A Memetic Algorithm for the Linear Ordering Problem with Cumulative Costs

TL;DR

This paper presents a memetic algorithm tailored for the linear ordering problem with cumulative costs, combining innovative operators and local search to improve solution quality, achieving new best bounds on benchmark instances.

Contribution

The paper introduces a novel memetic algorithm with specific operators and local search, significantly advancing solution quality for the linear ordering problem with cumulative costs.

Findings

Achieved 46 new upper bounds on benchmark instances.

The algorithm outperforms existing methods on several instances.

Critical algorithm components are analyzed for their impact on performance.

Abstract

This paper introduces an effective memetic algorithm for the linear ordering problem with cumulative costs. The proposed algorithm combines an order-based recombination operator with an improved forward-backward local search procedure and employs a solution quality based replacement criterion for pool updating. Extensive experiments on 118 well-known benchmark instances show that the proposed algorithm achieves competitive results by identifying 46 new upper bounds. Furthermore, some critical ingredients of our algorithm are analyzed to understand the source of its performance.