A Meta-Model-Based Multi-Objective Evolutionary Approach to Robust Job Shop Scheduling

In the real-world manufacturing system, various uncertain events can occur and disrupt the normal production activities. This paper addresses the multi-objective job shop scheduling problem with random machine breakdowns. As the key of our approach, the robustness of a schedule is considered jointly with the makespan and is defined as expected makespan delay, for which a meta-model is designed by using a data-driven response surface method. Correspondingly, a multi-objective evolutionary algorithm (MOEA) is proposed based on the meta-model to solve the multi-objective optimization problem. Extensive experiments based on the job shop benchmark problems are conducted. The results demonstrate that the Pareto solution sets of the MOEA are much better in both convergence and diversity than those of the algorithms based on the existing slack-based surrogate measures. The MOEA is also compared with the algorithm based on Monte Carlo approximation, showing that their Pareto solution sets are close to each other while the MOEA is much more computationally efficient.

Metrics for Quality Assessment of a Multiobjective Design Optimization Solution Set

In this paper, several new set quality metrics are introduced that can be used to evaluate the ‘goodness’ of an observed Pareto solution set. These metrics, which are formulated in closed-form and geometrically illustrated, include coverage difference, Pareto spread, accuracy of an observed Pareto frontier, number of distinct choices and cluster. The metrics should enable a designer either monitor the quality of an observed Pareto solution set as obtained by a multiobjective optimization method, or compare the quality of observed Pareto solution sets as reported by different multiobjective optimization methods. A vibrating platform example is used to demonstrate the calculation of these metrics for an observed Pareto solution set.

Metrics for Quality Assessment of a Multiobjective Design Optimization Solution Set

In this paper, several new set quality metrics are introduced that can be used to evaluate the “goodness” of an observed Pareto solution set. These metrics, which are formulated in closed-form and geometrically illustrated, include hyperarea difference, Pareto spread, accuracy of an observed Pareto frontier, number of distinct choices and cluster. The metrics should enable a designer to either monitor the quality of an observed Pareto solution set as obtained by a multiobjective optimization method, or compare the quality of observed Pareto solution sets as reported by different multiobjective optimization methods. A vibrating platform example is used to demonstrate the calculation of these metrics for an observed Pareto solution set.