Carlos A. Coello Coello

Oliver Schuetze, Carlos A. Coello Coello, Emilia Tantar et al.

Recently, a framework for the approximation of the entire set of $ε$-efficient solutions (denote by $E_ε$) of a multi-objective optimization problem with stochastic search algorithms has been proposed. It was proven that such an algorithm produces -- under mild assumptions on the process to generate new candidate solutions --a sequence of archives which converges to $E_ε$ in the limit and in the probabilistic sense. The result, though satisfactory for most discrete MOPs, is at least from the practical viewpoint not sufficient for continuous models: in this case, the set of approximate solutions typically forms an $n$-dimensional object, where $n$ denotes the dimension of the parameter space, and thus, it may come to perfomance problems since in practise one has to cope with a finite archive. Here we focus on obtaining finite and tight approximations of $E_ε$, the latter measured by the Hausdorff distance. We propose and investigate a novel archiving strategy theoretically and empirically. For this, we analyze the convergence behavior of the algorithm, yielding bounds on the obtained approximation quality as well as on the cardinality of the resulting approximation, and present some numerical results.

Yinghao Qin, Mosab Bazargani, Edmund K. Burke et al.

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.

Yiya Diao, Changhe Li, Sanyou Zeng et al.

The Nearest-Better Network (NBN) is a powerful method to visualize sampled data for continuous optimization problems while preserving multiple landscape features. However, the calculation of NBN is very time-consuming, and the extension of the method to combinatorial optimization problems is challenging but very important for analyzing the algorithm's behavior. This paper provides a straightforward theoretical derivation showing that the NBN network essentially functions as the maximum probability transition network for algorithms. This paper also presents an efficient NBN computation method with logarithmic linear time complexity to address the time-consuming issue. By applying this efficient NBN algorithm to the OneMax problem and the Traveling Salesman Problem (TSP), we have made several remarkable discoveries for the first time: The fitness landscape of OneMax exhibits neutrality, ruggedness, and modality features. The primary challenges of TSP problems are ruggedness, modality, and deception. Two state-of-the-art TSP algorithms (i.e., EAX and LKH) have limitations when addressing challenges related to modality and deception, respectively. LKH, based on local search operators, fails when there are deceptive solutions near global optima. EAX, which is based on a single population, can efficiently maintain diversity. However, when multiple attraction basins exist, EAX retains individuals within multiple basins simultaneously, reducing inter-basin interaction efficiency and leading to algorithm's stagnation.

Gilberto Rivera, Carlos A. Coello Coello, Laura Cruz-Reyes et al.

In this paper, we enriched Ant Colony Optimization (ACO) with interval outranking to develop a novel multiobjective ACO optimizer to approach problems with many objective functions. This proposal is suitable if the preferences of the Decision Maker (DM) can be modeled through outranking relations. The introduced algorithm (named Interval Outranking-based ACO, IO-ACO) is the first ant-colony optimizer that embeds an outranking model to bear vagueness and ill-definition of DM preferences. This capacity is the most differentiating feature of IO-ACO because this issue is highly relevant in practice. IO-ACO biases the search towards the Region of Interest (RoI), the privileged zone of the Pareto frontier containing the solutions that better match the DM preferences. Two widely studied benchmarks were utilized to measure the efficiency of IO-ACO, i.e., the DTLZ and WFG test suites. Accordingly, IO-ACO was compared with two competitive many-objective optimizers: The Indicator-based Many-Objective ACO and the Multiobjective Evolutionary Algorithm Based on Decomposition. The numerical results show that IO-ACO approximates the Region of Interest (RoI) better than the leading metaheuristics based on approximating the Pareto frontier alone.

Rohan Mohapatra, Snehanshu Saha, Carlos A. Coello Coello et al.

This paper introduces AdaSwarm, a novel gradient-free optimizer which has similar or even better performance than the Adam optimizer adopted in neural networks. In order to support our proposed AdaSwarm, a novel Exponentially weighted Momentum Particle Swarm Optimizer (EMPSO), is proposed. The ability of AdaSwarm to tackle optimization problems is attributed to its capability to perform good gradient approximations. We show that, the gradient of any function, differentiable or not, can be approximated by using the parameters of EMPSO. This is a novel technique to simulate GD which lies at the boundary between numerical methods and swarm intelligence. Mathematical proofs of the gradient approximation produced are also provided. AdaSwarm competes closely with several state-of-the-art (SOTA) optimizers. We also show that AdaSwarm is able to handle a variety of loss functions during backpropagation, including the maximum absolute error (MAE).