# A hybrid Benders decomposition and bees algorithm matheuristic approach to transmission expansion planning considering energy storage

## TL;DR

This paper presents a new hybrid algorithm combining Benders decomposition and the Bees Algorithm, designed for large-scale transmission expansion and energy storage planning, offering fast, high-quality solutions with potential for optimality guarantees.

## Contribution

The paper introduces the Bee-Benders Hybrid Algorithm (BBHA), a novel hybrid matheuristic that enhances solution speed and quality for complex MILP problems, especially in energy network planning.

## Key findings

- BBHA performs at least as well as individual methods.
- BBHA significantly outperforms standalone approaches.
- Algorithm is highly effective for large-scale energy planning problems.

## Abstract

This paper introduces a novel hybrid optimisation algorithm that combines elements of both metaheuristic search and integer programming. This new matheuristic combines elements of Benders decomposition and the Bees Algorithm, to create the Bee-Benders Hybrid Algorithm (BBHA) which retains many of the advantages both of the methods. Specifically it is designed to be easily parallelizable, to produce good solutions quickly while still retaining a guarantee of optimality when run for a sufficiently long time. The algorithm is tested using a transmission network expansion and energy storage planning model, a challenging and very large scale mixed integer linear programming problem. Transmission network planning problems are already difficult on their own. When including the planning for storage systems in the network, the variation of demand over time has to be taken into account significantly increasing the size and difficulty of the optimization problem. The BBHA is shown to be highly effective hybrid matheuristic algorithm that performs at least as well as either Benders decomposition or the Bees Algorithm where these are effective on their own, and significantly improves upon the individual approaches where neither component part has a pronounced advantage. While the paper demonstrates the effectiveness in terms of the concrete electricity network planning problem, the algorithm could be readily applied to any mixed integer linear program, and is expected to work particularly well whenever this has a structure that is amenable to Benders decomposition.