled and walked backward until Gincy and Kizzie caught up. Nancy Jane panted close behind. “I’ve got a monster in my eye!” moaned Mallie, plucking at the offender. Her efforts were vain, and each girl, in turn, was rewarded in the same way. Urilla and Miss Howard, far in the rear, were talking too earnestly to make much progress, or notice the group ahead. “I’m so glad your mother’s better,” the teacher was saying. “I know you want to stay, and we can’t spare such girls as you very well.”
- 29. Urilla’s face beamed. “Oh, Miss Howard, do you really mean it? I feel that I’m improving, I was so stupid at first—now I can see through things better. Gincy’s helped me, she’s always saying something nice and encouraging.” “Gincy’s a treasure!” said Miss Howard warmly. “But where are the girls, they were on the track a minute ago?” Another train thundered by. “I wish they wouldn’t keep so far ahead, that’s the 3:15, and it goes like lightning when it’s making up time,” Urilla remarked uneasily. They hurried along, scanning each clump of bushes and stack of grain, but no one was visible. “They couldn’t have gone in here!” exclaimed Miss Howard, looking at a little weather beaten cabin very near the track. Then she listened. Yes, there were voices that sounded familiar. Through the half-open door, the two caught glimpses of Gincy’s bright skirt and gay hat. “I wonder what they’re doing, and why we didn’t see them when they turned off the track,” said Urilla as they opened a rickety gate and went into the yard. “What a dreadful place to live!” Miss Howard agreed as she looked at the forlorn and desolate little cabin with not one home-like feature; even the yard was bare and wind-swept. “Why, there’s Talitha!” “What?” The two pushed up eagerly. “Mrs. Donnelly told me this morning she had gone to see some of her kinfolk, but I didn’t know they lived here,” said Urilla, looking curiously at the bare little cabin. Standing just inside the door, the missing girls were talking to Talitha, who, with her dress pinned up around her and a towel over her head, was busy cleaning. Three small children played near the
- 30. fireplace, and beyond, propped upon an old pillow, her bright eyes watching the newcomer, was the tiniest woman they had ever seen. “Have you had measles?” asked Talitha, waving her broom at them. “If you haven’t, stay out.” “Of course,” answered Urilla scornfully, “years ago; but I don’t see any.” Another wave directed them to a small bed near a darkened window. Two flushed faces peered above a ragged quilt. “Why!” gasped Urilla, taking in the situation. “But how did you know? I thought—” Miss Howard suddenly interrupted with, “This must be Mrs. Gantley. I intended to find you yesterday, but I thought you lived on the Big Hill pike. Are you feeling better?” The little woman shifted her position slightly, a shadow of a smile flitting across her face. “Yes, since Tally came I’m easier in my mind. The children ain’t bad sick—jest feverish and powerful troublesome; I couldn’t keep ’em from ketchin’ cold no way, out o’ bed.” Gincy and Talitha were having a quiet conference in another part of the room. “I found out this morning that she’s kin on mother’s side —way back,” said the latter in a low voice. “They used to live in Cowbell Hollow, but he ran away and left them a month ago.” Talitha looked unutterable things as she referred to the recreant Mr. Gantley. Accustomed as she was to the delinquencies of the mountain men, the desertion of a helpless family seemed the blackest of crimes. She glanced meaningly in the direction of a large basket in the corner, and whispered, “They were almost starving. Martin helped me or I couldn’t have got it here—Mrs. Donnelly gave me so many things, but—”
- 31. “See here,” said Gincy, slipping an arm around Talitha’s waist, “I’m going to stay and help; I can go for a walk any Saturday. We’ll scrub the children, gather wood, and cook. Won’t it be fun!” “Are you sure you want to?” asked Talitha, her tired face brightening. “Of course; the rest can trot along just the same.” “Dear me,” grumbled Lalla as they proceeded without Gincy, “I’d like to get hold of that man. Do you know anything about the family, Miss Howard?” “Not much, only he’s fond of moonshine. He sold the home about three weeks ago—told her he was getting ready to come to Bentville, where there was a good school for the children. When she found that he had really gone, she thought he might be here and followed him.” Miss Howard walked on with her head held high; she did not want the girls to read in her face the fulness of disgust which she felt for a man of that type. There were others like him whose sons and daughters were working their way through school, trying to redeem the family name and become worthy citizens. “It’s a shame!” said Mallie. “They ought to catch him and make him work good and hard—beat him if he didn’t—and give all his wages to his folks. I’d teach him to run away from those pretty children, and —” “There isn’t a chair in the house,” interrupted Nancy Jane, “and I didn’t see a dish. That poor woman might just as well chase a Bushy tail; she’ll never see him again—not until the children grow up, then he’ll come back and live on them.” “I should be glad to get rid of him,” said Urilla conclusively. “I’ve seen men like that before.” There was silence for a moment, and the group became more widely scattered. Lalla forged straight ahead until she was several rods in advance. She scanned the great slate boulders on either side and listened. There were voices, familiar ones, then all was quiet.
