In this paper, we present an efficient sampling method for a multimodal and high-dimensional distribution. For sampling from a high-dimensional distribution, DE-MC, which is based on the Markov chain Monte Carlo(MCMC) methods, has been proposed. It showed good performance in sampling from any probability distribution based on constructing a Markov chain that has the desired distribution. However, DE-MC has inherent difficulties in sampling from a multimodal distribution. To overcome this problem, we incorporate a replica exchange method into DE-MC and propose a replica exchange resampling DE-MC method (reRDE-MC) based on sampling importance resampling to improve its performance. The proposed method is evaluated by using three types of distributions with multimodal and high dimensions as artificial data. We verified that the proposed method can sample from a multimodal and highdimensional distribution more effectively than by a conventional method. We then evaluated the proposed method by using financial data as actual data, and confirmed that the proposed method can capture the behavior of financial data.
This paper proposes an effective algorithm for the recently proposed simultaneous design optimization problem of multiple car structures. In recent years, evolutionary algorithms typified by genetic algorithms have been extensively studied to solve single- and multi-objective real-world optimization problems. Mazda Motor Corporation developed the simultaneous design optimization benchmark problem that is based on a real car structures design and consists of many design variables and severe constraints. In this benchmark, three models of cars are simultaneously optimized and it is difficult to acquire optimal solutions with the limited number of evaluations with existing methods. This paper aims at proposing an algorithm based on NSGA-II, one of the most typical multi-objective evolutionary algorithm, and introduces several modifications considering the characteristics of the Mazda's benchmark problem. Specifically, we propose a method to effectively generate parent individuals using the characteristic that design variables of three cars are independent and genetic manipulation taking into consideration the characteristics of the objective function. In order to verify the effectiveness of the proposed method, we conduct experiments using the Mazda's benchmark problem. In the experiment, we compare NSGA-II with the proposed modifications with the original NSGA-II. The experimental result reveals that the proposed method can acquire extremely better solution set compared with the existing method.