Fred Glover

Tabu Search—Part II

This is the second half of a two part series devoted to the tabu search metastrategy for optimization problems. Part I introduced the fundamental ideas of tabu search as an approach for guiding other heuristics to overcome the limitations of local optimality, both in a deterministic and a probabilistic framework. Part I also reported successful applications from a wide range of settings, in which tabu search frequently made it possible to obtain higher quality solutions than previously obtained with competing strategies, generally with less computational effort. Part II, in this issue, examines refinements and more advanced aspects of tabu search. Following a brief review of notation, Part II introduces new dynamic strategies for managing tabu lists, allowing fuller exploitation of underlying evaluation functions. In turn, the elements of staged search and structured move sets are characterized, which bear on the issue of finiteness. Three ways of applying tabu search to the solution of integer programmin...

Future paths for integer programming and links to artificial intelligence

Abstract Integer programming has benefited from many innovations in models and methods. Some of the promising directions for elaborating these innovations in the future may be viewed from a framework that links the perspectives of artificial intelligence and operations research. To demonstrate this, four key areas are examined: 1. (1) controlled randomization, 2. (2) learning strategies, 3. (3) induced decomposition and 4. (4) tabu search. Each of these is shown to have characteristics that appear usefully relevant to developments on the horizon.

A user's guide to tabu search

We describe the main features of tabu search, emphasizing a perspective for guiding a user to understand basic implementation principles for solving combinatorial or nonlinear problems. We also identify recent developments and extensions that have contributed to increasing the efficiency of the method. One of the useful aspects of tabu search is the ability to adapt a rudimentary prototype implementation to encompass additional model elements, such as new types of constraints and objective functions. Similarly, the method itself can be evolved to varying levels of sophistication. We provide several examples of discrete optimization problems to illustrate the strategic concerns of tabu search, and to show how they may be exploited in various contexts. Our presentation is motivated by the emergence of an extensive literature of computational results, which demonstrates that a well-tuned implementation makes it possible to obtain solutions of high quality for difficult problems, yielding outcomes in some settings that have not been matched by other known techniques.

A Template for Scatter Search and Path Relinking

Scatter search and its generalized form called path relinking are evolutionary methods that have recently been shown to yield promising outcomes for solving combinatorial and nonlinear optimization problems. Based on formulations originally proposed in the 1960s for combining decision rules and problem constraints, these methods use strategies for combining solution vectors that have proved effective for scheduling, routing, financial product design, neural network training, optimizing simulation and a variety of other problem areas. These approaches can be implemented in multiple ways, and offer numerous alternatives for exploiting their basic ideas. We identify a template for scatter search and path relinking methods that provides a convenient and user friendly basis for their implementation. The overall design can be summarized by a small number of key steps, leading to versions of scatter search and path relinking that are fully specified upon providing a handful of subroutines. Illustrative forms of these subroutines are described that make it possible to create methods for a wide range of optimization problems.

Tabu Search and Adaptive Memory Programming — Advances, Applications and Challenges

Tabu search (TS) has provided advances for solving difficult optimization problems in many domains. At the same time, fundamental TS strategies are often not applied as effectively as they might be, and their underlying rationale is often not completely understood. We examine basic concepts and principles of tabu search, emphasizing those that have sometimes led to applying the label “adaptive memory programming” to this class of methods.

Simple but powerful goal programming models for discriminant problems

Abstract Conventional statistical analysis includes the capacity to systematically assign individuals to groups. We suggest alternative assignment procedures, utilizing a set of interrelated goal programming formulations. We further demonstrate via simple illustration the potential of these procedures to play a significant part in addressing the discriminant problem, and indicate fundamental ideas that lay the foundation for other more sophisticated approaches.

Scatter Search and Local NLP Solvers: A Multistart Framework for Global Optimization

The algorithm described here, called OptQuest/NLP or OQNLP, is a heuristic designed to find global optima for pure and mixed integer nonlinear problems with many constraints and variables, where all problem functions are differentiable with respect to the continuous variables. It uses OptQuest, a commercial implementation of scatter search developed by OptTek Systems, Inc., to provide starting points for any gradient-based local solver for nonlinear programming (NLP) problems. This solver seeks a local solution from a subset of these points, holding discrete variables fixed. The procedure is motivated by our desire to combine the superior accuracy and feasibility-seeking behavior of gradient-based local NLP solvers with the global optimization abilities of OptQuest. Computational results include 155 smooth NLP and mixed integer nonlinear program (MINLP) problems due to Floudas et al. (1999), most with both linear and nonlinear constraints, coded in the GAMS modeling language. Some are quite large for global optimization, with over 100 variables and 100 constraints. Global solutions to almost all problems are found in a small number of local solver calls, often one or two.

Principles of scatter search

Scatter search is an evolutionary method that has been successfully applied to hard optimization problems. The fundamental concepts and principles of the method were first proposed in the 1970s, based on formulations dating back to the 1960s for combining decision rules and problem constraints. In contrast to other evolutionary methods like genetic algorithms, scatter search is founded on the premise that systematic designs and methods for creating new solutions afford significant benefits beyond those derived from recourse to randomization. It uses strategies for search diversification and intensification that have proved effective in a variety of optimization problems. This paper provides the main principles and ideas of scatter search and its generalized form path relinking. We first describe a basic design to give the reader the tools to create relatively simple implementations. More advanced designs derive from the fact that scatter search and path relinking are also intimately related to the tabu search (TS) metaheuristic, and gain additional advantage by making use of TS adaptive memory and associated memory-exploiting mechanisms capable of being tailored to particular contexts. These and other advanced processes described in the paper facilitate the creation of sophisticated implementations for hard problems that often arise in practical settings. Due to their flexibility and proven effectiveness, scatter search and path relinking can be successfully adapted to tackle optimization problems spanning a wide range of applications and a diverse collection of structures, as shown in the papers of this volume.

Simulation optimization: a review, new developments, and applications

We provide a descriptive review of the main approaches for carrying out simulation optimization, and sample some recent algorithmic and theoretical developments in simulation optimization research. Then we survey some of the software available for simulation languages and spreadsheets, and present several illustrative applications.

The general employee scheduling problem: an integration of MS and AI

Abstract The general employee scheduling problem extends the standard shift scheduling problem by discarding key limitations such as employee homogeneity and the absence of connections across time period blocks. The resulting increased generality yields a scheduling model that applies to real world problems confronted in a wide variety of areas. The price of the increased generality is a marked increase in size and complexity over related models reported in the literature. The integer programming formulation for the general employee scheduling problem, arising in typical real world settings, contains from one million to over four million zero-one variables. By contrast, studies of special cases reported over the past decade have focused on problems involving between 100 and 500 variables. We characterize the relationship between the general employee scheduling problem and related problems, reporting computational results for a procedure that solves these more complex problems within 98–99% optimality and runs on a microcomputer. We view our approach as an integration of management science and artificial intelligence techniques. The benefits of such an integration are suggested by the fact that other zero-one scheduling implementations reported in the literature, including the one awarded the Lancaster Prize in 1984, have obtained comparable approximations of optimality only for problems from two to three orders of magnitude smaller, and then only by the use of large mainframe computers.