- 32. Everywhere the foothills hemmed them in. Suddenly a rock crashed in front of her. Looking up she saw Abner’s shock of light hair as, flat on his stomach, he peered over the edge of the cliff. The head disappeared and an improvised mask took its place. “Halt!” commanded a muffled voice which closely resembled Martin’s. Lalla threw up her hands in mock fright. “Come around behind that pine tree, we’re laying for some of our crowd. There’s something in the wind to-day, for Raphael Sloan and Joe Bradshaw sneaked off without letting us know—dropped out all of a sudden. Keep your eye peeled for them, won’t you? Likely they’re up at the springs.” “Don’t let the rest know we’re here,” warned Abner, peering over Martin’s shoulder, “it might spoil the fun.” “I guess not,” agreed Lalla with her old love for a joke. “Go ahead and have your fun; but what if they go back the other way?” “You mustn’t let ’em. Think up some scheme; you can do it.” Both heads disappeared as Nancy Jane’s voice was borne to them from below. Lalla picked a few violets and walked on carelessly, looking up at the mountains on the opposite side. “Hurry up or we’ll never get there!” she called back, waving her flowers; “there’ll be heaps of these at Slate Lick.” The gorge widened. A trickling, shallow stream crept through the bed. The foothills seemed suddenly to have become mountains and surrounded them, making a basin-like valley. On the opposite side, sheltered by walnuts, stood a few deserted houses and a building which seemed halfway between a store and a peanut stand. “There’s quite a colony here in summer,” said Miss Howard, when at last they stood in front of the spring house and fitted the long key into the padlock. “The sulphur water calls them, and the view. Isn’t it beautiful! I want to get the Knob painted in while the haze is over
- 33. it. You young folks run along and do your climbing; I’ll whistle for you when it’s time to go back.” “If Talitha and Gincy were only here!” sighed Kizzie after the first long climb. Together they stood panting for breath and watched the scene below. “Where’s Lalla? She beats everything for disappearing right before one’s eyes,” Nancy Jane frowned. “Couldn’t lose her though, that’s the beauty of it,” remarked Urilla as they looked around behind the trees and boulders. Below, Miss Howard sat intent upon her canvas. A tinkling cowbell was the only sound which greeted their ears. “I’m for going on. It’s one of Lalla’s tricks; she’s a good deal nearer than we think—probably laughing at us this minute.” But Lalla, when she dropped behind the rest, had taken a trail leading off to the left. She was sure that it came back to the main trail again, and it would give her a splendid opportunity to pop out and surprise them. She soon found that it led around an immense boulder, that it was steep, and grew steeper. As she paused quite breathless, the sound of men’s voices came from behind the rock. A clump of small evergreens made a convenient hiding-place; behind them Lalla listened. She was not in the least alarmed, only curious. The voices grew louder, one of them seemed to be chanting or reciting something; it was hard to tell which. Lalla stole out a little farther and crouched close to the rock, listening breathlessly. “Louder, Raf, so I can hear you at this distance.” Lalla fancied she could have touched Joe Bradshaw had not the rock projected a thin edge between them. She sank noiselessly into a bed of tall ferns. So here were the truants! Martin and Abner should hear about them; she would jump out and give Joe the scare of his life. On and on went the voices, the nearer one correcting and halting the speaker from time to time.
