Over the years, a number of methods have been proposed for the generation of uniform and globally optimal Pareto frontiers in multi-objective optimization problems. This has been the case irrespective of the problem d...Over the years, a number of methods have been proposed for the generation of uniform and globally optimal Pareto frontiers in multi-objective optimization problems. This has been the case irrespective of the problem definition. The most commonly applied methods are the normal constraint method and the normal boundary intersection method. The former suffers from the deficiency of an uneven Pareto set distribution in the case of vertical （or horizontal） sections in the Pareto frontier, whereas the latter suffers from a sparsely populated Pareto frontier when the optimization problem is numerically demanding （ill-conditioned）. The method proposed in this paper, coupled with a simple Pareto filter, addresses these two deficiencies to generate a uniform, globally optimal, well-populated Pareto frontier for any feasible bi-objective optimization problem. A number of examples are provided to demonstrate the performance of the algorithm.展开更多
Robust design (RD) has received much attention from researchers and practitioners for years, and a number of methodologies have been studied in the research community. The majority of existing RD models focus on the m...Robust design (RD) has received much attention from researchers and practitioners for years, and a number of methodologies have been studied in the research community. The majority of existing RD models focus on the minimum variability with a zero bias. However, it is often the case that the customer may specify upper bounds on one of the two process parameters (i.e., the process mean and variance). In this situation, the existing RD models may not work efficiently in incorporating the customer’s needs. To this end, we propose two simple RD models using the ε?constraint feasible region method - one with an upper bound of process bias specified and the other with an upper bound on process variability specified. We then conduct a case study to analyze the effects of upper bounds on each of the process parameters in terms of optimal operating conditions and mean squared error.展开更多
文摘Over the years, a number of methods have been proposed for the generation of uniform and globally optimal Pareto frontiers in multi-objective optimization problems. This has been the case irrespective of the problem definition. The most commonly applied methods are the normal constraint method and the normal boundary intersection method. The former suffers from the deficiency of an uneven Pareto set distribution in the case of vertical （or horizontal） sections in the Pareto frontier, whereas the latter suffers from a sparsely populated Pareto frontier when the optimization problem is numerically demanding （ill-conditioned）. The method proposed in this paper, coupled with a simple Pareto filter, addresses these two deficiencies to generate a uniform, globally optimal, well-populated Pareto frontier for any feasible bi-objective optimization problem. A number of examples are provided to demonstrate the performance of the algorithm.
基金This work was supported partly by the 2005 Inje University research grant.
文摘Robust design (RD) has received much attention from researchers and practitioners for years, and a number of methodologies have been studied in the research community. The majority of existing RD models focus on the minimum variability with a zero bias. However, it is often the case that the customer may specify upper bounds on one of the two process parameters (i.e., the process mean and variance). In this situation, the existing RD models may not work efficiently in incorporating the customer’s needs. To this end, we propose two simple RD models using the ε?constraint feasible region method - one with an upper bound of process bias specified and the other with an upper bound on process variability specified. We then conduct a case study to analyze the effects of upper bounds on each of the process parameters in terms of optimal operating conditions and mean squared error.
