8 A Review of Major Application Areas of Differential Evolution <s> Multiobjective Optimization <s> In this paper, we study the problem features that may cause a multi-objective genetic algorithm (GA) difficulty in converging to the true Pareto-optimal front. Identification of such features helps us develop difficult test problems for multi-objective optimization. Multi-objective test problems are constructed from single-objective optimization problems, thereby allowing known difficult features of single-objective problems (such as multi-modality, isolation, or deception) to be directly transferred to the corresponding multi-objective problem. In addition, test problems having features specific to multi-objective optimization are also constructed. More importantly, these difficult test problems will enable researchers to test their algorithms for specific aspects of multi-objective optimization. <s> BIB001 </s> 8 A Review of Major Application Areas of Differential Evolution <s> Multiobjective Optimization <s> In this paper, we provide a systematic comparison of various evolutionary approaches to multiobjective optimization using six carefully chosen test functions. Each test function involves a particular feature that is known to cause difficulty in the evolutionary optimization process, mainly in converging to the Pareto-optimal front (e.g., multimodality and deception). By investigating these different problem features separately, it is possible to predict the kind of problems to which a certain technique is or is not well suited. However, in contrast to what was suspected beforehand, the experimental results indicate a hierarchy of the algorithms under consideration. Furthermore, the emerging effects are evidence that the suggested test functions provide sufficient complexity to compare multiobjective optimizers. Finally, elitism is shown to be an important factor for improving evolutionary multiobjective search. <s> BIB002 </s> 8 A Review of Major Application Areas of Differential Evolution <s> Multiobjective Optimization <s> List of Figures. List of Tables. Preface. Foreword. 1. Basic Concepts. 2. Evolutionary Algorithm MOP Approaches. 3. MOEA Test Suites. 4. MOEA Testing and Analysis. 5. MOEA Theory and Issues. 3. MOEA Theoretical Issues. 6. Applications. 7. MOEA Parallelization. 8. Multi-Criteria Decision Making. 9. Special Topics. 10. Epilog. Appendix A: MOEA Classification and Technique Analysis. Appendix B: MOPs in the Literature. Appendix C: Ptrue & PFtrue for Selected Numeric MOPs. Appendix D: Ptrue & PFtrue for Side-Constrained MOPs. Appendix E: MOEA Software Availability. Appendix F: MOEA-Related Information. Index. References. <s> BIB003 </s> 8 A Review of Major Application Areas of Differential Evolution <s> Multiobjective Optimization <s> Developing multiobjective evolutionary algorithms (MOEAs) involves thoroughly addressing the issues of efficiency and effectiveness. Once convinced of an MOEA's effectiveness the researcher often desires to reduce execution time and/or resource expenditure, which naturally leads to considering the MOEA's parallelization. Parallel MOEAs (pMOEAs) or distributed MOEAs are relatively new developments with few associated publications. pMOEA creation is not a simple task, involving analyzing various parallel paradigms and associated parameters. Thus, a thorough discussion of the major parallelized MOEA paradigms is included in this paper and succinct observations are made regarding an analysis of the current literature. Specifically, a previous MOEA notation is extended into the pMOEA domain to enable precise description and identification of various sets of interest. Innovative concepts for pMOEA migration, replacement and niching schemes are discussed, as well as presenting the first known generic pMOEA formulation. Taken together, this paper's analyses in conjunction with an original pMOEA design serve as a pedagogical framework and example of the necessary process to implement an efficient and effective pMOEA. <s> BIB004
Multiobjective Optimization (MO) problems consist of several competing and incommensurable objective functions. Such problems are frequently encountered in numerous scientific and engineering applications. The need for the concurrent minimization of more than one objective functions, renders the use of EAs particularly attractive. In contrast to traditional gradient-based techniques, EAs operate on a set of potential solutions of the problem. Thus, EAs are capable of detecting several solutions of an MO problem in a single run BIB003 BIB001  BIB004  BIB002 . These solutions are called Pareto optimal, and each corresponds to a different trade-off among the objective functions. Typically, a large number of Pareto optimal solutions exist. Here we present a multi-population variant of DE, named Vector Evaluated Differential Evolution (VEDE), which is inspired by the Vector Evaluated Genetic Algorithm (VEGA) approach  . In VEDE, each population is evaluated using one of the objective functions of the problem under consideration. Information sharing among the populations takes place through the migration of the best individuals. The performance of a parallel version of VEDE, which incorporates a domination selection scheme, is investigated on widely used test problems and compared to the VEGA approach. The parallel computation of solutions of an MO problem is preferred, because besides the reduction in execution time, can also yield a better representation of the possible outcomes, thereby enhancing the performance of the algorithm BIB004 .