- 34. Lalla listened intently; her eyes grew larger. What was Raphael saying! She sat perfectly rigid as the truth flashed upon her. It was his speech for the Mountain Congress, and he was to speak against Abner. No wonder they stole away from the boys. For some minutes Lalla sat undecided. Raphael Sloan was a formidable opponent, and Abner new at the business of debating. If she could only give the latter a hint—she wouldn’t tell right out. How proud Gincy would be to have her brother win the debate. Her heart beat fast and she listened as she had never listened before; not a word must be lost and she must not be discovered now for the world! “You’ll have to be ready for the rebuttal; they’ll get you on that point —Abner’s working like a tiger.” And then there was an audible movement on the other side of the boulder which made Lalla’s heart beat like a trip-hammer. To her infinite relief, Raphael Sloan moved on up the trail and Joe after him. She could hear their voices growing fainter and fainter each moment. Cautiously she slipped from her hiding-place and retraced her steps to a point lower down. There was a way to cut across the other trail, but it was through blackberry bushes, wild grapevines, and a tangle of underbrush. Lalla did not hesitate, however; slipping and sliding, she fairly rushed forward, not stopping for scratches nor even bruises. From the thicket she suddenly emerged into a small opening—hardly a clearing—in which was a tiny shack of logs. To all appearances it was deserted, but Lalla decided to avoid it and come out just beyond. A gun sounded very near; a hound bayed. She shrank back where the shadows were deep, and silently threaded her way in the direction of the old trail. It could not be many rods farther on. For fully a half-hour she stumbled along, then she heard Nancy Jane’s voice, and the girls fell on her with loud reproaches.
- 35. “I was exploring,” Lalla said with shining eyes, and then she told them about the cabin. “It’s mighty secret; I’d never found it only for taking the short cut. Folks could do stillin’ and no one be the wiser.” “I wonder if they do make moonshine there,” said Mallie after a pause. “We heard that shot and were worrying about you. Don’t you run away again.” Lalla smiled, but did not answer. A long whistle came from below. It was repeated. “That’s Miss Howard!” exclaimed Kizzie. “She wants us right away; see how late it’s getting.” All the way down Lalla was very quiet. Her head was full of plans to help Abner and find out more about the mysterious cabin. Mystery appealed to her vivid imagination and stimulated her to immediate action. A thin trail of smoke came up to them as they made the last steep descent into the basin. “Oh, Lalla, Miss Howard’s getting supper and I’m so hungry,” said Kizzie. But Lalla was thinking of the two boys— which way could they have gone home?
- 36. XVI THE MOUNTAIN CONGRESS It was several days before Lalla saw Abner alone. He was certainly working like a tiger. He rushed over to meals, and when the boys were dismissed, was gone like a shot, not waiting to join the groups who visited in the yard. It wanted a week of the Mountain Congress when she followed him into the library one day and straight back to the stack room. There was a long table in one corner and piles of reference books on it. Abner had snatched his cap off and was digging for the bottom one of the nearest pile when Lalla touched his shoulder. “Working on your debate?” she whispered. “I hope you’ll win.” Abner looked up gratefully. “I don’t reckon on it much—Raphael’s an old hand, they tell me—but I’m learnin’ a lot, that’s one sure thing.” “I’ve thought of some points which will be likely to help you.” Lalla pushed a sheet his way. “You can never tell what they’re going to spring on you just at the last.” Abner took it with a look of surprise. “I didn’t know that you even knew the subject of the debate; we’ve tried to keep it a secret.” Lalla reddened—she had not thought of this emergency. “Of course I told Gincy,” Abner continued, “and I know she trusts you, so it’s all right.”
