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

TLDR

Evolutionary algorithms are well suited for multiobjective optimization, yet comparative studies are scarce and mainly qualitative. The paper quantitatively compares four multiobjective EAs on an extended 0/1 knapsack problem and introduces a new Strength Pareto EA. SPEA stores nondominated solutions in an external population, evaluates fitness based on domination counts, preserves diversity through Pareto dominance, and uses clustering to reduce the nondominated set while maintaining its characteristics. Results on artificial and hardware‑software synthesis problems show SPEA samples the entire Pareto front and outperforms the other four EAs on the 0/1 knapsack problem.

Abstract

Evolutionary algorithms (EAs) 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 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 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 EAs on the 0/1 knapsack problem.