Multiobjective evolutionary algorithms: a comparative case study and the strength pareto approach

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Multiobjective evolutionary algorithms: a comparative case study and the strength pareto approach (1999)

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by Eckart Zitzler , Lothar Thiele

Venue:	IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION
Citations:	810 - 22 self

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@ARTICLE{Zitzler99multiobjectiveevolutionary,
    author = {Eckart Zitzler and Lothar Thiele},
    title = {Multiobjective evolutionary algorithms: a comparative case study and the strength pareto approach},
    journal = {IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION},
    year = {1999},
    volume = {3},
    number = {4},
    pages = {257--271}
}

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Abstract

Evolutionary algorithms (EA’s) are often well-suited for optimization problems involving several, often conflicting objectives. Since 1985, various evolutionary approaches to multiobjective optimization have been developed that are capable of searching for multiple solutions concurrently in a single run. However, the few comparative studies of different methods presented up to now remain mostly qualitative and are often restricted to a few approaches. In this paper, four multiobjective EA’s are compared quantitatively where an extended 0/1 knapsack problem is taken as a basis. Furthermore, we introduce a new evolutionary approach to multicriteria optimization, the Strength Pareto EA (SPEA), that combines several features of previous multiobjective EA’s in a unique manner. It is characterized by a) storing nondominated solutions externally in a second, continuously updated population, b) evaluating an individual’s fitness dependent on the number of external nondominated points that dominate it, c) preserving population diversity using the Pareto dominance relationship, and d) incorporating a clustering procedure in order to reduce the nondominated set without destroying its characteristics. The proof-of-principle results obtained on two artificial problems as well as a larger problem, the synthesis of a digital hardware–software multiprocessor system, suggest that SPEA can be very effective in sampling from along the entire Pareto-optimal front and distributing the generated solutions over the tradeoff surface. Moreover, SPEA clearly outperforms the other four multiobjective EA’s on the 0/1 knapsack problem.

Keyphrases

multiobjective evolutionary algorithm strength pareto approach comparative case study knapsack problem multiobjective ea index term clustering strength pareto ea artificial problem abstract evolutionary algorithm tradeoff surface proof-of-principle result pareto optimality nondominated set different method multiple solution population diversity unique manner pareto dominance relationship single run evolutionary algorithm entire pareto-optimal front clustering procedure individual fitness dependent new evolutionary approach various evolutionary approach optimization problem several feature storing nondominated solution previous multiobjective ea updated population multiobjective optimization comparative study generated solution digital hardware software multiprocessor system external nondominated point

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