- 37. He had misconstrued her evident embarrassment, and was trying to reassure her. For one moment Lalla’s courage failed, but she was sure Abner stood little chance of winning without some help, and there was almost no risk of discovery, not even if Gincy told her brother that she had kept the secret. Lalla’s impetuous nature was capable of a good deal of self-sacrifice —mistaken at times, but nevertheless genuine in motive. She had a warm feeling of gratitude toward the girl who had not, by even so much as a look, hinted at her adventures with the master key. Indeed, Lalla felt that Gincy had entire confidence in her assurance that she would be perfectly straightforward from that time on. It was the mountain warfare over again, and Lalla did not feel any real compunction about the methods. She knew instinctively, however, that Gincy and Abner would look at it differently and was prepared for questions. However, they did not come. “These seem like dandy points; they might do me a heap of good when it comes to the final touchdown.” Abner showed her the result of his digging for the last few weeks—a whole tablet full of notes, disorderly enough but right to the point. Lalla glanced over them with a shrewd eye, and nodded. “Abner, they’re splendid! But won’t you be scared half to death in front of that crowd?” He shook his head resolutely. “I’m going to bluff it if I am; it doesn’t do to show one’s feelings.” “No, and Goose Creek folks aren’t the scary kind.” “You bet they aren’t—not the girls, anyhow.” Abner spoke with conviction. Devotional exercises the next morning were brief. Then the excitement began. Banners went up all over the chapel, and nominations were made for governor of Appalachian America. There
- 38. were speeches and special music to arouse enthusiasm for the Mountain Congress. The girls from Clay sat in the gallery—a row of bright faces keenly watching every movement below to see what counties were represented. “There’s Pike, and Letcher, and Magoffin!” whispered Gincy excitedly. “And Floyd, and Knott, and Breathitt!” added Talitha. “Perry, Harlan, Leslie, and—Oh, look at Clay! Goody! Goody!” Mallie almost lost her balance and fell into the crowd below. Nancy Jane pulled her back and kept a firm grip on the excited girl for some time. “It’s awfully interesting!” sighed Lalla, her eyes growing bigger as she watched the platform. “But I suppose the congress itself will be twice as exciting.” There were funny speeches from the candidates, each vying with the other in promising favour to his particular section of the country. The applause was frequent, and the college band played “Dixie.” Every one filed out full of enthusiasm; they would know the result of the election by evening. Lalla and Gincy walked over to Memorial Hall behind Abner and Martin. There was a grand rally out in front—practising yells and singing class songs. The noise was deafening. “I’m saving my voice until Friday night,” Lalla told Abner in the first lull. “I know you’re going to beat and then you’ll hear me yell!” Gincy smiled happily. “Abner’s going to do his best; that’s the main thing. I’m proud to think he’s even got a chance to do it, without his beating.” “Of course it’s an honour to have the chance,” said Lalla, “but, Gincy, just think how proud Goose Creek will be to have Abner come home
- 39. with the medal.” In spite of himself Abner flushed with pleased anticipation. He was making the fight of his life for a public honour and did not intend to be beaten. Every word of his speech was photographed upon his brain, ready for instant use, if—and here was the hard part—if his opponent did not think of some entirely new line of argument. Friday evening found the Hall alive with excitement. The girls were divided into factions. Raphael Sloan was the best debater Bentville had had for some time, and while Abner was popular, he was too new to inspire general confidence. Nearly everybody—except the Goose Creek folks—was sure of the boy who had never been defeated. The chapel was in an uproar when the girls arrived. Occupying the centre and front were delegates from each county to the Mountain Congress. Class colours were everywhere in evidence. Pennants were fluttering, and yell after yell went up when the Governor of Appalachian America—one of the senior boys—took his seat on the platform. Afterwards the whole thing seemed like a dream to Lalla. Raphael, tall, dark-eyed, with the flush of anticipated victory on his face. Abner, intense, pale at first and somewhat hesitating, but warming up with fiery eloquence toward the last and meeting every argument with growing confidence. Not once did he fail in the rebuttal, nor even hesitate, and Lalla saw an amazed look creep over Joe Bradshaw’s face as Abner answered with a glibness born of knowledge, sweeping the very foundation from under his opponent’s feet. There could be but one verdict, and the Goose Creek girls saw Abner hoisted upon strong, young shoulders and borne in triumph around the room. Once more the pennants waved and pandemonium broke loose. This time they joined in the yells. Lalla, in the centre of the circle of girls, never stopped until her voice gave out.
- 40. Joe Bradshaw took his roommate’s defeat quite philosophically. He was fond of Abner and Martin, but somewhat puzzled at the former’s quick replies to every argument. “You did splendidly!” he said, wringing Abner’s hand. “Clay County is right to the front to-night.” Abner gave Lalla a quick glance of gratitude. She was watching him as he talked to Joe and the surrounding boys, not forgetting to wave at the home girls who found it impossible to reach him. Gincy’s eyes were full of tears—proud ones. If her father and mother could only have been here to see Abner beat the best debater in all the mountain counties. It would have rewarded them for every sacrifice. There was to be a spread in the Industrial Building for the winner. Talitha and Martin held frequent conferences all the next day, and by four o’clock a constant procession of boys and girls were busy carrying parcels, bunting, and branches of pine for decoration, and making the rooms of the Agricultural Department attractive for the evening crowd. It was to be a great event for the Goose Creek folks, and they had prepared accordingly. Pete Shackley guarded the chickens. “I knew Abner’d beat, those roosters have been crowing under my bed for two nights. I toted the box into my room the minute I bought them; there’s no telling where they’d be to-day if I hadn’t.” Gincy and Mallie kept the door of Number 4 securely locked, but that precaution did not prevent savoury odours from escaping which the boys sniffed eagerly. “Cake!” exclaimed Martin delightedly. “Tally said Miss Browning was going to let them use the cooking room all day. I smell fruit cookies, too. My, but it’s going to be a spread! I wonder what Piny Twilliger’s doing ’round here; she likes good eating, I suppose.” “Of course, but didn’t you know she’s Abner’s cousin from Redbird?” and Isaac Shackley grasped a big pot of ferns and moved on, leaving Martin staring in astonishment.
