Differential Evolution based Multiobjective Optimization- A Review
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paper_title: Differential evolution for multi-objective optimization

paper_content:

Two test problems on multiobjective optimization (one simple general problem and the second one on an engineering application of cantilever design problem) are solved using differential evolution (DE). DE is a population based search algorithm, which is an improved version of genetic algorithm (GA), Simulations carried out involved solving (1) both the problems using Penalty function method, and (2) first problem using Weighing factor method and finding Pareto optimum set for the chosen problem, DE found to be robust and faster in optimization. To consolidate the power of DE, the classical Himmelblau function, with bounds on variables, is also solved using both DE and GA. DE found to give the exact optimum value within less generations compared to simple GA.
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paper_title: Improved Strategies of Multi-objective Differential Evolution (MODE) for Multi-objective Optimization

paper_content:

Multi-objective optimization using an evolutionary computation technique is used extensively for solving conflicting multi-objective optimization problems. In this work, an improved strategy of multi-objective differential evolution (MODE) where the mutation strategy is changed to a trigonometric mutation approach is proposed. The proposed strategy along with other well known strategies of MODE is used to compare the performance metrics (such as convergence and divergence) with other evolutionary algorithms from the literature. The Pareto optimal solutions are obtained for benchmark test functions and are compared using several strategies of MODE. Improved strategies of MODE show a competitive performance when compared with other evolutionary multi-objective optimization algorithms (EMOAs).
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paper_title: Vector evaluated differential evolution for multiobjective optimization

paper_content:

A parallel, multi-population differential evolution algorithm for multiobjective optimization is introduced. The algorithm is equipped with a domination selection operator to enhance its performance by favouring non-dominated individuals in the populations. Preliminary experimental results on widely used test problems are promising. Comparisons with the VEGA approach are provided and discussed.
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paper_title: Solving rotated multi-objective optimization problems using Differential Evolution

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This paper demonstrates that the self-adaptive technique of Differential Evolution (DE) can be simply used for solving a multi-objective optimization problem where parameters are interdependent The real-coded crossover and mutation rates within the NSGA-II have been replaced with a simple Differential Evolution scheme, and results are reported on a rotated problem which has presented difficulties using existing Multi-objective Genetic Algorithms The Differential Evolution variant of the NSGA-II has demonstrated rotational invariance and superior performance over the NSGA-II on this problem.
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paper_title: Vector evaluated differential evolution for multiobjective optimization

paper_content:

A parallel, multi-population differential evolution algorithm for multiobjective optimization is introduced. The algorithm is equipped with a domination selection operator to enhance its performance by favouring non-dominated individuals in the populations. Preliminary experimental results on widely used test problems are promising. Comparisons with the VEGA approach are provided and discussed.
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paper_title: Differential evolution for multiobjective optimization with self adaptation

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This paper presents performance assessment of differential evolution for multiobjective optimization with self adaptation algorithm, which uses the self adaptation mechanism from evolution strategies to adapt F and CR parameters of the candidate creation in DE. Results for several runs on CEC2007 special session test functions are presented and assessed with different performance metrics. Based on these metrics, algorithm strengths and weaknesses are discussed.
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paper_title: DEMO: Differential Evolution for multiobjective optimization

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Differential Evolution (DE) is a simple but powerful evolutionary optimization algorithm with many successful applications. In this paper we propose Differential Evolution for Multiobjective Optimization (DEMO) – a new approach to multiobjective optimization based on DE. DEMO combines the advantages of DE with the mechanisms of Pareto-based ranking and crowding distance sorting, used by state-of-the-art evolutionary algorithms for multiobjective optimization. DEMO is implemented in three variants that achieve competitive results on five ZDT test problems.
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paper_title: Elitist-Multi-objective Differential Evolution (E- MODE) Algorithm for Multi-objective Optimization

paper_content:

Several problems in the engineering domain are multi-objective in nature. The solution to multi-objective optimization is a set of solutions rather than a single point solution. Such a set of non-dominated solutions are called Pareto optimal solutions or non-inferior solutions. In this paper, a new algorithm, Elitist-Multi-objective Differential Evolution (E-MODE) is proposed. The proposed algorithm is applied successfully on several test functions, and the results are discussed extensively. Results obtained from the proposed algorithm are compared with those obtained using Multi-objective Differential Evolution (MODE) algorithm. E-MODE is found to give better solutions in terms of wide range of solutions, spread, and diversity of Pareto front than those obtained using MODE.
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paper_title: An Algorithm Based on Differential Evolution for Multi-Objective Problems

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Abstract: This paper presents a new multi-objective evolu-tionary algorithm based on differential evolution. The pro-posed approach adopts a secondary population in order to re-tain the nondominated solutions found during the evolution-ary process. Additionally, the approach also incorporates theconcept of † -dominance to get a good distribution of the solu-tions retained. The main goal of this work was to keep thefast convergence exhibited by Differential Evolution in globaloptimization when extending this heuristic to multi-objectiveoptimization. We adopted standard test functions and perfor-mance measures reported in the specialized literature to vali-date our proposal. Our results are compared with respect toanother multi-objective evolutionary algorithm based on differ-ential evolution (Pareto Differential Evolution) and with respectto two approaches that are representative of the state-of-the-artin the area: the NSGA-II and † -MOEA. I. Introduction Most real world problems involve the simultaneous opti-mization of two or more (often conﬂicting) objectives. Thesolution of such problems (called “multi-objective”) is differ-ent from that of a single-objective optimization problem. Themain difference is that multi-objective optimization problemsnormally have not one but a set of solutions which are allequally good.In the past, a wide variety of evolutionary algorithms (EA’s)have been used to solve multi-objective optimization prob-lems [5]. However, from the several types of EAs available,few researchers have attempted to extend Differential Evo-lution (DE) [25] to solve multi-objective optimization prob-lems. DE has been very successful in the solution of a va-riety of continuous (single-objective) optimization problemsin which it has shown a great robustness and a very fast con-vergence. These are precisely the characteristics of DE thatmake it attractive to extend it to solve multi-objective opti-mization problems.In this paper, we propose a new multi-objective evolution-ary algorithm based on differential evolution. Our approachuses an external archive in which the relaxed form of Paretodominance known as
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Title: Differential Evolution based Multiobjective Optimization- A Review

Section 1: INTRODUCTION
Description 1: This section introduces the fundamentals of multiobjective optimization (MOO) and the significance of Differential Evolution (DE) in solving such problems. It also gives a brief history and an overview of DE and its importance in addressing complex optimization tasks.

Section 2: MULTIOBJECTIVE OPTIMIZATION (MOP)
Description 2: This section describes the concept of Multiobjective Optimization, including definitions, characteristics, and the formulation of MOP problems. It also explains Pareto optimality and Pareto dominance principles.

Section 3: DEFFERENTIAL EVOLUTION BASED MOP
Description 3: This section discusses the extensions of Differential Evolution to solve MOPs, focusing on the challenges of promoting diversity and performing elitism within the population.

Section 4: Promoting Diversity
Description 4: This section elucidates methods to promote diversity in the population such as crowding distance and fitness sharing techniques.

Section 5: Performing Elitism
Description 5: This section explains the concept of elitism in evolutionary algorithms, including strategies for maintaining the best individuals across generations using non dominated sorting approaches.

Section 6: MULTIOBJECTIVE DE ALGORITHMS
Description 6: This section reviews different Differential Evolution algorithms tailored for multiobjective optimization, detailing each approach's unique characteristics, methodologies, and performance.

Section 7: CONCLUSION
Description 7: This section summarizes the review, highlighting the effectiveness and robustness of various DE-based algorithms in solving multiobjective optimization problems.