Many engineering design problems are characterized by presence of several conflicting objectives. This requires efficient search of the feasible design region for optimal solutions which simultaneously satisfy multiple design objectives. The search is further complicated in view of the fact that because of inherent manufacturing variations it is often necessary to allocate tolerances to design variables while guaranteeing low variances for product/process performance measures.

Particle swarm optimization (PSO) is a powerful search technique with faster convergence rates than traditional evolutionary algorithms. This paper introduces a new PSO-based approach to multiobjective engineering design by incorporating the central qualitycontrol notion of tolerance design Unlike classical optimization techniques which rely on single-point representation of designs, the modified PSO algorithm allocates tolerances to design variables and flies a swarm of hypercubic particles through the feasible space. To demonstrate the utility of the proposed method, the multiobjective design of an I-beam will be presented.