Carolina P. de Almeida

Upper Confidence Bound (UCB) Algorithms for Adaptive Operator Selection in MOEA/D

Adaptive Operator Selection (AOS) is a method used to dynamically determine which operator should be applied in an optimization algorithm based on its performance history. Recently, Upper Confidence Bound (UCB) algorithms have been successfully applied for this task. UCB algorithms have special features to tackle the Exploration versus Exploitation (EvE) dilemma presented on the AOS problem. However, it is important to note that the use of UCB algorithms for AOS is still incipient on Multiobjective Evolutionary Algorithms (MOEAs) and many contributions can be made. The aim of this paper is to extend the study of UCB based AOS methods. Two methods are proposed: MOEA/D-UCB-Tuned and MOEA/D-UCB-V, both use the variance of the operators’ rewards in order to obtain a better EvE tradeoff. In these proposals the UCB-Tuned and UCB-V algorithms from the multiarmed bandit (MAB) literature are combined with MOEA/D (MOEA based on decomposition), one of the most successful MOEAs. Experimental results demonstrate that MOEA/D-UCB-Tuned can be favorably compared with state-of-the-art adaptive operator selection MOEA/D variants based on probability (ENS-MOEA/D and ADEMO/D) and multi-armed bandits (MOEA/D-FRRMAB) methods.

MOEA/D-HH: A Hyper-Heuristic for Multi-objective Problems

Hyper-Heuristics is a high-level methodology for selection or automatic generation of heuristics for solving complex problems. Despite the hyper-heuristics success, there is still only a few multi-objective hyper-heuristics. Our approach, MOEA/D-HH, is a multi-objective selection hyper-heuristic that expands the MOEA/D framework. It uses an innovative adaptive choice function proposed in this work to determine the low level heuristic (Differential Evolution mutation strategy) that should be applied to each individual during a MOEA/D execution. We tested MOEA/D-HH in a well established set of 10 instances from the CEC 2009 MOEA Competition. MOEA/D-HH is compared with some important multi-objective optimization algorithms and the resultsobtained are promising.

Harmony Search for Multi-objective Optimization

This paper investigates the efficiency of Harmony Search based algorithms for solving multi-objetive problems. For this task, four variants of the Harmony Search algorithm were adapted in the Non-dominated Sorting Genetic Algorithm II (NSGA-II) framework. Harmony Search is a recent proposed music-inspired metaheuristic while NSGA-II is a very successful evolutionary multi-objective algorithm. The four proposed methods are tested against each other using a set of benchmark instances proposed in CEC 2009. The best proposed algorithm is also compared with NSGA-II. The preliminary results are very promising and stand the proposed approach as a candidate to the State-of-the-art for multi-objective optimization, encouraging further researches in the hybridization of the Harmony Search and Multi-objective Evolutionary Algorithms.

An experimental analysis of evolutionary heuristics for the biobjective traveling purchaser problem

Given a set of markets and a set of products to be purchased on those markets, the Biobjective Traveling Purchaser Problem (2TPP) consists in determining a route through a subset of markets to collect all products, minimizing the travel distance and the purchasing cost simultaneously. As its single objective version, the 2TPP is an NP-hard Combinatorial Optimization problem. Only one exact algorithm exists that can solve instances up to 100 markets and 200 products and one heuristic approach that can solve instances up to 500 markets and 200 products. Since the Transgenetic Algorithms (TAs) approach has shown to be very effective for the single objective version of the investigated problem, this paper examines the application of these algorithms to the 2TPP. TAs are evolutionary algorithms based on the endosymbiotic evolution and other interactions of the intracellular flow interactions. This paper has three main purposes: the first is the investigation of the viability of Multiobjective TAs to deal with the 2TPP, the second is to determine which characteristics are important for the hybridization between TAs and multiobjective evolutionary frameworks and the last is to compare the ability of multiobjective algorithms based only on Pareto dominance with those based on both decomposition and Pareto dominance to deal with the 2TPP. Two novel Transgenetic Multiobjective Algorithms are proposed. One is derived from the NSGA-II framework, named NSTA, and the other is derived from the MOEA/D framework, named MOTA/D. To analyze the performance of the proposed algorithms, they are compared with their classical counterparts. It is also the first time that NSGA-II and MOEA/D are applied to solve the 2TPP. The methods are validated in 365 uncapacitated instances of the TPPLib benchmark. The results demonstrate the superiority of MOTA/D and encourage further researches in the hybridization of Transgenetic Algorithms and Multiobjective Evolutionary Algorithms specially the ones based on decomposition.

Extreme Learning Surrogate Models in Multi-objective Optimization based on Decomposition

This paper proposes ELMOEA/D, a surrogate-assisted MOEA, for solving costly multi-objective problems in small evaluation budgets. The proposed approach encompasses a state-of-the-art MOEA based on decomposition and Differential Evolution (MOEA/D-DE) assisted by Extreme Learning Machines (ELMs). ELMOEA/D is tested in instances from three well-known benchmarks (ZDT, DTLZ and WFG) with 5-60 decision variables, 2 and 5 objectives. The ELMOEA/Ds performance is also analyzed on a real problem (Airfoil Shape Optimization). The impact of some ELMs parameters and an automatic model selection mechanism is investigated. The results obtained by ELMOEA/D are compared with those of two state-of-the-art surrogate approaches (MOEA/D-RBF and ParEGO) and a non-surrogate-based MOEA (MOEA/D). The ELMOEA/D variants are among the best results for most benchmark instances and for the real problem. HighlightsThe problem of solving expensive MOPs with small evaluation budgets is treated.The paper investigates the use of ELM as a surrogate model in MOEAs.A procedure is used to automatically select ELM parameters.The scalability of surrogates concerning the total of decision variables and number of objectives is evaluated.Experimental results show the good performance of ELMOEA/D in different problems.