- 41. Piny was so tall and snappy and altogether loud—such a contrast to Gincy—Martin had taken a special dislike to her the very first time she came to Harmonia. That was at the opening of the spring term and now it was getting pretty well along toward Commencement. But the girl’s voice did not seem to improve—it was still coarse and penetrating—she wore the gayest colours, and Martin couldn’t enumerate all the reasons why he disliked her, but he did. It was growing dusk when everything was ready for the spread. They were to serve it in the Domestic Science room at eight o’clock. Nancy Jane had the key and was instructed to remain in charge until the ice cream arrived, then hurry over to the Hall to dress. Nancy Jane turned on the lights and surveyed the room with satisfaction; there was a good deal to show for all their work. The cake was delicious, the chicken fried to a turn. There were great plates of rolls and plenty of pickles. The long table down the centre of the room was decorated with Abner’s class colours, while all around, in festoons, were the orange and black of the Mountain Society—the first typifying the brilliant autumn colouring of the hills; the second, the wealth of coal found in their mines. The building was far from deserted. There was a clatter of feet up and down the bare stairs—fully a dozen boys roomed on the third floor—and Nancy Jane locked the door to secure herself from unceremonious callers. “They’d like to play some game on us— those seniors,” she thought. “They’re pretty sore because a new pupil carried off the honours.” It was seven o’clock, but the cream had not come, and Nancy Jane was in a quandary. Some one rattled the door knob. “Who is it?” she asked. “Piny, Piny Twilliger. Let me in; I’ve come to take your place and let you get dressed. Martin had a message that the cream wouldn’t be here for half an hour yet. There wasn’t another soul ready, so Gincy asked me to come.”
- 42. Nancy Jane unlocked the door to let in—was it really Piny? The tall figure was attired in a bright red muslin much beruffled. A brilliant bow with generous outstanding loops surmounted the dozen or more puffs of hair, and excitement lent additional colour to cheeks that were always flushed. Nancy Jane hurried over to the Hall and up to her room. She didn’t even take time to ask Gincy why she had sent Piny Twilliger to guard the precious cream. It wouldn’t do to say much about kinfolk. But all the time she was hurrying into her white dotted lawn, she wondered if anything would happen to their eatables. Surely some of the girls would be ready in a few minutes. It was almost a quarter of eight when Nancy Jane ran down the front stairs. She rapped lightly at several doors, but there was no response. Evidently everybody who belonged to the Mountain Society had gone. It was only a short distance to the Industrial Building, and she ran across the campus toward the lights. There was the buzzing of excited voices—the front walk seemed thronged with students. What could have happened? Nancy Jane felt an awful premonition of disaster. Of course it was the cream. Piny must have left her post and some of the boys carried it off. “Is that you, Nancy Jane?” It was Mallie’s voice. “The cake’s gone— every scrap! Some one rapped on the door and Piny went out; it was the boys with the cream, and while they were talking some one tore the screen and jumped in the side window and took every smitch of cake off the table. Piny’s rushing ’round like a hornet and vows she’ll find out who did it before she sleeps a wink to-night. But I don’t believe she can; it’s either eaten up or hidden by this time.” Nancy Jane listened in dismay. All their lovely frosted cake gone! She ran into the room looking for Piny—somehow she wanted to hear the whole story from her lips. But among the babel of voices Piny’s could not be heard. She had disappeared completely and did not hear Martin’s angry comment.
