Solving optimization problems with multiple (often conflicting) objectives is, generally, a very difficult goal. Evolutionary algorithms (EAs) were initially extended and applied during the mid-eighties in an attempt to stochastically solve problems of this generic class. During the past decade, a variety of multiobjective EA (MOEA) techniques have been proposed and applied to many scientific and engineering applications. Our discussion's intent is to rigorously define multiobjective optimization problems and certain related concepts, present an MOEA classification scheme, and evaluate the variety of contemporary MOEAs. Current MOEA theoretical developments are evaluated; specific topics addressed include fitness functions, Pareto ranking, niching, fitness sharing, mating restriction, and secondary populations. Since the development and application of MOEAs is a dynamic and rapidly growing activity, we focus on key analytical insights based upon critical MOEA evaluation of c...

In this paper, we study the problem features that may cause a multi-objective genetic algorithm (GA) difficulty in converging to the true Pareto-optimal front. Identification of such features helps us develop difficult test problems for multi-objective optimization. Multi-objective test problems are constructed from single-objective optimization problems, thereby allowing known difficult features of single-objective problems (such as multi-modality, isolation, or deception) to be directly transferred to the corresponding multi-objective problem. In addition, test problems having features specific to multiobjective optimization are also constructed. More importantly, these difficult test problems will enable researchers to test their algorithms for specific aspects of multi-objective optimization. Keywords Genetic algorithms, multi-objective optimization, niching, pareto-optimality, problem difficulties, test problems. 1 Introduction After a decade since the pioneering wor...

This paper investigates a new technique for the solving of multimodal problems using genetic algorithms (GAs). The proposed technique, Restricted Tournament Selection, is based on the paradigm of local competition. The paper begins by discussing some of the drawbacks of using current multimodal techniques. The paper then presents the new technique along with an analysis of a class of sets of solutions it preserves and locates. This presentation researches the new technique's restriction on competition from the viewpoint of calculating probability distributions for its tournaments as well as its various niche takeover times. Empirical observations are then presented as evidence of the technique's abilities in a wide variety of settings. Finally, this paper explores the future trajectory of multimodal GA research. Finding Multimodal Solutions Using Restricted Tournament Selection Abstract This paper investigates a new technique for the solving of multimodal problems using genetic algor...

A technique to perform design calculations on imprecise representations of parameters has been developed and is presented. The level of imprecision in the description of design elements is typically high in the preliminary phase of engineering design. This imprecision is represented using the fuzzy calculus. Calculations can be performed using this method, to produce (imprecise) performance parameters from imprecise (input) design parameters. The Fuzzy Weighted Average technique is used to perform these calculations. A new metric, called the γ-level measure, is introduced to determine the relative coupling between imprecise inputs and outputs. The background and theory supporting this approach are presented, along with one example. 1.

A common engineering practice is the use of approximation models in place of expensive computer simulations to drive a multidisciplinary design process based on nonlinear programming techniques. The use of approximation strategies is designed to reduce the number of detailed, costly computer simulations required during optimization while maintaining the pertinent features of the design problem. To date the primary focus of most approximate optimization strategies is that application of the method should lead to improved designs. This is a laudable attribute and certainly relevant for practicing designers. However to date few researchers have focused on the development of approximate optimization strategies that are assured of converging to a solution of the original problem. Recent works based on trust region model management strategies have shown promise in managing convergence in unconstrained approximate minimization. In this research we extend these well established notions from the literature on trust-region methods to manage the convergence of the more general approximate optimization problem where equality, inequality and variable bound constraints are present.The primary concern addressed in this study is how to manage the interaction between the optimization and the fidelity of the approximation models to ensure that the process converges to a solution of the original constrained design problem. Using a trust-region model management strategy, coupled with an augmented Lagrangian approach for constrained approximate optimization, one can show that the optimization process converges to a solution of the original problem. In this research an approx1 Graduate Research Assistant.

. We propose the application of a genotype-phenotype mapping to the solution of constrained optimization problems. The method consists of strictly separating the search space of genotypes from the solution space of phenotypes. A mapping from genotypes into phenotypes provides for the appropriate expression of information represented by the genotypes. The mapping is constructed as to guarantee feasibility of phenotypic solutions for the problem under study. This enforcing of constraints causes multiple genotypes to result in one and the same phenotype. Neutral variants are therefore frequent and play an important role in maintaining genetic diversity. As a specific example, we discuss Binary Genetic Programming (BGP), a variant of Genetic Programming that uses binary strings as genotypes and program trees as phenotypes. Published in: Proceedings PARALLEL PROBLEM SOLVING FROM NATURE III Y. Davidor, H.-P. Schwefel and R. Manner (Eds.) Springer, Berlin, 1994 pp. 322 --- 332 1 Introduction...

Due to an increasing interest in solving real-world optimization problems using evolutionary algorithms (EAs), researchers have developed a number of real-parameter genetic algorithms (GAs) in the recent past. In such studies, the main research effort is spent on developing an efficient recombination operator. Such recombination operators use probability distributions around the parent solutions to create an ospring. Some operators emphasize solutions at the center of mass of parents and some around the parents. In this paper, we propose a generic parent-centric recombination operator (PCX) and a steady-state, elite-preserving, scalable, and computationally fast population-alteration model (we called the G3 model). The performance of the G3 model with the PCX operator is investigated on three commonly-used test problems and is compared with a number of evolutionary and classical optimization algorithms including other real-parameter GAs with UNDX and SPX operators, the correlated self-adaptive evolution strategy, the dierential evolution technique and the quasi-Newton method. The proposed approach is found to be consistently and reliably performing better than all other methods used in the study. A scale-up study with problem sizes up to 500 variables shows a polynomial computational complexity of the proposed approach. This extensive study clearly demonstrates the power of the proposed technique in tackling real-parameter optimization problems.

this paper, we briefly outline the principles of multi-objective optimization. Thereafter, we discuss why classical search and optimization methods are not adequate for multi-criterion optimization by discussing the working of two popular methods. We then outline several evolutionary methods for handling multi-criterion optimization problems. Of them, we discuss one implementation (non-dominated sorting GA or NSGA [38]) in somewhat greater details. Thereafter, we demonstrate the working of the evolutionary methods by applying NSGA to three test problems having constraints and discontinuous Pareto-optimal region. We also show the efficacy of evolutionary algorithms in engineering design problems by solving a welded beam design problem. The results show that evolutionary methods can find widely different yet near-Pareto-optimal solutions in such problems. Based on the above studies, this paper also suggests a number of immediate future studies which would make this emerging field more mature and applicable in practice. 1.2 PRINCIPLES OF MULTI-CRITERION OPTIMIZATION

Methods for incorporating imprecision in engineering design decision-making are briefly reviewed and compared. A tutorial is presented on the Method of Imprecision (MoI), a formal method, based on the mathematics of fuzzy sets, for representing and manipulating imprecision in engineering design. The results of a design cost estimation example, utilizing a new informal cost specification, are presented. The MoI can provide formal information upon which to base decisions during preliminary engineering design and can facilitate set-based concurrent design.

Simulation optimization can be defined as the process of finding the best input variable values from among all possibilities without explicitly evaluating each possibility. The objective of simulation optimization is to minimize the resources spent while maximizing the information obtained in a simulation experiment. The purpose of this paper is to review the area of simulation optimization. A critical review of the methods employed and applications developed in this relatively new area are presented and notable successes are highlighted. Simulation optimization software tools are discussed. The intended audience is simulation practitioners and theoreticians as well as beginners in the field of simulation.