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.

Carlos Coello Coello, Marko Djurasevic, Domagoj Jakobovic et al.

Evolutionary algorithms have been successfully applied to attacking Physically Unclonable Functions (PUFs). CMA-ES is recognized as the most powerful option for a type of attack called the reliability attack. While there is no reason to doubt the performance of CMA-ES, the lack of comparison with different metaheuristics and results for the challenge-response pair-based attack leaves open questions if there are better-suited metaheuristics for the problem. In this paper, we take a step back and systematically evaluate several metaheuristics for the challenge-response pair-based attack on strong PUFs. Our results confirm that CMA-ES has the best performance, but we also note several other algorithms with similar performance while having smaller computational costs. More precisely, if we provide a sufficient number of challenge-response pairs to train the algorithm, various configurations show good results. Consequently, we conclude that EAs represent a strong option for challenge-response pair-based attacks on PUFs.

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.

Lucija Planinic, Marko Djurasevic, Luca Mariot et al.

This paper investigates the influence of genotype size on evolutionary algorithms' performance. We consider genotype compression (where genotype is smaller than phenotype) and expansion (genotype is larger than phenotype) and define different strategies to reconstruct the original variables of the phenotype from both the compressed and expanded genotypes. We test our approach with several evolutionary algorithms over three sets of optimization problems: COCO benchmark functions, modeling of Physical Unclonable Functions, and neural network weight optimization. Our results show that genotype expansion works significantly better than compression, and in many scenarios, outperforms the original genotype encoding. This could be attributed to the change in the genotype-phenotype mapping introduced with the expansion methods: this modification beneficially transforms the domain landscape and alleviates the search space traversal.

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).