Solving a Multi-Objective Mathematical Model for a Multi-Skilled Project Scheduling Problem by Particle Swarm Optimization and Differential Evolution Algorithms

Abstract

A Multi-Skilled Project Scheduling Problem (MSPSP) that is an extension of a Multi-Mode Resource-Constrained Project Scheduling Problem (MM-RCPSP) has been generally addressed to schedule a project with staff members as resources. In MSPSP, each activity requires different specialties and each staff member has a known skill level in performing an activity. This causes to encounter a huge number of modes while performing activities of a project. This research focuses on a special type of MSPSP known as Multi-Objective Multi-Skilled Project Scheduling Problem (MOMSPSP) which incorporates some new objectives in the MSPSP and develops a multi-objective mixed-integer nonlinear programming (MINLP) model. The model is exactly solved for small-sized instances using CPLEX solver. To solve such a NP-hard problem for medium and large-sized instances, two efficient meta-heuristic algorithms based on Differential Evolution (DE) and Particle Swarm Optimization (PSO) are proposed. To evaluate the efficiency of the proposed algorithms, the results are compared with each other as well as to the optimal ones obtained by the CPLEX solver for small instances. Finally, the designed DE algorithm is identified as the superior proposed algorithm for solving the propounded MOMSPSP in terms of some performance metrics.