20 IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION, VOL. 17, NO. 1, FEBRUARY 2013 A Hybrid Multiobjective Evolutionary Algorithm for Multiobjective Optimization Problems Lixin Tang, Member, IEEE, and Xianpeng Wang Abstract—Recently, the hybridization between evolutionary algorithms and other metaheuristics has shown very good perfor- mances in many kinds of multiobjective optimization problems (MOPs), and thus has attracted considerable attentions from both academic and industrial communities. In this paper, we propose a novel hybrid multiobjective evolutionary algorithm (HMOEA) for real-valued MOPs by incorporating the concepts of personal best and global best in particle swarm optimization and multiple crossover operators to update the population. One major feature of the HMOEA is that each solution in the population maintains a nondominated archive of personal best and the update of each solution is in fact the exploration of the region between a selected personal best and a selected global best from the external archive. Before the exploration, a selfadaptive selection mechanism is developed to determine an appropriate crossover operator from several candidates so as to improve the robustness of the HMOEA for different instances of MOPs. Besides the selection of global best from the external archive, the quality of the external archive is also considered in the HMOEA through a propagating mecha- nism. Computational study on the biobjective and three-objective benchmark problems shows that the HMOEA is competitive or superior to previous multiobjective algorithms in the literature. Index Terms—Evolutionary algorithm, multiobjective opti- mization, multiple crossover operators with selfadaptive selection strategy. I. INTRODUCTION I N MANY OPTIMIZATION problems in science and engineering, it is often necessary to optimize multiple objectives that are generally conflicting with each other. Since the pioneering attempt of Schaffer [1] to solve multiobjec- tive optimization problems, many kinds of multiobjective evolutionary algorithms (MOEAs), ranging from traditional evolutionary algorithms to newly developed techniques, have been proposed and widely used in different applications [2], [3]. Based on the adopted type of selection mechanism, these MOEAs can be classified into the following three categories: aggregating function approaches, population-based approaches, Manuscript received December 22, 2010; revised May 13, 2011; accepted January 13, 2012. Date of publication February 10, 2012; date of current ver- sion nulldate. This work was supported by the Key Program of the National Natural Science Foundation of China, under Grant 71032004, and by the Na- tional Natural Science Foundation of China, under Grant 70902065. The authors (corresponding) are with the Liaoning Key Laboratory of Manufacturing Systems and Logistics, Logistics Institute, Northeastern University, Shenyang 110819, China (e-mail: qhjytlx@mail.neu.edu.cn; wangxianpeng@ise.neu.edu.cn). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TEVC.2012.2185702 and Pareto-based approaches [4]. The aggregating function approach combines multiple objectives into a scalar objective via an aggregating function [5], [6]. By repeating the evolution process for a given number of runs with different settings of the aggregating function, the whole tradeoff surface can be obtained. However, the main difficulty of this approach is how to determine appropriate weight for each objective. The pop- ulation-based approaches treat multiple objectives separately during the evolution by dividing the population into several subpopulations and letting each subpopulation treat only one objective. The main disadvantage of this approach is that it can only manage to find certain extreme solutions along the Pareto tradeoffs [1]. Most MOEAs belong to the Pareto-based approaches, which incorporate the Pareto optimality into the selection process. The representative methods of this category are the niched Pareto genetic algorithm [7], the nondominated sorting genetic algorithm (NSGA) [8] and its improved version NSGA-II [9], the Pareto archive evolutionary strategy [10], the microGA [11], the strength Pareto evolutionary algorithm (SPEA) [12] and its improved version SPEA2 [13], the incre- menting multiobjective evolutionary algorithm (MOEA) [14], and the MOEA based on decomposition [15], [16]. Besides the traditional MOEAs, some other evolutionary metaheuristics have also been widely used for MOPs, such as scatter search (SS) [17], [18], particle swarm optimization [19 ]–[29], and differential evolution (DE) [30 ]–[32]. In recent years, a new trend of developing hybrid MOEAs by combining different concepts or components of more than one MOEA or multiobjective metaheuristic or other simple heuristics has appeared. Proper combination of different MOEAs or meta- heuristics may further enhance the effectiveness of the solution space search by adopting the advantages of each MOEA or metaheuristic, and consequently may overcome the inherent limitations of single MOEA or metaheuristic. Molina et al. [33] proposed a scatter tabu search procedure for non-linear mul- tiobjective optimization by incorporating the tabu search into scatter search to generate the initial population and improve the new trial solutions generated from the reference set. Nebro et al. [34] presented an archive-based hybrid scatter search (AbYSS) for MOPs, which follows the scatter search but uses mutation and crossover operators from evolutionary algorithms (EAs). In fact, the AbYSS is no longer a multiobjective SS, but a hybridization of SS with randomized operators typically used in EAs. Computational results on benchmark instances of MOPs showed that the AbYSS is very competitive with or superior to the state-of-the-art MOEAs, such as NSGA-II and SPEA2. Soliman et al. [35] combined ideas from coevolution and local search into multiobjective DE to guide the search 1089-778X/$31.00 © 2012 IEEE