An efficient merge search matheuristic for maximising net present value in project scheduling

Resource constrained project scheduling (RCPS) is an important combinatorial optimisation problem with many practical applications. With complex requirements such as precedence constraints, limited resources, and finance-based objectives, finding optimal solutions for large problem instances is very challenging. To address this challenge, we propose a new matheuristic algorithm based on merge search and parallel computing to solve RCPS with the aim of maximising the net present value. This paper presents merge search, a novel matheuristic designed for RCPS, which is a variable partitioning and merging mechanism to formulate restricted integer programs. Parallel ant colony optimisation can generate excellent solutions for RCPS, and we use this method to generate the solution pool. The experimental results show that the proposed method outperforms the current state-of-the-art algorithms on known benchmark problem instances. Further analyses also demonstrate that the proposed algorithm is substantially more efficient compared to its counterparts in respect to its convergence properties.