Improved Sampling of Decision Space for Pareto Estimation

Pareto Estimation (PE) is a novel method for increasing the density of Pareto optimal solutions across the entire Pareto Front or in a specific region of interest. PE identifies the inverse mapping of Pareto optimal solutions, namely, from objective space to decision space. This identification can be performed using a number of modeling techniques, how- ever, for the sake of simplicity in this work we use a radial basis neural network. In any modeling method, the quality of the resulting model depends heavily on the training samples used. The original version of PE uses the result- ing set of Pareto optimal solutions from any multi-objective optimization algorithm and then utilizes this set to identify the aforementioned mapping. However, we argue that this selection may not always be the best possible and propose an alternative scheme to improve the resulting set of Pareto optimal solutions in order to produce higher quality samples for the identification scheme in PE. The proposed approach is integrated with MAEA-gD, and the resulting solutions are used with PE. The results show that the proposed method shows promise, in that there is measurable improvement in the quality of the estimated PE in terms of the coverage and density

Evolutionary Many-objective Optimization of Hybrid Electric Vehicle Control: From General Optimization to Preference Articulation

Many real-world optimization problems have more than three objectives, which has triggered increasing research interest in developing efficient and effective evolutionary algorithms for solving many-objective optimization problems. However, most many-objective evolutionary algorithms have only been evaluated on benchmark test functions and few applied to real-world optimization problems. To move a step forward, this paper presents a case study of solving a many-objective hybrid electric vehicle controller design problem using three state-of-the-art algorithms, namely, a decomposition based evolutionary algorithm (MOEA/D), a non-dominated sorting based genetic algorithm (NSGA-III), and a reference vector guided evolutionary algorithm (RVEA). We start with a typical setting aiming at approximating the Pareto front without introducing any user preferences. Based on the analyses of the approximated Pareto front, we introduce a preference articulation method and embed it in the three evolutionary algorithms for identifying solutions that the decision-maker prefers. Our experimental results demonstrate that by incorporating user preferences into many-objective evolutionary algorithms, we are not only able to gain deep insight into the trade-off relationships between the objectives, but also to achieve high-quality solutions reflecting the decision-maker’s preferences. In addition, our experimental results indicate that each of the three algorithms examined in this work has its unique advantages that can be exploited when applied to the optimization of real-world problems