Showing papers on "Metaheuristic published in 2005"

Vehicle Routing Problem with Time Windows, Part I: Route Construction and Local Search Algorithms

Abstract: This paper presents a survey of the research on the vehicle routing problem with time windows (VRPTW). The VRPTW can be described as the problem of designing least cost routes from one depot to a set of geographically scattered points. The routes must be designed in such a way that each point is visited only once by exactly one vehicle within a given time interval, all routes start and end at the depot, and the total demands of all points on one particular route must not exceed the capacity of the vehicle. Both traditional heuristic route construction methods and recent local search algorithms are examined. The basic features of each method are described, and experimental results for Solomon's benchmark test problems are presented and analyzed. Moreover, we discuss how heuristic methods should be evaluated and propose using the concept of Pareto optimality in the comparison of different heuristic approaches. The metaheuristic methods are described in the second part of this article.

Vehicle Routing Problem with Time Windows, Part II: Metaheuristics

Abstract: This paper surveys the research on the metaheuristics for the Vehicle Routing Problem with Time Windows (VRPTW). The VRPTW can be described as the problem of designing least cost routes from one depot to a set of geographically scattered points. The routes must be designed in such a way that each point is visited only once by exactly one vehicle within a given time interval; all routes start and end at the depot, and the total demands of all points on one particular route must not exceed the capacity of the vehicle. Metaheuristics are general solution procedures that explore the solution space to identify good solutions and often embed some of the standard route construction and improvement heuristics described in the first part of this article. In addition to describing basic features of each method, experimental results for Solomon's benchmark test problems are presented and analyzed.

A tutorial for competent memetic algorithms: model, taxonomy, and design issues

Abstract: The combination of evolutionary algorithms with local search was named "memetic algorithms" (MAs) (Moscato, 1989). These methods are inspired by models of natural systems that combine the evolutionary adaptation of a population with individual learning within the lifetimes of its members. Additionally, MAs are inspired by Richard Dawkin's concept of a meme, which represents a unit of cultural evolution that can exhibit local refinement (Dawkins, 1976). In the case of MA's, "memes" refer to the strategies (e.g., local refinement, perturbation, or constructive methods, etc.) that are employed to improve individuals. In this paper, we review some works on the application of MAs to well-known combinatorial optimization problems, and place them in a framework defined by a general syntactic model. This model provides us with a classification scheme based on a computable index D, which facilitates algorithmic comparisons and suggests areas for future research. Also, by having an abstract model for this class of metaheuristics, it is possible to explore their design space and better understand their behavior from a theoretical standpoint. We illustrate the theoretical and practical relevance of this model and taxonomy for MAs in the context of a discussion of important design issues that must be addressed to produce effective and efficient MAs.

Improving PSO-Based multi-objective optimization using crowding, mutation and ∈-dominance

Abstract: In this paper, we propose a new Multi-Objective Particle Swarm Optimizer, which is based on Pareto dominance and the use of a crowding factor to filter out the list of available leaders. We also propose the use of different mutation (or turbulence) operators which act on different subdivisions of the swarm. Finally, the proposed approach also incorporates the ∈-dominance concept to fix the size of the set of final solutions produced by the algorithm. Our approach is compared against five state-of-the-art algorithms, including three PSO-based approaches recently proposed. The results indicate that the proposed approach is highly competitive, being able to approximate the front even in cases where all the other PSO-based approaches fail.

Metaheuristics in Combinatorial Optimization

Abstract: The emergence of metaheuristics for solving difficult combinatorial optimization problems is one of the most notable achievements of the last two decades in operations research This paper provides an account of the most recent developments in the field and identifies some common issues and trends Examples of applications are also reported for vehicle routing and scheduling problems

A Numerical Evaluation of Several Stochastic Algorithms on Selected Continuous Global Optimization Test Problems

Abstract: There is a need for a methodology to fairly compare and present evaluation study results of stochastic global optimization algorithms. This need raises two important questions of (i) an appropriate set of benchmark test problems that the algorithms may be tested upon and (ii) a methodology to compactly and completely present the results. To address the first question, we compiled a collection of test problems, some are better known than others. Although the compilation is not exhaustive, it provides an easily accessible collection of standard test problems for continuous global optimization. Five different stochastic global optimization algorithms have been tested on these problems and a performance profile plot based on the improvement of objective function values is constructed to investigate the macroscopic behavior of the algorithms. The paper also investigates the microscopic behavior of the algorithms through quartile sequential plots, and contrasts the information gained from these two kinds of plots. The effect of the length of run is explored by using three maximum numbers of function evaluations and it is shown to significantly impact the behavior of the algorithms.

