A Harmony Search Algorithm for Multi-Skilled Rcpsp with Time-Dependent Resource Capacities

In this paper, we address the multi-skilled RCPSP with time-dependent resource capacities and generalized precedence relations between activities. In this problem, a set of multi-skilled workforces are required to execute project activities. Each worker is able to perform several skills. The availability of workforces is time-dependent due to holidays, weekends, sicknesses, etc. Therefore, in this study, a mathematical formulation is proposed for the multi-skilled RCPSP with time-dependent resource availabilities. The objective function of the model is minimization of project completion time. The proposed model in this study is an NP-Hard problem in the strong sense. Hence, we develop a new meta-heuristic algorithm based on harmony search algorithm to solve the proposed model. New crossover and mutation operators have been designed for the proposed method to produce diverse solutions and to prevent the proposed algorithm from converging to a local optima. Hence, the proposed method not only uses the common procedure in harmony search algorithm, but also it employs the proposed crossover and mutation operators to explore solution space more accurately. The generated solutions are all combined and the harmony memory is updated. The effectiveness of this method has been compared to particle swarm optimization (PSO) and genetic algorithm (GA) in solving 30 test problems. The results show that the proposed method has been superior in terms of multiple performance measures.