a multi-objective resource-constrained optimization of time-cost trade-off problems in scheduling project

this paper presents a multi-objective resource-constrained project scheduling problem with positive and negative cash flows. the net present value (npv) maximization and making span minimization are this study objectives. and since this problem is considered as complex optimization in np-hard context, we present a mathematical model for the given problem and solve three evolutionary algorithms; nsga-ii, mosa and mopso are applied to find the set of pareto solutions for this multi-objective scheduling problem. in order to show performance of the algorithms, different metrics are applied and comparisons between the two algorithms are also considered. the computational results for a set of test problems taken from the project scheduling problem bandar abbas gas condensate refinery project and library are presented and discussed. finally, the computational results illustrate the superior performance of the nsga-ii, mosa and mopso algorithm with regard to the proposed metrics. in order to solve proposed method from nsga-ii algorithm, the results are compared with gams software in some problems. the proposed method is a converge to the optimum and efficient solution algorithm.