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Resource constrained project scheduling is an important combinatorialoptimisation problem with many practical applications. With complexrequirements such as precedence constraints, limited resources, andfinance-based objectives, finding optimal solutions for large problem instancesis very challenging even with well-customised meta-heuristics andmatheuristics. To address this challenge, we propose a new math-heuristicalgorithm based on Merge Search and parallel computing to solve the resourceconstrained project scheduling with the aim of maximising the net presentvalue. This paper presents a novel matheuristic framework designed for resourceconstrained project scheduling, Merge search, which is a variable partitioningand merging mechanism to formulate restricted mixed integer programs with theaim of improving an existing pool of solutions. The solution pool is obtainedvia a customised parallel ant colony optimisation algorithm, which is alsocapable of generating high quality solutions on its own. The experimentalresults show that the proposed method outperforms the current state-of-the-artalgorithms on known benchmark problem instances. Further analyses alsodemonstrate that the proposed algorithm is substantially more efficientcompared to its counterparts in respect to its convergence properties whenconsidering multiple cores.

An Efficient Merge Search Matheuristic for Maximising the Net Present Value of Project Schedules