BPGA-EDA for the multi-mode resource constrained project scheduling problem

Estimation of distribution algorithms for the Multi-Mode Resource Constrained Project scheduling problem

“…We denote the start and finish times of activity i by st i and f t i respectively. The precedence constraint is presented in (1) while the renewable and non-renewable resource constraints are respectively presented in (2) and (3). In (2) and (3), k i is the allocated mode of i and can only be one of the predefined modes of i.…”

“…It is also more efficient than other schedule improvement procedures as it focuses on improving the finish time of one activity rather than the entire schedule. This method has also been used in [12] and [3] and has led to significant improvements in the quality of solutions produced. The mode improvement method is embedded in the SGS and referred to as the extended SGS.…”

“…The MRCPSP has previously been solved with hybrid approaches. In [3], different algorithms were used for each sub-problem of the MRCPSP. The Genetic Algorithm (GA) was applied to the activity scheduling sub-problem while EDA was applied to the mode assignment sub-problem.…”

“…Existing approaches of solving the MRCPSP include EDAs [4], [5], Differential Evolution (DE) [6], GAs [7], [8], [9], [10], Particle Swarm Optimisation (PSO) [11] and Scatter Search (SS) [12]. Although there is considerably more research on GAs applied to MRCPSP than EDAs, the use of EDA for the Mode Assignment problem has been reported to improve on the GA [3]. Previous attempts to apply EDA to both sub-problems have resulted in algorithms with relatively poor performance [13].…”

“…In this paper, we apply RK-EDA [14], an EDA designed for permutation problems to the activity scheduling sub problem. This is combined with a previously published EDA approach to mode assignment [3] yielding a pure EDA approach that performs competitively across the board and is particularly strong on larger problems.…”