Catálogo de publicaciones - libros

Evolutionary algorithms have been adequately applied in solving single and multi-objective optimization problems. In the single-objective case various studies have shown the usefulness of combining gradient based classical methods with evolutionary algorithms. However there seems to be limited number of such studies for the multi-objective case. In this paper, we take two classical methods for unconstrained multi-optimization problems and discuss their use as a local search operator in a state-of-the-art multi-objective evolutionary algorithm. These operators require gradient information which is obtained using finite difference method and using a stochastic perturbation technique requiring only two function evaluations. Computational studies on a number of test problems of varying complexity demonstrate the efficiency of resulting hybrid algorithms in solving a large class of complex multi-objective optimization problems. We also discuss a new convergence metric which is useful as a stopping criteria for problems having an unknown Pareto-optimal front.

Archives are used in Multi-Objective Evolutionary Algorithms to establish elitism. Depending on the optimization problem, an unconstrained archive may grow to an immense size. With the growing number of nondominated solutions in the archive, testing a new solution for nondominance against this archive becomes the main bottleneck during optimization. As a remedy to this problem, we will propose a new data structure on the basis of Binary Decision Diagrams (BDDs) that permits a nondominance test with a runtime that is independent from the archive size. For this purpose, the region in the objective space weakly dominated by the solutions in the archive is represented by a BDD. We will present the algorithms for constructing the BDD as well as the nondominance test. Moreover, experimental results from using this symbolic data structure will show the efficiency of our approach in test cases where many candidates have to be tested but only few have to be added to the archive.

In this paper we study a number of issues related to the design of a cellular genetic algorithm (cGA) for multiobjective optimization. We take as an starting point an algorithm following the canonical cGA model, i.e., each individual interacts with those ones belonging to its neighborhood, so that a new individual is obtained using the typical selection, crossover, and mutation operators within this neighborhood. An external archive is used to store the non-dominated solutions found during the evolution process. With this basic model in mind, there are many different design issues that can be faced. Among them, we focus here on the synchronous/asynchronous feature of the cGA, the feedback of the search experience contained in the archive into the algorithm, and two different replacement strategies. We evaluate the resulting algorithms using a benchmark of problems and compare the best of them against two state-of-the-art genetic algorithms for multiobjective optimization. The obtained results indicate that the cGA model is a promising approach to solve this kind of problem.

We present a new multiobjective evolutionary algorithm (MOEA), called fast Pareto genetic algorithm (FastPGA). FastPGA uses a new fitness assignment and ranking strategy for the simultaneous optimization of multiple objectives where each solution evaluation is computationally- and/or financially-expensive. This is often the case when there are time or resource constraints involved in finding a solution. A population regulation operator is introduced to dynamically adapt the population size as needed up to a user-specified maximum population size. Computational results for a number of well-known test problems indicate that FastPGA is a promising approach. FastPGA outperforms the improved nondominated sorting genetic algorithm (NSGA-II) within a relatively small number of solution evaluations.

Among the multi-objective optimization methods proposed so far, Genetic Algorithms (GA) have been shown to be more effective in recent decades. Most of such methods were developed to solve primarily unconstrained problems. However, many real-world problems are constrained, which necessitates appropriate handling of constraints. Despite much effort devoted to the studies of constraint-handling methods, it has been reported that each of them has certain limitations. Hence, further studies for designing more effective constraint-handling methods are needed.

For this reason, we investigated the guidelines for a method to effectively handle constraints. Based on these guidelines, we designed a new constraint-handling method, Pareto Descent Repair operator (PDR), in which ideas derived from multi-objective local search and gradient projection method are incorporated. An experiment comparing GA that use PDR and some of the existing constraint-handling methods confirmed the effectiveness of PDR.

The multi-objective covariance matrix adaptation evolution strategy (MO-CMA-ES) combines a mutation operator that adapts its search distribution to the underlying optimization problem with multi-criteria selection. Here, a generational and two steady-state selection schemes for the MO-CMA-ES are compared. Further, a recently proposed method for computationally efficient adaptation of the search distribution is evaluated in the context of the MO-CMA-ES.

