EA/G-GA for Single Machine Scheduling Problems with Earliness/Tardiness Costs

Shih-Hsin Chen,Min-Chih Chen,Pei-Chann Chang,Yuh-Min Chen

doi:10.3390/e13061152

Abstract

An Estimation of Distribution Algorithm (EDA), which depends on explicitly sampling mechanisms based on probabilistic models with information extracted from the parental solutions to generate new solutions, has constituted one of the major research areas in the field of evolutionary computation. The fact that no genetic operators are used in EDAs is a major characteristic differentiating EDAs from other genetic algorithms (GAs). This advantage, however, could lead to premature convergence of EDAs as the probabilistic models are no longer generating diversified solutions. In our previous research [1], we have presented the evidences that EDAs suffer from the drawback of premature convergency, thus several important guidelines are provided for the design of effective EDAs. In this paper, we validated one guideline for incorporating other meta-heuristics into the EDAs. An algorithm named “EA/G-GA” is proposed by selecting a well-known EDA, EA/G, to work with GAs. The proposed algorithm was tested on the NP-Hard single machine scheduling problems with the total weighted earliness/tardiness cost in a just-in-time environment. The experimental results indicated that the EA/G-GA outperforms the compared algorithms statistically significantly across different stopping criteria and demonstrated the robustness of the proposed algorithm. Consequently, this paper is of interest and importance in the field of EDAs.

Highlights

In recent years, Estimation of Distribution Algorithms (EDAs) have received numerous attention [2,3,4,5,6]
In order to show the performance of the Evolutionary Algorithm (EA)/G-genetic algorithms (GAs), we compare the proposed algorithm with the original version of EA/G [6], Artificial Chromosomes with Genetic Algorithms (ACGA) [13], and Adaptive EA/G [1]
We compare the proposed algorithms with the EA/G, ACGA, and Adaptive EA/G discussed in other literature

Summary

Introduction

Estimation of Distribution Algorithms (EDAs) have received numerous attention [2,3,4,5,6]. In the procedures of research, explicitly learning and building a probabilistic model from the parental distribution, and sampling new solutions according to the probabilistic model [7]. Building the probabilistic model is a statistical learning problem which is a probability estimation in terms of a generalized relative entropy [8]. Sampling from probabilistic models avoids the disturbance of some of the salient genes represented by the model, which is contrary to what could occur when genetic operators such as crossover and mutation are applied [9]. Is the use of probability learning and sampling from the probabilistic model. Please refer to [7]

Methods

Results

Conclusion