A New Frequency Analysis Operator for Population Improvement in Genetic Algorithms to Solve the Job Shop Scheduling Problem

Abstract

Job Shop Scheduling is currently one of the most addressed planning and scheduling optimization problems in the field. Due to its complexity, as it belongs to the NP-Hard class of problems, meta-heuristics are one of the most commonly used approaches in its resolution, with Genetic Algorithms being one of the most effective methods in this category. However, it is well known that this meta-heuristic is affected by phenomena that worsen the quality of its population, such as premature convergence and population concentration in regions of local optima. To circumvent these difficulties, we propose, in this work, the use of a guidance operator responsible for modifying ill-adapted individuals using genetic material from well-adapted individuals. We also propose, in this paper, a new method of determining the genetic quality of individuals using genetic frequency analysis. Our method is evaluated over a wide range of modern GAs and considers two case studies defined by well-established JSSP benchmarks in the literature. The results show that the use of the proposed operator assists in managing individuals with poor fitness values, which improves the population quality of the algorithms and, consequently, leads to obtaining better results in the solution of JSSP instances. Finally, the use of the proposed operator in the most elaborate GA-like method in the literature was able to reduce its mean relative error from 1.395% to 0.755%, representing an improvement of 45.88%.

Keywords: combinatorial optimization; evolutionary algorithm; genetic algorithm; genetic improvement; job shop scheduling problem.

Figure 1

Calculating the frequency vectors (${\overrightarrow{v}}_i$) of the three jobs in each coordinate of the four best chromosomes in the population.

Figure 2

Computation of the representative individual ($\mathbf{c}$) and its genetic relevance (w).

Figure 3

Determination of the most significant genes of a representative individual.

Figure 4

Genetic improvement proposed. The genes highlighted on a black background are the most relevant, while the genes highlighted with the red sectioned circle are those that need correction.

Figure 5

Flow chart of our proposed Genetic Improvement operator for Genetic Algorithm.

Figure 6

Experiments with respect to $N_{\mathrm{Top}}$ and $N_{\mathrm{Worst}}$ settings. In each heatmap, the average enhancement values $\mathrm{AvgImp}(N_{Top},N_{Worst})$ for $N_{\mathrm{Top}}$ and $N_{\mathrm{Worst}}$ are varying in grid on set $\{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,20,30,40,50\}$. For the computation of these values, $N_{\mathrm{run}}=35$ executions for each method were considered. (a) LA01. (b) LA21. (c) LA25.