Indicator-based differential evolution using exclusive hypervolume approximation and parallelization for multi-core processors

  • Authors:

  • Kiyoharu Tagawa;Hidehito Shimizu;Hiroyuki Nakamura

  • Affiliations:

  • Kinki University, Osaka, Japan;Panasonic Electronic Devices Co., Ltd, Osaka, Japan;Panasonic Electronic Devices Co., Ltd, Osaka, Japan

  • Venue:
  • Proceedings of the 13th annual conference on Genetic and evolutionary computation
  • Year:
  • 2011

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Abstract

A new Multi-Objective Evolutionary Algorithm (MOEA) based on Differential Evolution (DE), i.e., Indicator-Based DE (IBDE) is proposed. IBDE employs a strategy of DE for generating a series of offspring. In order to evaluate the quality of each individual in the population, IBDE uses the exclusive hypervolume as an indicator function. A fast algorithm called Incremental Hypervolume by Slicing Objectives (IHSO) has been reported for calculating the exclusive hypervolume. However, the computational time spent by IHSO increases exponentially with the number of objectives and considered individuals. Therefore, an exclusive hypervolume approximation, in which IHSO can be also used effectively, is proposed. Furthermore, it is proven that the proposed exclusive hypervolume approximation gives an upper bound of the accurate exclusive hypervolume. The procedure of IHSO is parallelized by using the multiple threads of the Java language. By using the parallelized IHSO, not only the exclusive hypervolume but also the exclusive hypervolume approximation can be calculated concurrently on a multi-core processor. By the results of numerical experiments and statistical tests conducted on test problems, the usefulness of the proposed approach is demonstrated.