Penalty Function Methods for Constrained Optimization with Genetic Algorithms

Abstract: Genetic Algorithms are most directly suited to unconstrained optimization. Application of Genetic Algorithms to constrained optimization problems is often a challenging effort. Several methods have been proposed for handling constraints. The most common method in Genetic Algorithms to handle constraints is to use penalty functions. In this paper, we present these penalty-based methods and discuss their strengths and weaknesses.

Pareto Multi Objective Optimization

Abstract: The goal of this chapter is to give fundamental knowledge on solving multi-objective optimization problems. The focus is on the intelligent metaheuristic approaches (evolutionary algorithms or swarm-based techniques). The focus is on techniques for efficient generation of the Pareto frontier. A general formulation of MO optimization is given in this chapter, the Pareto optimality concepts introduced, and solution approaches with examples of MO problems in the power systems field are given

Constraint-based local search

Abstract: The ubiquity of combinatorial optimization problems in our society is illustrated by the novel application areas for optimization technology, which range from supply chain management to sports tournament scheduling Over the last two decades, constraint programming has emerged as a fundamental methodology to solve a variety of combinatorial problems, and rich constraint programming languages have been developed for expressing and combining constraints and specifying search procedures at a high level of abstraction Local search approaches to combinatorial optimization are able to isolate optimal or near-optimal solutions within reasonable time constraints This book introduces a method for solving combinatorial optimization problems that combines constraint programming and local search, using constraints to describe and control local search, and a programming language, COMET, that supports both modeling and search abstractions in the spirit of constraint programming After an overview of local search including neighborhoods, heuristics, and metaheuristics, the book presents the architecture and modeling and search components of constraint-based local search and describes how constraint-based local search is supported in COMET The book describes a variety of applications, arranged by meta-heuristics It presents scheduling applications, along with the background necessary to understand these challenging problems The book also includes a number of satisfiability problems, illustrating the ability of constraint-based local search approaches to cope with both satisfiability and optimization problems in a uniform fashion

Two improved differential evolution schemes for faster global search

Abstract: Differential evolution (DE) is well known as a simple and efficient scheme for global optimization over continuous spaces. In this paper we present two new, improved variants of DE. Performance comparisons of the two proposed methods are provided against (a) the original DE, (b) the canonical particle swarm optimization (PSO), and (c) two PSO-variants. The new DE-variants are shown to be statistically significantly better on a seven-function test bed for the following performance measures: solution quality, time to find the solution, frequency of finding the solution, and scalability.

A hierarchical particle swarm optimizer and its adaptive variant

Abstract: A hierarchical version of the particle swarm optimization (PSO) metaheuristic is introduced in this paper. In the new method called H-PSO, the particles are arranged in a dynamic hierarchy that is used to define a neighborhood structure. Depending on the quality of their so-far best-found solution, the particles move up or down the hierarchy. This gives good particles that move up in the hierarchy a larger influence on the swarm. We introduce a variant of H-PSO, in which the shape of the hierarchy is dynamically adapted during the execution of the algorithm. Another variant is to assign different behavior to the individual particles with respect to their level in the hierarchy. H-PSO and its variants are tested on a commonly used set of optimization functions and are compared to PSO using different standard neighborhood schemes.

The harmony search heuristic algorithm for discrete structural optimization

Abstract: Many methods have been developed and are in use for structural size optimization problems, in which the cross-sectional areas or sizing variables are usually assumed to be continuous. In most practical structural engineering design problems, however, the design variables are discrete. This paper proposes an efficient optimization method for structures with discrete-sized variables based on the harmony search (HS) heuristic algorithm. The recently developed HS algorithm was conceptualized using the musical process of searching for a perfect state of harmony. It uses a stochastic random search instead of a gradient search so that derivative information is unnecessary. In this article, a discrete search strategy using the HS algorithm is presented in detail and its effectiveness and robustness, as compared to current discrete optimization methods, are demonstrated through several standard truss examples. The numerical results reveal that the proposed method is a powerful search and design optimization tool f...

Combining metaheuristics and exact algorithms in combinatorial optimization: a survey and classification

Abstract: In this survey we discuss different state-of-the-art approaches of combining exact algorithms and metaheuristics to solve combinatorial optimization problems. Some of these hybrids mainly aim at providing optimal solutions in shorter time, while others primarily focus on getting better heuristic solutions. The two main categories in which we divide the approaches are collaborative versus integrative combinations. We further classify the different techniques in a hierarchical way. Altogether, the surveyed work on combinations of exact algorithms and metaheuristics documents the usefulness and strong potential of this research direction.

