Multi-objective evolutionary algorithms which use non-dominated sorting and sharing have been mainly criticized for their (i) O(MN computational complexity (where M is the number of objectives and N is the population size), (ii) non-elitism approach, and (iii) the need for specifying a sharing parameter. In this paper, we suggest a non-dominated sorting based multi-objective evolutionary algorithm (we called it the Non-dominated Sorting GA-II or NSGA-II) which alleviates all the above three difficulties. Specifically, a fast non-dominated sorting approach with O(MN ) computational complexity is presented. Second, a selection operator is presented which creates a mating pool by combining the parent and child populations and selecting the best (with respect to fitness and spread) N solutions. Simulation results on a number of difficult test problems show that the proposed NSGA-II, in most problems, is able to find much better spread of solutions and better convergence near the true Pareto-optimal front compared to PAES and SPEA - two other elitist multi-objective EAs which pay special attention towards creating a diverse Pareto-optimal front. Moreover, we modify the definition of dominance in order to solve constrained multi-objective problems eciently. Simulation results of the constrained NSGA-II on a number of test problems, including a five-objective, seven-constraint non-linear problem, are compared with another constrained multi-objective optimizer and much better performance of NSGA-II is observed. Because of NSGA-II's low computational requirements, elitist approach, parameter-less niching approach, and simple constraint-handling strategy, NSGA-II should find increasing applications in the coming years.

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...

From the user's point of view, setting the parameters of a genetic algorithm (GA) is far from a trivial task. Moreover, the user is typically not interested in population sizes, crossover probabilities, selection rates, and other GA technicalities. He is just interested in solving a problem, and what he would really like to do, is to hand-in the problem to a blackbox algorithm, and simply press a start button. This paper explores the development of a GA that fulfills this requirement. It has no parameters whatsoever. The development of the algorithm takes into account several aspects of the theory of GAs, including previous research work on population sizing, the schema theorem, building block mixing, and genetic drift.

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 proposes an algorithm that uses an estimation of the joint distribution of promising solutions in order to generate new candidate solutions. The algorithm is settled into the context of genetic and evolutionary computation and the algorithms based on the estimation of distributions. The proposed algorithm is called the Bayesian Optimization Algorithm (BOA). To estimate the distribution of promising solutions, the techniques for modeling multivariate data by Bayesian networks are used. TheBOA identifies, reproduces, and mixes building blocks up to a specified order. It is independent of the ordering of the variables in strings representing the solutions. Moreover, prior information about the problem can be incorporated into the algorithm, but it is not essential. First experiments were done with additively decomposable problems with both nonoverlapping as well as overlapping building blocks. The proposed algorithm is able to solve all but one of the tested problems in linear or close to linear time with respect to the problem size. Except for the maximal order of interactions to be covered, the algorithm does not use any prior knowledge about the problem. The BOA represents a step toward alleviating the problem of identifying and mixing building blocks correctly to obtain good solutions for problems with very limited domain information.

Self-adaptation is an essential feature of natural evolution. However, in the context of function optimization, self-adaptation features of evolutionary search algorithms have been explored only with evolution strategy (ES) and evolutionary programming (EP). In this paper, we demonstrate the selfadaptive feature of real-parameter genetic algorithms (GAs) using simulated binary crossover (SBX) operator and without any mutation operator. The connection between the working of self-adaptive ESs and real-parameter GAs with SBX operator is also discussed. Thereafter, the self-adaptive behavior of real-parameter GAs is demonstrated on a number of test problems commonly-used in the ES literature. The remarkable similarity in the working principle of real-parameter GAs and self-adaptive ESs shown in this study suggests the need of emphasizing further studies on self-adaptive GAs.

The convergence speed of building blocks depends on their marginal fitness contribution or on the salience structure of the problem. We use a sequential parameterization approach to build models of the differential convergence behavior, and derive time complexities for the boundary case which is obtained with an exponentially scaled problem (BinInt). We show that this domino convergence time complexity is linear in the number of building blocks (O(l)) for selection algorithms with constant selection intensity (such as tournament selection and ( ; ) or truncation selection), and exponential (O(2 l )) for proportionate selection. These complexities should be compared with the convergence speed for uniformly salient problems which are respectively (O( p l)) and (O(l ln l)). In addition we relate this facetwise model to a genetic drift model, and identify where and when the stochastic uctuations due to drift overwhelms the domino convergence, resulting in drift stall. The combined mo...

this article, I will argue rather strongly that computational innovation---at least certain important facets of the processes of innovation---has been achieved, and that computational creativity is plausibly within our sights. Specifically, I will argue that modern research in genetic algorithms---search

This paper presents the linkage identification by non-monotonicity detection (LIMD) procedure and its extension for overlapping functions by introducing the tightness detection (TD) procedure. The LIMD identifies linkage groups directly by performing order-2 simultaneous perturbations on a pair of loci to detect monotonicity/non-monotonicity of fitness changes. The LIMD can identify linkage groups with at most order of k when it is applied to O(2 k ) strings. The TD procedure calculates tightness of linkage between a pair of loci based on the linkage groups obtained by the LIMD. By removing loci with weak tightness from linkage groups, correct linkage groups are obtained for overlapping functions, which were considered difficult for linkage identification procedures. 1 Introduction The power of genetic search lies in its processing of building blocks (BBs) --- essential subcomponents of solutions --- through crossover and selection. Recent work (Goldberg, Deb, & Thierens, 1993; Thie...

This paper develops a macro-level theory of efficient time utilization for genetic and evolutionary algorithms. Building on population sizing results that estimate the critical relationship between solution quality and time, the paper considers the tradeoff between large populations that converge in a single convergence epoch and smaller populations with multiple epochs. Two models suggest a link between the salience structure of a problem and the appropriate populationtime configuration for best efficiency.