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تعداد صفحات این فایل: ۳۸ صفحه

بخشی از مقاله انگلیسیعنوان انگلیسی:Multi-objective optimization using genetic algorithms: A tutorial~~en~~

Abstract

Multi-objective formulations are realistic models for many complex engineering optimization problems. In many real-life problems, objectives under consideration conflict with each other, and optimizing a particular solution with respect to a single objective can result in unacceptable results with respect to the other objectives. A reasonable solution to a multi-objective problem is to investigate a set of solutions, each of which satisfies the objectives at an acceptable level without being dominated by any other solution. In this paper, an overview and tutorial is presented describing genetic algorithms (GA) developed specifically for problems with multiple objectives. They differ primarily from traditional GA by using specialized fitness functions and introducing methods to promote solution diversity.

۱ Introduction

The objective of this paper is present an overview and tutorial of multiple-objective optimization methods using genetic algorithms (GA). For multiple-objective problems, the objectives are generally conflicting, preventing simultaneous optimization of each objective. Many, or even most, real engineering problems actually do have multipleobjectives, i.e., minimize cost, maximize performance, maximize reliability, etc. These are difficult but realistic problems. GA are a popular meta-heuristic that is particularly well-suited for this class of problems. Traditional GA are customized to accommodate multi-objective problems by using specialized fitness functions and introducing methods to promote solution diversity.

There are two general approaches to multiple-objective optimization. One is to combine the individual objective functions into a single composite function or move all but one objective to the constraint set. In the former case, determination of a single objective is possible with methods such as utility theory, weighted sum method, etc., but the problem lies in the proper selection of the weights or utility functions to characterize the decision-maker’s preferences. In practice, it can be very difficult to precisely and accurately select these weights, even for someone familiar with the problem domain. Compounding this drawback is that scaling amongst objectives is needed and small perturbations in the weights can sometimes lead to quite different solutions. In the latter case, the problem is that to move objectives to the constraint set, a constraining value must be established for each of these former objectives. This can be rather arbitrary. In both cases, an optimization method would return a single solution rather than a set of solutions that can be examined for trade-offs. For this reason, decision-makers often prefer a set of good solutions considering the multiple objectives.

The second general approach is to determine an entire Pareto optimal solution set or a representative subset. A Pareto optimal set is a set of solutions that are nondominated with respect to each other. While moving from one Pareto solution to another, there is always a certain amount of sacrifice in one objective(s) to achieve a certain amount of gain in the other(s). Pareto optimal solution sets are often preferred to single solutions because they can be practical when considering real-life problems since the final solution of the decision-maker is always a trade-off. Pareto optimal sets can be of varied sizes, but the size of the Pareto set usually increases with the increase in the number of objectives.

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