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

TL;DR

This paper introduces a novel parallel merge search matheuristic that significantly improves solution quality and efficiency for resource constrained project scheduling aimed at maximizing net present value.

Contribution

It presents a new merge search framework combined with parallel ant colony optimization to enhance solution quality and computational efficiency in complex project scheduling problems.

Findings

Outperforms state-of-the-art algorithms on benchmark instances.

Demonstrates superior convergence properties with parallel computing.

Achieves higher net present value solutions more efficiently.

Abstract

Resource constrained project scheduling 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 even with well-customised meta-heuristics and matheuristics. To address this challenge, we propose a new math-heuristic algorithm based on Merge Search and parallel computing to solve the resource constrained project scheduling with the aim of maximising the net present value. This paper presents a novel matheuristic framework designed for resource constrained project scheduling, Merge search, which is a variable partitioning and merging mechanism to formulate restricted mixed integer programs with the aim of improving an existing pool of solutions. The solution pool is obtained via a customised parallel ant colony optimisation algorithm, which is also capable of generating high quality solutions on its own. 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 when considering multiple cores.