A multi-objective implementation in swarm intelligence and its applications in designs of computer experiments

As technology has advanced nowadays, it is common for a system to be optimized under more than one objective function, which leads to inconclusive results if two contradictory objectives exist. Traditional approaches suggest a simple aggregation of multiple objectives into one via a linear combination, but it is hard to justify the weights quantitatively. This paper proposes a systematic therapy to multiple objective optimization problem: (1) When the importance of criteria are known in prior, a sequential optimization is conducted; and (2) When the criteria are known to be equally important, a simple aggregated objective function with equal weights is suggested. The Swarm Intelligence Based (SIB) method is extended for multiple objectives, namely Multiple Objective Swarm Intelligence Based (MOSIB) method. This method is then applied to the search of optimal designs of computer experiments, Latin hypercube designs (LHDs), under several common criteria. Numerical studies show that the MOSIB method successfully generates a new series of optimal LHDs that possess better design properties than those suggested in the literature.