Zitzler and Thiele : Multiobjective Evolutionary Algorithms | Comparison and Strength Pareto Approach

| Evolutionary algorithms (EAs) are often well-suited for optimization problems involving several, often connicting 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 diierent methods presented up to now remain mostly qualitative and are often restricted to a few approaches. In this paper, four multiobjective EAs 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 EAs in a unique manner. It is characterized by (a) storing nondominated solutions externally in a second, continuously updated population, (b) evaluating an individual's tness 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 artiicial problems as well as a larger problem, the synthesis of a digital hardware-software multiprocessor system , suggest that SPEA can be very eeective in sampling from along the entire Pareto-optimal front and distributing the generated solutions over the trade-oo surface. Moreover , SPEA clearly outperforms the other four multiobjec-tive EAs on the 0/1 knapsack problem.