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

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.

When Hillclimbers Beat Genetic Algorithms in Multimodal Optimization

It has been shown in the past that a multistart hillclimbing strategy compares favourably to a standard genetic algorithm with respect to solving instances of the multimodal problem generator. We extend that work and verify if the utilization of diversity preservation techniques in the genetic algorithm changes the outcome of the comparison. We do so under two scenarios: (1) when the goal is to find the global optimum, (2) when the goal is to find all optima. A mathematical analysis is performed for the multistart hillclimbing algorithm and a through empirical study is conducted for solving instances of the multimodal problem generator with increasing number of optima, both with the hillclimbing strategy as well as with genetic algorithms with niching. Although niching improves the performance of the genetic algorithm, it is still inferior to the multistart hillclimbing strategy on this class of problems. An idealized niching strategy is also presented and it is argued that its performance should be close to a lower bound of what any evolutionary algorithm can do on this class of problems.

Affine Image Registration Transformation Estimation Using a Real Coded Genetic Algorithm with SBX

This paper describes the application of a real coded genetic algorithm (GA) to align two or more 2-D images by means of image registration. The proposed search strategy is a transformation parameters-based approach involving the affine transform. The real coded GA uses Simulated Binary Crossover (SBX), a parent-centric recombination operator that has shown to deliver a good performance in many optimization problems in the continuous domain. In addition, we propose a new technique for matching points between a warped and static images by using a randomized ordering when visiting the points during the matching procedure. This new technique makes the evaluation of the objective function somewhat noisy, but GAs and other population-based search algorithms have been shown to cope well with noisy fitness evaluations. The results obtained are competitive to those obtained by state-of-the-art classical methods in image registration, confirming the usefulness of the proposed noisy objective function and the suitability of SBX as a recombination operator for this type of problem.