Manuel Laguna

Fine-Tuning of Algorithms Using Fractional Experimental Designs and Local Search

Researchers and practitioners frequently spend more time fine-tuning algorithms than designing and implementing them. This is particularly true when developing heuristics and metaheuristics, where the right choice of values for search parameters has a considerable effect on the performance of the procedure. When testing metaheuristics, performance typically is measured considering both the quality of the solutions obtained and the time needed to find them. In this paper, we describe the development of CALIBRA, a procedure that attempts to find the best values for up to five search parameters associated with a procedure under study. Because CALIBRA uses Taguchis fractional factorial experimental designs coupled with a local search procedure, the best values found are not guaranteed to be optimal. We test CALIBRA on six existing heuristic-based procedures. These experiments show that CALIBRA is able to find parameter values that either match or improve the performance of the procedures resulting from using the parameter values suggested by their developers. The latest version of CALIBRA can be downloaded for free from the website that appears in the online supplement of this paper at http://or.pubs.informs.org/Pages.collect.html.

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.

Grasp and Path Relinking for 2-Layer Straight Line Crossing Minimization

In this article, we develop a greedy randomized adaptive search procedure (GRASP) for the problem of minimizing straight line crossings in a 2-layer graph. The procedure is fast and is particularly appealing when dealing with low-density graphs. When a modest increase in computational time is allowed, the procedure may be coupled with a path relinking strategy to search for improved outcomes. Although the principles of path relinking have appeared in the tabu search literature, this search strategy has not been fully implemented and tested. We perform extensive computational experiments with more than 3,000 graph instances to first study the effect of changes in critical search parameters and then to compare the efficiency of alternative solution procedures. Our results indicate that graph density is a major influential factor on the performance of a solution procedure.

Genetic algorithms and tabu search: hybrids for optimization

Abstract Genetic algorithms and tabu search have a number of significant differences. They also have some common bonds, often unrecognized. We explore the nature of the connections between the methods, and show that a variety of opportunities exist for creating hybrid approaches to take advantage of their complementary features. Tabu search has pioneered the systematic exploration of memory functions in search processes, while genetic algorithms have pioneered the implementation of methods that exploit the idea of combining solutions. There is also another approach, related to both of these, that is frequently overlooked. The procedure called scatter search, whose origins overlap with those of tabu search (and roughly coincide with the emergence of genetic algorithms) also proposes mechanisms for combining solutions, with useful features that offer a bridge between tabu search and genetic algorithms. Recent generalizations of scatter search concepts, embodied in notions of structured combinations and path relinking, have produced effective strategies that provide a further basis for integrating GA and TS approaches. A prominent TS component called strategic oscillation is susceptible to exploitation by GA processes as a means of creating useful degrees of diversity and of allowing effective transitions between feasible and infeasible regions. The independent success of genetic algorithms and tabu search in a variety of applications suggests that each has features that are valuable for solving complex problems. The thesis of this paper is that the study of methods that may be created from their union can provide useful benefits in diverse settings.

Tabu search for the multilevel generalized assignment problem

Abstract The multilevel generalized assignment problem (MGAP) differs from the classical GAP in that agents can perform tasks at more than one efficiency level. Important manufacturing problems, such as lot sizing, can be formulated as MGAPs; however, the large number of variables in the related 0–1 integer program makes the use of commercial optimization packages impractical. In this paper, we present a heuristic approach to the solution of the MGAP, which consists of a novel application of tabu search (TS). Our TS method employs neighborhoods defined by ejection chains, that produce moves of greater power without significantly increasing the computational effort.

Intensification and diversification with elite tabu search solutions for the linear ordering problem

