The paper describes a rank-based fitness assignment method for Multiple Objective Genetic Algorithms (MOGAs). Conventional niche formation methods are extended to this class of multimodal problems and theory for setting the niche size is presented. The fitness assignment method is then modified to allow direct intervention of an external decision maker (DM). Finally, the MOGA is generalised further: the genetic algorithm is seen as the optimizing element of a multiobjective optimization loop, which also comprises the DM. It is the interaction between the two that leads to the determination of a satisfactory solution to the problem. Illustrative results of how the DM can interact with the genetic algorithm are presented. They also show the ability of the MOGA to uniformly sample regions of the trade-off surface.

The application of evolutionary algorithms (EAs) in multiobjective optimization is currently receiving growing interest from researchers with various backgrounds. Most research in this area has understandably concentrated on the selection stage of EAs, due to the need to integrate vectorial performance measures with the inherently scalar way in which EAs reward individual performance, i.e., number of offspring. In this review, current multiobjective evolutionary approaches are discussed, ranging from the conventional analytical aggregation of the different objectives into a single function to a number of populationbased approaches and the more recent ranking schemes based on the definition of Pareto-optimality. The sensitivity of different methods to

Despite the relatively high volume of research conducted on evolutionary multiobjective optimization in the last few years, little attention has been paid to the decision making process that is required to select a final solution to the multiobjective optimization problem at hand. This paper reviews the most important preference handling approaches used with evolutionary algorithms, analyzing their advantages and disadvantages, and then, it proposes some of the potential areas of future research in this discipline. 1 Introduction Most real-world problems are multiobjective in nature, because they consider several objectives (or alternatives) that are to be optimized simultaneously. Normally, these objectives are non-commensurable (i.e., they are measured in different units), and are in conflict with each other. Multiobjective optimization problems (MOPs) have received considerable attention in Operations Research (see for example [23, 7, 27, 12]), and they have recently become a very ...

Recent advances in navigation and data communication technologies make it feasible for individual aircraft to plan and fly their trajectories in the presence of other aircraft in the airspace. This way, individual aircraft can take advantage of the atmospheric and traffic conditions to optimally plan their paths. This capability is termed as the free flight concept. While the free flight concept provides new degrees of freedom to the aircraft operators, it also brings-in complexities not present in the current air traffic control system. In the free flight concept, each aircraft has the responsibility for navigating around other aircraft in the airspace. While this is not a difficult task under low speed, low traffic density conditions, the complexities of dealing with potential conflict with multiple aircraft can significantly increase the pilot's work load.

Abstract — In this paper we present new methods for the automated learning of heuristics in knowledge-lean applications and for finding heuristics that can be generalized to unlearned domains. These applications lack domain knowledge for credit assignment; hence, operators for composing new heuristics are generally modelfree, domain independent, and syntactic in nature. The operators we have used are genetics-based; examples of which include mutation and cross-over. Learning is based on a generate-and-test paradigm that maintains a pool of competing heuristics, tests them to a limited extent, creates new ones from those that perform well in the past, and prunes poor ones from the pool. We hav e studied three important issues in learning better heuristics: (a) anomalies in performance evaluation, (b) rational scheduling of limited computational resources in testing candidate heuristics in single-objective as well as multiobjective learning, and (c) finding heuristics that can be generalized to unlearned domains. We show experimental results in learning better heuristics for (a) process placement for distributed-memory multicomputers, (b) node decomposition in a branch-and-bound search, (c) generation of test patterns in VLSI circuit testing, and (d) VLSI cell placement and routing. Index Terms — Branch-and-bound search, generalization, genetics-based learning, heuristics, knowledge-lean

Genetic algorithms (GAs) are stochastic search techniques inspired by the principles of natural selection and natural genetics which have revealed a number of characteristics particularly useful for applications in optimization, engineering, and computer science, among other fields. In control engineering, they have found application mainly in problems involving functions difficult to characterize mathematically or known to present difficulties to more conventional numerical optimizers, as well as problems involving non-numeric and mixed-type variables. In addition, they exhibit a large degree of parallelism, making it possible to effectively exploit the computing power made available through parallel processing. Despite their early recognized potential for multiobjective optimization (almost all engineering problems involve multiple, often conflicting objectives), genetic algorithms have, for the most part, been applied to aggregations of the objectives in a single-objective fashion, like conventional optimizers. Although alternative approaches based on the notion of Pareto-dominance have been suggested, multiobjective optimization with genetic algorithms has received comparatively

In this thesis we present new methods for the automated design of new heuristics in knowledge-lean applications and for finding heuristics that can be generalized to unlearned test cases. These applications lack domain knowledge for credit assignment; hence, operators for composing new heuristics are generally model free, domain independent, and syntactic in nature. The operators we have used are genetics based; examples of which include mutation and crossover. Learning is based on a generate-and-test paradigm that maintains a pool of competing heuristics, tests them to a limited extent, creates new ones from those that perform well in the past, and prunes poor ones from the pool. We have studied four important issues in learning better heuristics: (a) partitioning of a problem domain into smaller subsets, called subdomains, so that performance values within each subdomain can be evaluated statistically, (b) anomalies in performance evaluation within a subdomain, (c) rational scheduling of limited computational resources in testing candidate heuristics in single-objective as well as multi-objective learning, and (d) finding heuristics that can be generalized to unlearned subdomains. We show experimental results in learning better heuristics for (a) process placement for distributed-memory multicomputers, (b) node decomposition in a branch-and-bound search, (c) generation of test patterns in VLSI circuit testing, (d) VLSI cell placement and routing, and (e) blind equalization.

Abstract. Several research groups recently demonstrated

Abstract. Conventional multi-objective Particle Swarm Optimization (PSO) algorithms aim to find a representative set of Pareto-optimal solutions from which the user may choose preferred solutions. For this purpose, most multi-objective PSO algorithms employ computationally expensive comparison procedures such as non-dominated sorting. We propose a PSO algorithm, Reference point-based PSO using a Steady-State approach (RPSO-SS), that finds a preferred set of solutions near user-provided reference points, instead of the entire set of Pareto-optimal solutions. RPSO-SS uses simple replacement strategies within a steadystate environment. The efficacy of RPSO-SS in finding desired regions of solutions is illustrated using some well-known two and three-objective test problems. 1