Fig 1.
Research methodology and overall organization of the proposed study.
Table 1.
A 4x3 sample problem.
Table 2.
Estimated process, idle and on/off energies of the sample problem.
Fig 2.
BWSA-RL framework illustrating the algorithmic control flow and integration of the reinforcement learning module.
Fig 3.
Encoding and decoding of OSV and MAV. a) an encoded solution, b) step by step decoding using G&T algorithm.
Fig 4.
Procreation mechanism for parent selection based on a tournament selection strategy.
Fig 5.
Procreation process for generating offspring spiders from parents P1 and P2:(a) OSV generation steps, and (b) MAV generation steps.
Fig 6.
Mutation operator consisting of (a) operation swapping and (b) random reassignment of machines.
Fig 7.
Cannibalization process illustrating the elimination of weaker solution spiders from the population.
Fig 8.
State-agent interaction diagram illustrating the reinforcement learning mechanism.
Table 3.
State definition table.
Fig 9.
Proposed rescheduling framework for handling the insertion of new jobs in a dynamic scheduling environment.
Table 4.
Priority based decision matrix for rescheduling after arrival of new job.
Table 5.
Taguchi design of experiment parameters with four selected levels.
Table 6.
IGD results for P10 and P17 for Taguchi design of experiment.
Fig 10.
Taguchi design of experiment showing main effect plots for problems P10 and P17.
Table 7.
CPLEX versus BWSA-RL: Test results for problems S01 to S10.
Fig 11.
C-metric comparison of the proposed conversion operator (BWSA-RL) with BWSA-Fixed and BWSA-SLGA operators.
Fig 12.
Comparison of GD and IGD metrics for the proposed conversion operator (BWSA-RL) against BWSA-Fixed and BWSA-SLGA operators.
Table 8.
Levene and Shapiro-Wilk test results for IGD data of comparison with other conversion condition operators.
Table 9.
Friedman test results for IGD values of comparison with other conversion condition operators.
Fig 13.
C-metric comparison between (a) HCD and MCDO and (b) HCD and HDED, highlighting the superior performance of HCD.
Fig 14.
GD and IGD comparison of HCD with MCDO and HDED using (a) box plots of GD and (b) box plots of IGD metrics.
Table 10.
Levene and Shapiro-Wilk test results for IGD data of crowding distance comparison.
Table 11.
Friedman test results for IGD data of crowding distance comparison.
Table 12.
Setting of weights to evaluate effectiveness ADP objective on due-date compliance.
Fig 15.
Comparison of average due-date non-conformance across different weight configurations.
Fig 16.
Effect of different weight settings on optimization objectives:(a) makespan, (b) total energy consumption, and (c) average due-date penalty.
Table 13.
Comparison of BWSA-RL with other algorithms for performance metrics.
Fig 17.
C-metric comparison of BWSA-RL with four competing algorithms:(a) EARL, (b) QHH-BS, (c) RMOEAD, and (d) ENSGA.
Fig 18.
Comparison of GD and IGD metrics between BWSA-RL and competing algorithms using (a) GD box plots and (b) IGD box plots.
Table 14.
Levene and Shapiro-Wilk test results for IGD data of comparison with other algorithms.
Table 15.
Friedman test results for IGD values of comparison with other algorithms.
Fig 19.
Convergence behavior of BWSA-RL for benchmark problem P15 in terms of (a) makespan, (b) total energy consumption, and (c) average due-date penalty.
Fig 20.
Comparative performance of complete rescheduling (RS1) and the proposed heuristic (RS2) for (a) makespan, (b) total energy consumption, (c) average due-date penalty, and (d) instability, demonstrating the superior stability of RS2 with minimal impact on other objectives.
Table 16.
P-value comparison of variance for the results of RS1 and RS2 for all optimization objectives.