Scheduling with Genetic Algorithms Based on Binary Matrix Encoding

Abstract

AbstractMetaheuristic optimization approaches like genetic algorithms have been successfully applied to automatic scheduling in various fields. Scheduling problems are known for high computational complexity. This is especially true for problems with precedence constraints like RCPSP (resource constrained project scheduling problem). Thus, scheduling algorithms need further improvements to deal with large practical problems.The paper proposes a novel binary matrix approach for encoding order in scheduling algorithms. Such encoding makes it simple to extract information about relative position of jobs (tasks, activities). It’s shown that precedence constraints can be also encoded as binary matrix of such type. The paper also introduces mutation and crossover operators for the proposed encoding to be used in genetic algorithms. Unlike the classical crossover operators, the proposed one produces offspring individuals which preserve relative and not absolute order of some subsets of elements.It is also proven that the proposed binary matrices can be reduced to canonical vector form. This makes it possible to apply Holland’s schema theorem to justify the convergence of modified genetic algorithms based on binary matrix encoding.The efficiency of the modified genetic algorithm in comparison with classical encodings and genetic operators has been tested on some instances of scheduling problems. It is shown that the proposed method demonstrates quite promising results on large scale problems. KeywordsSchedulingGenetic algorithmsCrossover operatorCombinatorial optimization