Bilevel Late Acceptance Hill Climbing for the Electric Capacitated Vehicle Routing Problem

TL;DR

This paper introduces a bilevel optimization framework and a novel Late Acceptance Hill Climbing algorithm for the Electric Capacitated Vehicle Routing Problem, achieving state-of-the-art results efficiently.

Contribution

It proposes a lightweight bilevel LAHC algorithm with a surrogate objective, effectively solving large-scale E-CVRP instances with improved solutions.

Findings

Achieves near-optimal solutions on small instances.

Sets 9 out of 10 new best-known results on large instances.

Demonstrates the surrogate objective's strong correlation with total cost.

Abstract

This paper tackles the Electric Capacitated Vehicle Routing Problem (E-CVRP) through a bilevel optimization framework that handles routing and charging decisions separately or jointly depending on the search stage. By analyzing their interaction, we introduce a surrogate objective at the upper level to guide the search and accelerate convergence. A bilevel Late Acceptance Hill Climbing algorithm (b-LAHC) is introduced that operates through three phases: greedy descent, neighborhood exploration, and final solution refinement. b-LAHC operates with fixed parameters, eliminating the need for complex adaptation while remaining lightweight and effective. Extensive experiments on the IEEE WCCI-2020 benchmark show that b-LAHC achieves superior or competitive performance against eight state-of-the-art algorithms. Under a fixed evaluation budget, it attains near-optimal solutions on small-scale instances and sets 9/10 new best-known results on large-scale benchmarks, improving existing records by an average of 1.07%. Moreover, the strong correlation (though not universal) observed between the surrogate objective and the complete cost justifies the use of the surrogate objective while still necessitating a joint solution of both levels, thereby validating the effectiveness of the proposed bilevel framework and highlighting its potential for efficiently solving large-scale routing problems with a hierarchical structure.