Chaotic Multi-Objective Simulated Annealing and Threshold Accepting for Job Shop Scheduling Problem

Abstract

The Job Shop Scheduling Problem (JSSP) has enormous industrial applicability. This problem refers to a set of jobs that should be processed in a specific order using a set of machines. For the single-objective optimization JSSP problem, Simulated Annealing is among the best algorithms. However, in Multi-Objective JSSP (MOJSSP), these algorithms have barely been analyzed, and the Threshold Accepting Algorithm has not been published for this problem. It is worth mentioning that the researchers in this area have not reported studies with more than three objectives, and the number of metrics they used to measure their performance is less than two or three. In this paper, we present two MOJSSP metaheuristics based on Simulated Annealing: Chaotic Multi-Objective Simulated Annealing (CMOSA) and Chaotic Multi-Objective Threshold Accepting (CMOTA). We developed these algorithms to minimize three objective functions and compared them using the HV metric with the recently published algorithms, MOMARLA, MOPSO, CMOEA, and SPEA. The best algorithm is CMOSA (HV of 0.76), followed by MOMARLA and CMOTA (with HV of 0.68), and MOPSO (with HV of 0.54). In addition, we show a complexity comparison of these algorithms, showing that CMOSA, CMOTA, and MOMARLA have a similar complexity class, followed by MOPSO.

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

“…Several meta-heuristics have been proposed in the literature to treat the JSSP, such as GA [11,13,15,20,[29][30][31][32][33][34][35]; Simulated Annealing [36,37]; Hybrid social spider optimization [38]; Harris hawk optimizer [39]; Grey Wolf Optimization [40]; Bat Algorithm [41]; Chicken Swarm Optimization [42], Single seekers society: [43] and Particle Swarm Optimization: [44]. However, GAs remain one of the most common approaches used in resolving JSSPs.…”

SAIPO-TAIPO and Genetic Algorithms for Investment Portfolios

“…The parameters of this algorithm are the number of iterations n iter , number of steps n steps , and a threshold sequence, as shown in Algorithm 3. Both SA and TA algorithms have been applied to successfully solve different problems [45,46]. T k = T i 3:…”

“…The values ∆E max and ∆E min are used in the Boltzmann distribution for determining the initial and final temperatures. To obtain these values, a set of previous executions must be carried out [46]. The parameters used in the tuning process are shown in Table 1.…”

“…The cooling scheme establishes the method behind decreases in temperature using a factor α. For rapid decrements, an α value equal to 0.7 is commonly used, and for slow decrements, the figure is 0.99 [46]. Given a current temperature T k , the next temperature value T k+1 is calculated with Equation (5).…”

“…That is, during the processing of 90% of temperatures, Tol has the same value of T k ; in this case, δ is equal to 1. For the remaining temperatures, δ takes the value of 0.96, obtained by experimentation, making the process more restrictive in the last iterations [46].…”