- 43. “I shouldn’t wonder if she had hidden it herself; she’d think that was a great joke.” “Hush, Martin,” said Talitha, “Piny isn’t mean if she is fond of a joke.” But Martin’s eyes continued to flash as he walked out into the dark, around the building, and looked up at the outside stairs. They were built more as a fire-escape, but the boys on the upper floor often used them. Martin stood in the shadow of the wood-working department and eyed the row of lighted windows. A dark object was crouched on the upper step and as he eyed it intently, it rose and began a noiseless descent. Martin edged as close as he dared. It passed the lower window and he saw, to his utter amazement, that it was Piny Twilliger, who seemed in great haste to get down. He intercepted her as she reached the ground. “What is it, Piny?” he whispered. “I’ve found them!” she gasped, “and the cake isn’t eaten yet. Get all the boys together you can. Some will have to watch the door of their room—it’s Seth Laney and that crowd. You’d better get the Shackley boys and go up on the outside—that’s the only way you’ll get in. While the rest are making an awful racket in the hall to attract their attention, you can climb in the window.” “You do beat everything!” exclaimed Martin, quite conscience- smitten to think he had ever suspected Piny. “You’re a regular general! You bet we’ll get that cake,” and he ran around the building and into the big front entrance like a shot. It took only a minute to plan the campaign as outlined by Piny. There was an instant siege—within ten minutes an unconditional surrender—and the cake was saved. Borne down in triumph by Martin and Abner, they paused in front of her with a low bow. “Madam,” they said, “the honour belongs to you. Have a piece.” But Piny laughingly refused to be made a heroine of, and waited until every one else was served. She blushed furiously when they toasted her in lemonade for her presence of mind and courage. “I
- 44. reckon hit wan’t much,” she said, modestly disclaiming all honours. “I’d promised to watch things, an’ I wan’t goin’ to be beaten nohow.” The spread was a great success. Afterwards, Abner walked back to the Hall with Gincy and Lalla. “You helped me a lot,” he assured the latter. “I worked up all those notes you gave me and they seemed to strike the nail on the head. I don’t see how you ever thought of them.” “That wasn’t anything,” said Lalla, “you had a dozen points a good deal better than mine. I’m glad the decision was unanimous for you, though; it was a bigger honour.” “I didn’t know you helped Abner,” remarked Gincy as they sat in her room waiting for the warning bell to ring. “I’m so proud of him and grateful to you. Miss Howard says you do splendidly in your work this term, Lalla.” “You always say such nice things,” answered Lalla, evading Gincy’s eye. “There isn’t another girl in Bentville who has encouraged me the way you have. I guess I remember, and—” She broke off suddenly. Perhaps after all she would better tell Gincy the truth about the debate. Gincy listened, her hard-working hands tightly clasped, and a sinking at her heart. It was just plain cheating and the Gooch family had never done anything like that. Of course Abner didn’t know or he never would have used the paper Lalla gave him—that was one comfort. Then Gincy thought of Raphael. Perhaps after all the medal really belonged to him; but how could she straighten it all out? Why were there so many tangles in life, anyhow? “Gincy,” said Lalla, abruptly changing the subject, “that Mr. Gantley has come back. Talitha told me this evening and I forgot to tell you. The college folks found him up in that shack on the mountain, and they told him he’d got to go to work or they’d lock him up, and then they gave him a job in the garden. You needn’t worry about the family any more.”
- 45. Lalla ran to her room at the sound of the bell, leaving Gincy in a brown study. If she told it might get Lalla and Abner into all kinds of trouble. Perhaps they would even have the debate all over again with a new subject, or Abner might have to give up the medal in disgrace. There were so many terrible possibilities, Gincy slept little that night. Early the next morning she arose fully decided on a course of action. Miss Howard should settle it; she could hardly wait to find her. The little teacher listened patiently. “I’ll tell you this evening. Come to my room at half-past seven; meanwhile don’t worry.” Somewhat comforted, Gincy went about her work. Promptly at seven she presented herself at Miss Howard’s door. “I just couldn’t wait another minute,” she said by way of apology. “You don’t need to,” was the assurance. “It’s all right. Professor Ames says the decision might not have been unanimous, but Abner would have received the medal anyhow on his main argument. It isn’t necessary that anything be said about it except to Lalla. We want her to cultivate higher ideas of honour than those she has been used to at home.” Gincy left the room jubilant; a great burden had rolled off her mind. She could go to bed with a clear conscience and make up the sleep she had lost the night before.
