A Monte Carlo simulation based chaotic differential evolution algorithm for scheduling a stochastic parallel processor system

• A simulation-based evolutionary optimization is proposed for a parallel processor system.
• A lower level Monte Carlo and an upper level differential evolution are suggested.
• Simulation is used to assess quality of candidate solutions and optimizer is utilized to guide the search at upper level.
• Chaos theory is employed to enhance quality of results via preventing premature convergence and locality.

One of the main limitation of the application of evolutionary algorithms (EA) is the tendency to converge prematurely to a local optimum. The EAs suffer with the disadvantage of premature convergence and hence the study on convergence of EAs is always one of the most important research fields. Due to outstanding capability of chaos to avoid being trapped in local optimum, it can be considered as an efficient search tool. Therefore, in current paper, in order to taking properties of chaos, eight chaotic maps are employed within a differential evolution (DE) algorithm for solving a stochastic job scheduling problem. To speedup searching and avoid local optimum traps, the random sequences produced from chaotic maps are utilized instead of random variables in DE. Furthermore, to address the uncertainties arising in scheduling environments, Monte Carlo simulation is used. However, simulation is not an optimization approach. Therefore, we design the simulation-based optimization approach where a simulator is combined with chaotic DE. The simulation experiments are used to evaluate the quality of candidate solutions and the chaotic DE is utilized to find best-compromised solutions and then guide the search direction. The performance of simulation-based chaotic DE algorithm is investigated in a computational study, and the results show the outperformance of suggested method with respect to the traditional methods.