In trying to solve multiobjective optimization problems, many traditional methods scalarize the objective vector into a single objective. In those cases, the obtained solution is highly sensitive to the weight vector used in the scalarization process and demands the user to have knowledge about the underlying problem. Moreover, in solving multiobjective problems, designers may be interested in a set of Pareto-optimal points, instead of a single point. Since genetic algorithms(GAs) work with a population of points, it seems natural to use GAs in multiobjective optimization problems to capture a number of solutions simultaneously. Although a vector evaluated GA (VEGA) has been implemented by Schaffer and has been tried to solve a number of multiobjective problems, the algorithm seems to have bias towards some regions. In this paper, we investigate Goldberg's notion of nondominated sorting in GAs along with a niche and speciation method to find multiple Pareto-optimal points sim...

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

This paper proposes the use of a genetic algorithm to develop neural networks to play the Capture Game, a subgame of Go. The motivation for this is twofold: to evaluate and possibly improve upon current genetic algorithm variants in order to produce a good player and (more importantly) to use this process to examine the properties and processes that are present in evolutionary systems in an attempt to shed some light on the phenomena that are required for an evolutionary process to produce robust, perpetually improving individuals and avoid local minima without any outside interaction. A brief survey of related work in the area is given, which highlights some of the interesting research questions that remain. This is followed by an outline of a distributed system that has been developed for use in the experimental evaluation of some of the proposed ideas and some of the initial results generated by the system. 1

Abstract. Multi-objective optimization methods are essential to resolve real-world problems as most involve several types of objects. Several multi-objective genetic algorithms have been proposed. Among them, SPEA2 and NSGA-II are the most successful. In the present study, two new mechanisms were added to SPEA2 to improve its searching ability a more effective crossover mechanism and an archive mechanism to maintain diversity of the solutions in the objective and variable spaces. The new SPEA2 with these two mechanisms was named SPEA2+. To clarify the characteristics and effectiveness of the proposed method, SPEA2+ was applied to several test functions. In the comparison of SPEA2+ with SPEA2 and NSGA-II, SPEA2+ showed good results and the effects of the new mechanism were clarified. From these results, it was concluded that SPEA2+ is a good algorithm for multi-objective optimization problems. 1

A genetic algorithm (GA) is a search and optimization method developed by mimicking the evolutionary principles and chromosomal processing in natural genetics. A GA begins its search with a random set of solutions usually coded in binary string structures. Every solution is assigned a fitness which is directly related to the objective function of the search and optimization problem. Thereafter, the population of solutions is modified to a new population by applying three operators similar to natural genetic operators---reproduction, crossover, and mutation. A GA works iteratively by successively applying these three operators in each generation till a termination criterion is satisfied. Over the past one decade, GAs have been successfully applied to a wide variety of problems, because of their simplicity, global perspective, and inherent parallel processing. In this paper, we outline the working principle of a GA by describing these three operators and by outlining an intuitive sketch ...

We present an investigation into the design of an evolutionary mechanism for multiagent protocol constraint optimisation. Starting with a review of common population based mechanisms we discuss the properties of the mechanisms used by these search methods. We derive a novel algorithm for optimisation of vectors of real numbers and empirically validate the efficacy of the design by comparing against well known results from the literature. We discuss the application of an optimiser to a novel problem and remark upon the relevance of the no free lunch theorem. We show the relative performance of the optimiser is strong and publish details of a new best result for the Keane optimisation problem. We apply the final algorithm to the multi-agent protocol optimisation problem and show the design process was successful. iii Declaration I declare that this thesis was composed by myself, that the work contained herein is my own except where explicitly stated otherwise in the text, and that this work has not been submitted for any other degree or professional qualification except as specified. iv (Mark Collins) For:

AERODYNAMIC OPTIMIZATION OF TURBINE CASCADES USING AN EULER/BOUNDARY-LAYER SOLVER COUPLED GENETIC ALGORITHM ksz, zhan M. S., Department of Aerospace Engineering Supervisor : Prof. Dr. I. Sinan Akmandor August 2002, 137 Pages A new methodology is developed to find the optimal aerodynamic performance of a turbine cascade. A boundary layer coupled Euler algorithm and a genetic algorithm are linked within an automated optimization loop. The multi-parameter objective function is based on the blade loading. For a given inlet Mach number and baseline cascade geometry, the flow inlet and exit angles, the blade thickness and the solidity are optimized by a robust genetic algorithm. Firstly, the Sanz subcritical turbine cascade is selected as the baseline cascade and is used for flow solver validation.

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The game of Tic-tac-toe is one of the most commonly known games. This game does not allow one to win all the time and a significant proportion of games played results in a draw. Thus, the best a player can hope is to not lose the game. This study is aimed at evolving a number of no-loss strategies using genetic algorithms and comparing them with existing methodologies. To efficiently evolve no-loss strategies, we have developed innovative ways of representing and evaluating a solution, initializing the GA population, developing GA operators including an elite preserving scheme. Interestingly, our GA implementation is able to find more than 72 thousands no-loss strategies for playing the game. Moreover, an analysis of these solutions has given us insights about how to play the game to not lose it. Based on this experience, we have developed specialized efficient strategies having a high win-to-draw ratio. The study and its results are interesting and can be encouraging for the techniques to be applied to other board games for finding efficient strategies.

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