A modified single-objective genetic algorithm for solving the rural postman problem with load-dependent costs

This study addresses the rural postman problem with load-dependent costs, a variant of the arc routing problem where the traversal cost of an edge depends on its length and the vehicle’s load. The objective is to find a minimum-cost tour that services all required edges, a problem of particular importance when the demand weight is significant compared to the vehicle’s curb weight. We present an integer linear programming model for the problem and propose a heuristic algorithm based on bio-inspired methodologies to efficiently obtain near-optimal solutions within short computing times. The effectiveness of the approach is demonstrated through computational experiments on benchmark instances, and the results highlight the practicality of the proposed methods.