ELMOEA/D-DE: Extreme Learning Surrogate Models in Multi-objective Optimization Based on Decomposition and Differential Evolution

Despite the success of Evolutionary Algorithms in solving complex problems, they may require many function evaluations. This becomes an issue when dealing with costly problems. Surrogate models may overcome this difficulty, though their use in problems with medium to large dimensionality is underexplored in the literature. Problems with multiple conflicting objectives can be formulated as Multi-objective Optimization Problems (MOPs). MOPs have received a great attention lately, mainly with Multi-objective Evolutionary Algorithms (MOEAs). This paper proposes ELMOEA/D-DE, a surrogate-assisted MOEA, for solving expensive MOPs in small evaluation budgets. ELMOEA/D-DE encompasses a state-of-the-art MOEA based on decomposition, Differential Evolution (DE) operators and Extreme Learning Machines. This paper tests three variants of ELMOEA/D-DE, using different DE operators, for solving five known benchmark MOPs with 10 to 60 decision variables. All variants achieve good results in terms of hyper volume metric and the best variant with operator DE/rand/1/bin is compared with two state-of-the-art approaches (MOEA/D-RBF and a non-surrogate-based MOEA), achieving the best results in all but one problems instances.

TA-PFP: A Transgenetic Algorithm to Solve the Protein Folding Problem

This work reports the application of a transgenetic algorithm to the protein folding problem in the 3D HP model, which is a particular instance of the string folding problem and is known to be NP-hard. The proposed algorithm uses two kinds of plasmids, two kinds of transposons, two information sources, adaptation of parameters and is hybridized with tabu search. The computational experiments consider seven instances of the Tortilla benchmark. The results are favorably comparable with that reported in the literature, attesting the efficiency of the methodology.

MOEA/D with adaptive operator selection for the environmental/economic dispatch problem

Adaptive Operator Selection (AOS) is a method used to dynamically determine which operator should be applied in an optimization algorithm based on its performance history. Upper Confidence Bound (UCB) algorithms have been successfully applied for this task due to its ability to tackle the Exploration versus Exploitation (EvE) dilemma presented on AOS. However, it is important to note that the use of UCB algorithms for AOS is still incipient on Multiobjective Evolutionary Algorithms (MOEAs) and many contributions can be made. The aim of this paper is to extend the study of UCB based AOS methods, applying it to a real world problem: the Environmental/Economic Load Dispatch (EELD). Three methods are proposed: MOEA/D-UCB1, MOEA/D-UCB-T and MOEA/D-UCB-V. In these proposals the UCB-based algorithms from the Multi-Armed Bandit (MAB) literature are combined with MOEA/D (MOEA based on decomposition), one of the most successful MOEAs. A pool of operators composed of four Differential Evolution operators is used. The proposed approaches are evaluated in three known instances of the multi-objective environmental/economic dispatch problem, formulated as a nonlinear constrained optimization problem with competing objectives. Experimental results demonstrate that MOEA/D-UCB1 and MOEA/D-UCB-T can be favorably compared with state-of-the-art algorithms reported in the literature for all considered instances.

Decomposition Based Multiobjective Hyper Heuristic with Differential Evolution

Hyper-Heuristics is a high-level methodology for selection or generation of heuristics for solving complex problems. Despite their success, there is a lack of multi-objective hyper-heuristics. Our approach, named MOEA/D-HH\(_{SW}\), is a multi-objective selection hyper-heuristic that expands the MOEA/D framework. MOEA/D decomposes a multiobjective optimization problem into a number of subproblems, where each subproblem is handled by an agent in a collaborative manner. MOEA/D-HH\(_{SW}\) uses an adaptive choice function with sliding window proposed in this work to determine the low level heuristic (Differential Evolution mutation strategy) that should be applied by each agent during a MOEA/D execution. MOEA/D-HH\(_{SW}\) was tested in a well established set of 10 instances from the CEC 2009 MOEA Competition. MOEA/D-HH\(_{SW}\) was favourably compared with state-of-the-art multi-objective optimization algorithms.

Improved Cultural Immune Systems to solve the economic load dispatch problems

This work considers Artificial Immune Systems to solve the economic load dispatch problem. The Immune Systems are based on the clonal selection principle. Cultural Algorithms using normative, situational, historical and topographical knowledge sources are used to improve the global optimization property of immune systems. A new main influence function is proposed which improves the results obtained by the cultural version. All the proposed approaches have several points of self-adaptation and use a local search operator that is based on a quasi-simplex technique. The Immune System and its cultural versions are validated in test problems that consider 13 and 40 thermal generators and take into account valve-point loading effects. They are also validated in a test problem with 20 thermal generators, valve-point loading effects and transmission losses. The proposed cultural method including the new influence function outperforms other modern metaheuristics reported in recent literature, finding the minimum fuel cost value for all test systems.