A new solution approach for multi-objective energy efficient job shop scheduling problem: WASPAS based NSGA-2

Today, with the development of industry, there has been an increase in energy consumption and greenhouse gas emissions, which has led to negative consequences such as environmental pollution and global warming. Studies aimed at reducing environmental damage have gained importance in recent years due to these reasons, as well as the increase in operating costs along with the increase in energy consumption. Businesses have turned to designing their facilities and manufacturing processes with environmental awareness. Businesses can be enabled to manufacture with environmental awareness through various methods, such as providing more suitable machinery and equipment and developing existing manufacturing processes. In a manufacturing environment where existing machinery and equipment are used, it is a very effective option for businesses to focus on scheduling studies, which determine the order in which each operation will be performed, using which machinery and equipment, in a way that meets the specified targets. In scheduling studies, various manufacturing targets are determined, such as reducing the completion time and costs of the jobs and reducing the number of delayed jobs, and the job order is tried to be determined in order to achieve these targets in the optimum way. With the prominence of environmental issues, in addition to these manufacturing targets, environmental targets such as reducing energy consumption and greenhouse gas emissions while scheduling have also been included in the studies. In solving this type of problem, heuristic and metaheuristic algorithms have been frequently preferred in many studies. In this study, a multi-objective energy efficient job shop scheduling problem is considered, where the makespan and total energy consumption are both targeted to be minimized. In order to solve the problem, a hybrid method, WSBNSGA-2 (WASPAS Based NSGA-2), was proposed and implemented by integrating the NSGA-2 (Nondominated Sorting Genetic Algorithm II) method, which is an algorithm applied to many scheduling problems in the literature, and the WASPAS (Weighted Aggregated Sum Product Assessment) method, which is a multi-criteria decision-making method. The applications are implemented by utilizing 15 multi-objective energy efficient job shop scheduling test problems of different sizes. In the first phase of the application, the parameters on which the NSGA-2 and WSBNSGA-2 algorithms showed the best performance were tried to be determined. The population size, crossover rate and mutation rate parameters that can affect the performance of the algorithms are determined as factors, and 3 different values that can be preferred for each parameter are determined as the levels of these factors. As a result of processing the determined factors and levels into the Taguchi module in the Minitab program, 9 experiments with different parameter combinations were presented by the program. With these parameter combinations, NSGA-2 and WSBNSGA-2 methods were applied on 15 test problems with 5 repetitions for each experimental combination. The average of TEC (total energy consumption) and Cmax (maximum completion time) results obtained with 5 repetitions for each experimental combination was used as the result value of that experimental combination. In order to combine the TEC and Cmax values into a single objective function value, the normalization process was applied using min-max normalization. As a result of normalization, the objective function values were calculated by assuming that the importance level of the problem's objectives was equal. These objective function values were used as the result values of Taguchi experimental combinations and the best parameters were determined by obtaining S/N graphs with the Taguchi Method for both algorithms in all problem sizes. ANOVA test was applied to the result values obtained with the Taguchi method. In all test problems, ANOVA test results were used for both algorithms to evaluate whether the parameters contributed to the results and the contribution rates of the contributing parameters. In order to evaluate whether more effective results can be obtained as a result of applying the parameters determined by the Taguchi method, both methods were applied on 15 test problems with 35 repetitions using the determined parameter values. While applying the WSBNSGA-2 method, the WASPAS method was used instead of the Fast Non Dominated Sorting step of the NSGA-2 method. The WASPAS method was applied with the chromosomes in the population as alternatives and the problem targets as criteria, and the chromosomes were assigned to the fronts with the order obtained as a result of WASPAS. The chromosomes in each front are sorted within themselves using Crowding Distance calculation values, as in the NSGA-2 method. Thus, a ranking was obtained for all chromosomes. With this order, chromosome pairs were determined for crossover and mutation operations. By crossover and mutation, new generations of individuals are produced and added to the population. Instead of Fast Non Dominated Sorting, which is applied by the NSGA-2 method in the process of eliminating chromosomes exceeding the N population size, the WASPAS method was applied again. Fronts were created using the WASPAS method and then the chromosomes in the fronts were ranked using Crowding Distance. Chromosomes exceeding the population size were eliminated from the population. TEC and Cmax values were obtained by applying the algorithms 35 times to each of the 15 test problems. These results were normalized together with the TEC and Cmax results calculated with the applications made in 9 experimental combinations. The objective function values were calculated using the normalized TEC and Cmax values. The averages of the objective function values obtained with 35 repetitions were calculated. In all problems, the objective function values of 35 trials using the best parameters for both methods were compared with the application results made with 9 parameter combinations. As a result of the comparisons, it was seen that in all problems, better results were obtained with the parameters determined by Taguchi for both methods. This shows that Taguchi provides effective performance in parameter optimization. The methods were applied by running them 35 times on test problems using the parameters determined by Taguchi. When the obtained results were evaluated in terms of TEC and Cmax, it was seen that the WSBNSGA-2 method was superior to the NSGA-2 method in TEC values in 14 out of 15 test problems and in Cmax values in 12 of them. RPI (Relative Percentage Increase) values were used as another criterion in the comparison of the methods. It was seen that the average RPI results obtained with the TEC values of the proposed method were better in all 15 test problems and in 12 of the results obtained with the Cmax values. When the average Minf(x) values of the 35 repeated results were examined separately for all problems, it was determined that the proposed method provided more successful results by reaching smaller values in 14 out of 15 problems. For the average Minf(x) values, statistical methods were used to evaluate whether this success obtained by the proposed method was coincidental. First of all, it was statistically analyzed whether there was a significant difference between the means of Minf(x) values obtained from 35 repeated applications on multi-objective energy efficient job shop scheduling problems with WSBNSGA-2 and NSGA-2 methods. In two of the 15 test problems, the best population size values determined by Taguchi were different for the two methods. Therefore, the two methods were applied using different starting populations in the applications on these test problems. In testing these results, 2 Sample t Test, a parametric test used in independent samples, was used. In the other test problems, the methods were applied on the same starting populations. Therefore, Paired Sample t Test, a parametric test used in dependent samples, was used. When the statistical results of the applications were examined; While the WSBNSGA-2 method obtained more successful results in 12 of the 15 test problems, it was seen that there was no statistically significant difference between the results of the two methods in 3 test problems. The comparisons show that the WSBNSGA-2 method is more successful than the NSGA-2 method in most of the multi-objective energy efficient job shop scheduling test problems and is an applicable method in this problem type.