- 46. XVII KID SHACKLEY GETS A GLIMPSE OF THE WORLD The Shackley cabin stood high and dry above the bed of Goose Creek; for, while there was nothing to fear from the narrow, trickling stream of summer, the moody, tempestuous torrent of spring threatened everything within reach, and Enoch Shackley was a cautious man. It was ten o’clock, but the flickering of flambeaux, the sound of hurrying feet over the bare floor of the long living-room, the uneasy tugging of old Bob at his chain, and a saddled mule in front of the door, indicated some unusual nocturnal adventure. Presently, far in the distance could be heard the creak of a jolt wagon and the sound of voices singing “Sourwood Mountain.” The cabin door suddenly flew open and Kid Shackley appeared. He was a chunky, muscular boy, a worthy successor of his father, when the blacksmith should grow too old to follow his trade. “They’re comin’, mammy! Good-bye, I’ll tell you and pappy all ’bout hit when I git back. Looks like a feller kin hear ter Kingdom Come in the night time.” His place in the doorway was filled by a tall, gaunt figure in a meagre dress of blue calico, who peered out anxiously after him. “Ain’t ye hongry, son? Whar d’ye reckon ye’ll git yore breakfast?”
- 47. “Sam Gooch ’lows we’ll be at Redbird somewhar near the Twilligers —Eli’s kin. Likely they’ll want ter go on ’count of Piny. We’ll get ter the Branch ’bout sun-up.” Kid was in the saddle now, facing the newcomers. The jolt wagon with its oxen threading along the stony bed of Goose Creek—a lantern hung in front of the driver—cast long shadows which seemed to multiply like those of a mysterious moving caravan. They filled the gorge. “G’lang, Billy,” and Kid was slowly descending the steep incline to join the travellers who suddenly halted. “Come on, come on!” chorused the voices from below. Kid greeted the half-dozen occupants of the wagon in true mountain fashion. “Howdy, Dan Gooch,” to the man guiding the oxen, “you’re here on time. I heerd our rooster speakin’ up a spell back. He reckoned ’twas mornin’ by the clatter.” “He’d better watch out or Brer Fox’ll get him. Them pesky varmints tuk nigh onto twenty little uns fer us last night. G’lang, Bright!” and the cracking whip and groaning wagon drowned the greetings of the others. Kid fell in behind. There was no possible chance for conversation, so they sang old English ballads, and “The Old Time Religion,” which Talitha had taught them. As they rode along in the damp coolness, Kid watched the lumbering wagon ahead, full of indistinct figures, with a curious feeling of something new and strange about to enter his life. Right and left, the great pine-covered mountains both guarded and threatened with their looming shapes. The highest part of the creek bed made the only passable wagon road, and that was poor enough. The air was full of moist odours, and above, the deep blue dome was pierced with twinkling points of light.
- 48. The night wore on until the twinkling lights were lost, and a greyness settled over the mountain world. They were travelling northwest, leaving range after range of the Cumberlands, broken only by the deep gorge of a river bed, behind them. Ahead, were the foothills, and beyond, Kid had never seen. He only knew from the glowing accounts of Pete, and Isaac, and Talitha—who had made him promise to come to Bentville—that the Blue Grass in all its richness lay very near the college. Leaving the river bed they struck a mountain road which led, at long intervals, past lonely, unpainted cabins more humble than those in the small settlement at Goose Creek. Early as it was, people were astir, noisily harnessing their mules, or yoking oxen. Here and there a jaded saddle-horse or spirited colt was being pressed into service. They were all bound for the same place. “Hit’s like a circus, er buryin’, er baptizin’—” and here words failed him. But he remembered Talitha’s description, and tried to imagine how it would seem to see thousands of people on one level, wooded space. They had stopped singing now. A faint, rosy glow was spreading above the mountains back of them, and glimpses of a great rolling valley came from the front. The road ran steeply down, causing the occupants of the wagon to sway in their chairs. Dan Gooch plied the brake, vociferating to his oxen: “Hi thar, Bright! Steady, Star! See, yon’s Redbird!” Sam Coyle straightened an inert figure. He had been half dozing, conscious of little except his broken rest. His journey to Bentville was prompted by a curiosity which had been growing ever since Abner had won the medal. There was a little pricking below the jealousy in his heart when he thought what a “sorry” father he had been. Dan Gooch was growing more enthusiastic every day over “larnin’.” Sam wondered if it were too late—here he glanced at his wife’s worn but radiant face. She was looking in the direction of
