Nasrin Mehranfar - Department of Industrial Engineering, Shomal University, Amol, Iran
M. Hajiaghaei-Keshteli - Department of Industrial Engineering, University of Science and Technology of Mazandaran, Behshahr, Iran
Amir Mohammad Fathollahi-Fard - Department of Industrial Engineering and Management Systems, Amirkabir University of Technology, Tehran, Iran

Nowadays, there is a great deal of attention for regulations of carbon emissions to enforce the decision-makers of production and distribution networks to redesign their systems satisfactorily. The literature has seen a rapid interest in developing novel metaheuristics to solve this problem as a complicated optimization problem. Such difficulties motivate us to address a production-distribution network design problem considering carbon emissions policies among the first studies in this area by a novel hybrid whale optimization algorithm. Accordingly, a mixed integer non-linear programming model has been developed. To tackle the proposed problem, a new hybrid metaheuristic based on whale optimization algorithm and simulated annealing as a successful optimizer is employed to solve the proposed problem. The calibration of the algorithms has been designed by Taguchi method, comprehensively. Finally, an extensive analysis has been evaluated through a comparative study along with some assessment metrics of Pareto solutions.

Production-Distribution Networks, optimization, carbon emissions, Nature-inspired algorithm, Whale Optimization Algorithm, Simulated Annealing