Abstract In this paper, we develop a new heuristic procedure for the linear ordering problem (LOP). This NP-hard problem has a significant number of applications in practice. The LOP, for example, is equivalent to the so-called triangulation problem for input–output tables in economics. In this paper, we concentrate on matrices that arise in the context of this real-world application. The proposed algorithm is based on the tabu search methodology and incorporates strategies for search intensification and diversification. For search intensification, we experiment with path relinking, a strategy proposed several years ago in connection with tabu search, which has been rarely used in actual implementations. Extensive computational experiments with input–output tables show that the proposed procedure outperforms the best heuristics reported in the literature. Furthermore, the experiments also show the merit of achieving a balance between intensification and diversification in the search. Scope and purpose The linear ordering problem (LOP) has a wide range of applications in several fields. Perhaps, the best know application of the LOP occurs in the field of economics. In this application, the economy (regional or national) is first subdivided into sectors. Then, an input/output matrix is created, in which the entry ( i, j ) represents the flow of money from sector i to sector j. Economists are often interested in ordering the sectors so that suppliers tend to come first followed by consumers. This is achieved by permuting the rows and columns of the matrix so that the sum of entries above the diagonal is maximized, which is the objective of the LOP. In group decision making, for example, the linear ordering problem can be used to provide a ranking by paired comparison (or aggregation of individual preferences). A matrix entry ( i, j ) in this context may represent the strength of the preference that the group shows for option i over option j. Since the data may be inconsistent, there may not be a direct way of finding an ordering for the options. The solution to the corresponding LOP emerges as viable alternative for ranking the options under consideration. Due to its combinatorial nature, the linear ordering problem has been shown to be hard (computationally speaking While other computationally hard problems have captured the attention of researcher for many years (e.g., the travelling salesman problem), developing efficient solution procedure for the LOP has been somewhat neglected. The goal of our paper is two-fold: (1) to develop an efficient heuristic procedure for this problem, and (2) to experiment with the use of specialized strategies for search intensification and diversification, within the context of the search methodology that we have chosen to apply.

Experimental Testing of Advanced Scatter Search Designs for Global Optimization of Multimodal Functions

AbstractScatter search is an evolutionary method that, unlike genetic algorithms, operates on a small set of solutions and makes only limited use of randomization as a proxy for diversification when searching for a globally optimal solution. The scatter search framework is flexible, allowing the development of alternative implementations with varying degrees of sophistication. In this paper, we test the merit of several scatter search designs in the context of global optimization of multimodal functions. We compare these designs among themselves and choose one to compare against a well-known genetic algorithm that has been specifically developed for this class of problems. The testing is performed on a set of benchmark multimodal functions with known global minima.

Heuristic solutions to the problem of routing school buses with multiple objectives

In this paper we address the problem of routing school buses in a rural area. We approach this problem with a node routing model with multiple objectives that arise from conflicting viewpoints. From the point of view of cost, it is desirable to minimise the number of buses used to transport students from their homes to school and back. From the point of view of service, it is desirable to minimise the time that a given student spends en route. The current literature deals primarily with single-objective problems and the models with multiple objectives typically employ a weighted function to combine the objectives into a single one. We develop a solution procedure that considers each objective separately and search for a set of efficient solutions instead of a single optimum. Our solution procedure is based on constructing, improving and then combining solutions within the framework of the evolutionary approach known as scatter search. Experimental testing with real data is used to assess the merit of our proposed procedure.

An Experimental Evaluation of a Scatter Search for the Linear Ordering Problem

Scatter search is a population-based method that has recently been shown to yield promising outcomes for solving combinatorial and nonlinear global optimization problems. Based on formulations originally proposed in the 1960s for combining decision rules and problem constraints, such as in generating surrogate constraints, scatter search uses strategies for combining solution vectors that have proved effective in a variety of problem settings. In this paper, we present a scatter search implementation designed to find high quality solutions for the NP-hard linear ordering problem, which has a significant number of applications in practice. The LOP, for example, is equivalent to the so-called triangulation problem for input-output tables in economics. Our implementation incorporates innovative mechanisms to combine solutions and to create a balance between quality and diversification in the reference set. We also use a tracking process that generates solution statistics disclosing the nature of combinations and the ranks of antecedent solutions that produced the best final solutions. Extensive computational experiments with more than 300 instances establishes the effectiveness of our procedure in relation to approaches previously identified to be best.

New advances and applications of combining simulation and optimization

The design of efficient parallel discrete-event simulation (PDES) models often appears to be a mysterious art practiced primarily by academic researchers who have been rigorously ordained in this task. This tutorial attempts to unravel some of the mysteries. It describes the process of generating an efficient parallel implementation of a discrete-event simulation (DES) model. Common pitfalls in the parallel execution of the models are described together with suggestions on their avoidance.