- 49. Redbird, but he knew that her heart was going out to Martin and Talitha in Bentville, and that she had nothing to regret. Billy and Sudie grew more excited each moment. “I’m that hongry I could eat a bear; I hope they’ll have one fer breakfast!” exclaimed the former. “More like it’ll be a chicken,” laughed Kid as he guided Nick nearer the wagon. “I saw Zeb Twilliger in the hen yard a minute ago.” A lank, high cheek-boned mountaineer came slouching toward the gate as they drove up. “Light and hitch,” he commanded hospitably. “I reckon yo’re bound fer Bentville. Piny’s been pesterin’ the life out o’ us ter come; she sent word agin this week, an’ I ’low ef she’s honin’ fer us, we’d shore ought ter go.” “That’s what I told pappy,” interrupted Kid eagerly. “He and mammy bide in the Hollow till they’re fair mossy. Pete and Ike’ll come back plumb shamed of we-uns.” And then the boy flushed at what the words implied. Sam Coyle failed to make his usual sarcastic retort to the thrust at Goose Creek. Indeed he was quite amiable to Kid on their way up to the door of the rather untidy looking cabin. There was plenty of bacon and cornbread, with coffee and fresh buttermilk for breakfast. The chickens were for their dinner and had been cooked the day before. “I never count on eatin’ chicken till I get a holt of the drumstick,” whispered Billy to Kid, rolling his eyes. Mrs. Twilliger was large and loud-voiced. The older children had all married and left home except Piny. “We’d planned ter keep her fer a spell yit, but I don’t reckon nothin’ ever’ll suit her ’round here now she’s taken ter schoolin’; she air a queer gal.” “I wouldn’t let hit fret me,” said Mrs. Gooch with unexpected spirit, “the mountings air needin’ a few idees; I’m glad Gincy’s gittin’ ’em. I’m plumb wore out with the old ones. She and Tally’d much better
- 50. be larnin’ out o’ books than marryin’ some no ’count chap thet goes r’arin’ ’round, shootin’ up things ginerally.” Mrs. Twilliger bristled up instantly; the description fitted her eldest son-in-law too closely for her liking. However, Mrs. Gooch had an unexpected ally in the master of the house. “Thet’s my idee; Piny’s harum-scarum ’nough without gittin’ in with these chaps ’round yere. We hev ’nough o’ them fellers in the fambly a’ready.” Breakfast over, every one hurried to get a good start for the last part of the journey to Bentville. The Twilliger outfit was a span of fat mules and a light wagon. They took the lead, and the oxen were soon far behind. “You’d better push on, Kid,” advised Dan Gooch as the oxen toiled up the last foothill before reaching the valley. “Yon’s Bentville—almost in sight. Zeb Twilliger will be thar an hour ahead of us. Nick hez sperit ’nough ter ketch up ter ’em stid of pokin’ ’long so powerful slow.” Kid took the advice. As he reached the top of the hill, he reined Nick in for a moment to look at the panorama of colour which spread below him. There were fields of corn and hemp threaded with a narrow, silver path of water. Beyond the valley, on a little plateau, was the white tower of a chapel. The trees were thick, but they could not entirely screen the angular outlines of the college buildings occupying the highest part of the little town. The boy’s heart beat fast. He had never been more than ten miles away from home in all his life before. Somehow the blacksmith’s trade did not seem so alluring as it had yesterday; perhaps Pete and Isaac were right after all. He was proud of them anyhow. Down, down toward the bridge which crossed Brushy Fork and the Big Hill Pike with the hard part of the journey behind him, Kid overtook the Twilligers. He exchanged a few remarks, then cantered past, and joined the long procession of vehicles and horsemen, all
- 51. Welcome to our website – the ideal destination for book lovers and knowledge seekers. With a mission to inspire endlessly, we offer a vast collection of books, ranging from classic literary works to specialized publications, self-development books, and children's literature. Each book is a new journey of discovery, expanding knowledge and enriching the soul of the reade Our website is not just a platform for buying books, but a bridge connecting readers to the timeless values of culture and wisdom. With an elegant, user-friendly interface and an intelligent search system, we are committed to providing a quick and convenient shopping experience. Additionally, our special promotions and home delivery services ensure that you save time and fully enjoy the joy of reading. Let us accompany you on the journey of exploring knowledge and personal growth! ebookfinal.com