Recent advances in quantum cascade lasers (QCLs) have enabled their use as (tunable) emission sources for chemical and biological spectroscopy, as well as allowed their demonstration in applications in medical diagnostics and potential homeland security systems. Finding the optimal design solution can be challenging, especially for lasers that operate in the terahertz region. The production process is prohibitive, so an optimization algorithm is needed to find high quality QCL designs. Past research attempts using multiobjective evolutionary algorithms (MOEAs) have found good solutions, but lacked a local search element that could enable them to find more effective solutions. This research looks at two memetic MOEAs that use a neighborhood search. Our baseline memetic MOEA used a simple neighborhood search, which is similar to other MOEA neighborhood searches found in the literature. Alternatively, our innovative multi-tiered memetic MOEA uses problem domain knowledge to change the temporal focus of the neighborhood search based on the generation. It is empirically shown that the multi-tiered memetic MOEA is able to find solutions that dominate the baseline memetic algorithm. Additional experiments suggest that using local search on only non-dominated individuals improves the effectiveness and efficiency of the algorithm versus applying the local search to dominated individuals as well. This research validates the importance of using multiobjective problem (MOP) domain knowledge in order to obtain the best results for a real world solution. It also introduces a new multi-tiered local search procedure that is able to focus the local search on specific critical elements of the problem at different stages in the optimization process.

In this paper, we propose a memetic EMO algorithm that enhances the similarity of two sets of non-dominated solutions. We employ our algorithm in vehicle routing problems (VRPs) where the demand of customers varies. We consider two periods of different demand in a problem that are Normal Demand Period (NDP) and High Demand Period (HDP). In each period, we can find a set of non-dominated solutions with respect to several objectives such as minimizing total cost for delivery, minimizing maximum cost, minimizing the number of vehicles, minimizing total delay to the date of delivery and so on. Although a set of non-dominated solutions can be searched independently in each period, drivers of vehicles prefer to have similar routes in NDP and HDP in order to reduce their fatigue to drive on a different route. In this paper, we propose a local search that enhance the similarity of routes in NDP and HDP. Simulation results show that the proposed memetic EMO algorithm can find a similar set of non-dominated solutions in HDP to the one in NDP.

When multi-objective genetic algorithms are applied to real-world problems for deriving Pareto-optimal solutions, the high calculation cost becomes a problem. One solution to this problem is to use a small population size. However, this often results in loss of diversity of the solutions, and therefore solutions with sufficient precision cannot be derived. To overcome this difficulty, the solutions should be replaced when they have converged on a certain point. To perform this replacement, inverse analysis is required to derive the design variables from objects as the solutions are located in the objective space. For this purpose, an Artificial Neural Network (ANN) is applied. Using ANN, the solutions concentrating on certain points are replaced and the diversity of the solutions is maintained. In this paper, a new mechanism using ANN to maintain the diversity of the solutions is proposed. The proposed mechanism was introduced into NSGA-II and applied to test functions. In some functions, the proposed mechanism was useful compared to the conventional method. In other numerical experiments, the results of the proposed algorithm with large populations are discussed and the effectiveness of the proposed mechanism is also described.

The Pareto-based Differential Evolution (PDE) algorithm is one of the current state-of-the-art Multi-objective Evolutionary Algorithms (MOEAs). This paper describes a series of experiments using PDE for evolving artificial neural networks (ANNs) that act as game-playing agents. Three systems are compared: (i) a canonical PDE system, (ii) a co-evolving PDE system (PCDE) with 3 different setups, and (iii) a co-evolving PDE system that uses an archive (PCDE-A) with 3 different setups. The aim of this study is to provide insights on the effects of including co-evolutionary techniques on a well-known MOEA by investigating and comparing these 3 different approaches in evolving intelligent agents as both first and second players in a deterministic zero-sum board game. The results indicate that the canonical PDE system outperformed both co-evolutionary PDE systems as it was able to evolve ANN agents with higher quality game-playing performance as both first and second game players. Hence, this study shows that a canonical MOEA without co-evolution is desirable for the synthesis of cognitive game AI agents.