For the first time, a running time analysis of a multi-objective evolutionary algorithm for a discrete optimization problem is given. To this end, a simple pseudo-Boolean problem (Lotz: leading ones - trailing zeroes) is defined and a population-based optimization algorithm (FEMO). We show, that the algorithm performs a black box optimization in #(n 2 log n) function evaluations where n is the number of binary decision variables. 1

Mu l ip often conflicting objectives arise naturalj in most real worl optimization scenarios. As evol tionaryalAxjO hms possess several characteristics that are desirabl e for this type of probl em, this clOv of search strategies has been used for mul tiobjective optimization for more than a decade. Meanwhil e evol utionary mul tiobjective optimization has become establ ished as a separate subdiscipl ine combining the fiel ds of evol utionary computation and cl assical mul tipl e criteria decision ma ing. This paper gives an overview of evol tionary mu l iobjective optimization with the focus on methods and theory. On the one hand, basic principl es of mu l iobjective optimization and evol tionary alA#xv hms are presented, and various al gorithmic concepts such as fitness assignment, diversity preservation, and el itism are discussed. On the other hand, the tutorial incl udes some recent theoretical resul ts on the performance of mu l iobjective evol tionaryalvDfifl hms and addresses the question of how to simpl ify the exchange of methods and appl ications by means of a standardized interface. 1

In recent years, several researchers have concentrated on using probabilistic models in evolutionary algorithms. These Estimation of Distribution Algorithms (EDA) incorporate methods for automated learning of correlations between variables of th encoded solutions. The process of sampling new individuals from a probabilistic model respects these mutual dependencies such that disruption of important building blocks is avoided, in comparison with classical recombination operators. The goal of this paper is to investigate the usefulness of this concept in multi-objective optimization, where the aim is to approximate the set of Pareto-optimal solutions. We integrate the model building and sampling techniques of a special EDA called Bayesian Optimization Algorithm, based on binary decision trees, into an evolutionary multi-objective optimizer using a special selection scheme. The behavior of the resulting Bayesian Multi-objective Optimization Algorithm (BMOA) is empirically investigated on the multi-objective knapsack problem.

Abstract. Designing an adequate fitness function requires substantial knowledge of a problem and of features that indicate progress towards a solution. Coevolution takes the human out of the loop by dynamically constructing the evaluation function based on interactions between evolving individuals. A question is to what extent such automatic evaluation can be adequate. We define the notion of an ideal evaluation function. It is shown that coevolution can in principle achieve ideal evaluation. Moreover, progress towards ideal evaluation can be measured. This observation leads to an algorithm for coevolution. The algorithm makes stable progress on several challenging abstract test problems.

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Optimization principles are often used in engineering design activities for nding solutions which can not be bettered. The use of a single objective for design usually results in only one optimum solution, whereas the consideration of multiple conicting objectives results in a number of trade-off Pareto-optimal solutions. Investigating the Pareto-optimal solutions for any similarity or relationship among their design variables may provide vital design principles, which may not be possible to get by any other means. In this paper, we illustrate the concept of optimization in the presence of multiple conflicting objectives and then present one multiobjective optimization algorithm based on evolutionary algorithms. Thereafter, a number of engineering design optimization case studies are presented to first find a set of Pareto-optimal solutions and then analyze them to unveil important design principles which would be of great importance to a designer. The breadth of case studies considered in this paper and the demonstrated discovery of useful design principles should encourage the study of multiobjective evolutionary optimization and motivate researchers and practitioners to perform similar studies involving other engineering design problems.

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. 1

In this paper we are concerned with finding the Pareto optimal front or a good approximation to it. Since non-dominated solutions represent the goal in multiobjective optimisation, the dominance relation is frequently used to establish preference between solutions during the search. Recently, relaxed forms of the dominance relation have been proposed in the literature for improving the performance of multiobjective search methods. This paper investigates the influence of different fitness evaluation methods on the performance of two multiobjective methodologies when applied to a highly constrained two-objective optimisation problem. The two algorithms are: the Pareto archive evolutionary strategy and a population-based annealing algorithm. We demonstrate here, on a highly constrained problem, that the method used to evaluate the fitness of candidate solutions during the search affects the performance of both algorithms and it appears that the dominance relation is not always the best method to use.

Abstract. In this paper, we revisit a general class of multi-criteria multi-constrained network design problems and attempt to solve, in a novel way, with Evolutionary Algorithms (EAs). A major challenge to solving such problems is to capture possibly all the (representative) equivalent and diverse solutions. In this work, we formulate, without loss of generality, a bi-criteria bi- constrained communication network topological design problem. Two of the primary objectives to be optimized are network delay and cost subject to satisfaction of reliability and flowconstraints. This is a NP-hard problem so we use a hybrid approach (for initialization of the population) along with EA. Furthermore, the twoobjective optimal solution front is not known a priori. Therefore, we use a multiobjective EA which produces diverse solution space and monitors convergence; the EA has been demonstrated to work effectively across complex problems of unknown nature. We tested this approach for designing networks of different sizes and found that the approach scales well with larger networks. Results thus obtained are compared with those obtained by two traditional approaches namely, the exhaustive search and branch exchange heuristics. 1

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