Evolutionary multiobjective optimization : theoretical advances and applications

Abstract: Evolutionary Multiobjective Optimization Recent Trends in Evolutionary Multiobjective Optimization Self-adaptation and Convergence of Multiobjective Evolutionary Algorithms in Continuous Search Spaces A simple approach to evolutionary multi-objective optimization Quad-trees: A Data Structure for Storing Pareto-sets in Multi-objective Evolutionary Algorithms with Elitism Scalable Test Problems for Evolutionary Multi-Objective Optimization Particle Swarm Inspired Evolutionary Algorithm (PS-EA) for Multi-Criteria Optimization Problems Evolving Continuous Pareto Regions MOGADES: Multi-Objective Genetic Algorithm with Distributed Environment Scheme Use of Multiobjective Optimization Concepts to Handle Constraints in Genetic Algorithms Multi- Criteria Optimization of Finite State Automata: Maximizing Performance while Minimizing Description Length Multi-objective Optimization of Space Structures under Static and Seismic Loading Conditions

A generic framework for constrained optimization using genetic algorithms

Abstract: In this paper, we propose a generic, two-phase framework for solving constrained optimization problems using genetic algorithms. In the first phase of the algorithm, the objective function is completely disregarded and the constrained optimization problem is treated as a constraint satisfaction problem. The genetic search is directed toward minimizing the constraint violation of the solutions and eventually finding a feasible solution. A linear rank-based approach is used to assign fitness values to the individuals. The solution with the least constraint violation is archived as the elite solution in the population. In the second phase, the simultaneous optimization of the objective function and the satisfaction of the constraints are treated as a biobjective optimization problem. We elaborate on how the constrained optimization problem requires a balance of exploration and exploitation under different problem scenarios and come to the conclusion that a nondominated ranking between the individuals will help the algorithm explore further, while the elitist scheme will facilitate in exploitation. We analyze the proposed algorithm under different problem scenarios using Test Case Generator-2 and demonstrate the proposed algorithm's capability to perform well independent of various problem characteristics. In addition, the proposed algorithm performs competitively with the state-of-the-art constraint optimization algorithms on 11 test cases which were widely studied benchmark functions in literature.

Performance evaluation of an advanced local search evolutionary algorithm

Abstract: One natural question when testing performance of global optimization algorithm is: how performances compare to a restart local search algorithm. One purpose of this paper is to provide results for such comparisons. To this end, the performances of a restart (advanced) local-search strategy, the CMA-ES with small initial step-size, are investigated on the 25 functions of the CEC 2005 real-parameter optimization test suit. The second aim is to clarify the theoretical background of the performance criterion proposed to quantitatively compare the search algorithms. The theoretical analysis allows us to generalize the criterion proposed and to define a new criterion that can be applied more appropriate in a different context.

Sequential parameter optimization

Abstract: Sequential parameter optimization is a heuristic that combines classical and modern statistical techniques to improve the performance of search algorithms. To demonstrate its flexibility, three scenarios are discussed: (1) no experience how to choose the parameter setting of an algorithm is available, (2) a comparison with other algorithms is needed, and (3) an optimization algorithm has to be applied effectively and efficiently to a complex real-world optimization problem. Although sequential parameter optimization relies on enhanced statistical techniques such as design and analysis of computer experiments, it can be performed algorithmically and requires basically the specification of the relevant algorithm's parameters

Dynamic multi-swarm particle swarm optimizer with local search

Abstract: In this paper, the performance of a modified dynamic multi-swarm particle swarm optimizer (DMS-PSO) on the set of benchmark functions provided by CEC2005 is reported. Different from the existing multi-swarm PSOs and local versions of PSO, the swarms are dynamic and the swarms' size is small. The whole population is divided into many small swarms, these swarms are regrouped frequently by using various regrouping schedules and information is exchanged among the swarms. The quasi-Newton method is combined to improve its local search ability

Application and comparison of metaheuristic techniques to generation expansion planning problem

Abstract: This work presents both application and comparison of the metaheuristic techniques to generation expansion planning (GEP) problem. The Metaheuristic techniques such as the genetic algorithm, differential evolution, evolutionary programming, evolutionary strategy, ant colony optimization, particle swarm optimization, tabu search, simulated annealing, and hybrid approach are applied to solve GEP problem. The original GEP problem is modified using the proposed methods virtual mapping procedure (VMP) and penalty factor approach (PFA), to improve the efficiency of the metaheuristic techniques. Further, intelligent initial population generation (IIPG), is introduced in the solution techniques to reduce the computational time. The VMP, PFA, and IIPG are used in solving all the three test systems. The GEP problem considered synthetic test systems for 6-year, 14-year, and 24-year planning horizon having five types of candidate units. The results obtained by all these proposed techniques are compared and validated against conventional dynamic programming and the effectiveness of each proposed methods has also been illustrated in detail.

Unified particle swarm optimization for solving constrained engineering optimization problems

Abstract: We investigate the performance of the recently proposed Unified Particle Swarm Optimization method on constrained engineering optimization problems. For this purpose, a penalty function approach is employed and the algorithm is modified to preserve feasibility of the encountered solutions. The algorithm is illustrated on four well–known engineering problems with promising results. Comparisons with the standard local and global variant of Particle Swarm Optimization are reported and discussed.