ROTATED PROBLEMS AND ROTATIONALLY INVARIANT CROSSOVER IN EVOLUTIONARY MULTI-OBJECTIVE OPTIMIZATION

2008 ◽  
Vol 07 (02) ◽  
pp. 149-186 ◽  
Author(s):  
ANTONY IORIO ◽  
XIAODONG LI
Keyword(s):  
Evolutionary Algorithms ◽  
Coordinate System ◽  
Test Problems ◽  
Multi Objective Optimization ◽  
Problem Domain ◽  
Nsga Ii ◽  
Multi Objective ◽  
Parameter Interactions ◽  
Rotationally Invariant ◽  
Single Objective

Problems that are not aligned with the coordinate system can present difficulties to many optimization algorithms, including evolutionary algorithms, by trapping the search on a ridge. The ridge problem in single-objective optimization is understood, but until now little work has been done on understanding this issue in the multi-objective domain. Multi-objective problems with parameter interactions present difficulties to an optimization algorithm, which are not present in the single-objective domain. In this work, we have explained the nature of these difficulties, and investigated the behavior of the NSGA-II, which has difficulties with problems not aligned with the principle coordinate system. This study has investigated Simplex Crossover (SPX), Unimodal Normally Distributed Crossover (UNDX), Parent-Centric Crossover (PCX), and Differential Evolution (DE), as possible alternatives to the Simulated Binary Crossover (SBX) operator within the NSGA-II, on problems exhibiting parameter interactions through a rotation of the coordinate system. An analysis of these operators on three rotated bi-objective test problems, and a four-and eight-objective problem is provided. New observations on the behavior of rotationally invariant crossover operators in the multi-objective problem domain have been reported.

On Benchmark Problems and Metrics for Decision Space Performance Analysis in Multi-Objective Optimization

2017 ◽  
Vol 16 (01) ◽  
pp. 1750006 ◽  
Author(s):  
Bin Zhang ◽  
Kamran Shafi ◽  
Hussein Abbass
Keyword(s):  
Performance Analysis ◽  
Fitness Landscape ◽  
Benchmark Problems ◽  
Test Problems ◽  
Multi Objective Optimization ◽  
Decision Space ◽  
Nsga Ii ◽  
Multi Objective ◽  
Objective Space ◽  
Problem Instances

A number of benchmark problems exist for evaluating multi-objective evolutionary algorithms (MOEAs) in the objective space. However, the decision space performance analysis is a recent and relatively less explored topic in evolutionary multi-objective optimization research. Among other implications, such analysis can lead to designing more realistic test problems, gaining better understanding about optimal and robust design areas, and design and evaluation of knowledge-based optimization algorithms. This paper complements the existing research in this area and proposes a new method to generate multi-objective optimization test problems with clustered Pareto sets in hyper-rectangular defined areas of decision space. The test problem is parametrized to control number of decision variables, number and position of optimal areas in the decision space and modality of fitness landscape. Three leading MOEAs, including NSGA-II, NSGA-III, and MOEA/D, are evaluated on a number of problem instances with varying characteristics. A new metric is proposed that measures the performance of algorithms in terms of their coverage of the optimal areas in the decision space. The empirical analysis presented in this research shows that the decision space performance may not necessarily be reflective of the objective space performance and that all algorithms are sensitive to population size parameter for the new test problems.

Multi-Objective Optimization of Manufacturing Processes Using Evolutionary Algorithms

2012 ◽  
pp. 44-66
Author(s):  
M. Kanthababu
Keyword(s):  
Genetic Algorithm ◽  
Evolutionary Algorithms ◽  
Multiple Objectives ◽  
Manufacturing Processes ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Local Optima ◽  
Multi Objective ◽  
Research Areas

Recently evolutionary algorithms have created more interest among researchers and manufacturing engineers for solving multiple-objective problems. The objective of this chapter is to give readers a comprehensive understanding and also to give a better insight into the applications of solving multi-objective problems using evolutionary algorithms for manufacturing processes. The most important feature of evolutionary algorithms is that it can successfully find globally optimal solutions without getting restricted to local optima. This chapter introduces the reader with the basic concepts of single-objective optimization, multi-objective optimization, as well as evolutionary algorithms, and also gives an overview of its salient features. Some of the evolutionary algorithms widely used by researchers for solving multiple objectives have been presented and compared. Among the evolutionary algorithms, the Non-dominated Sorting Genetic Algorithm (NSGA) and Non-dominated Sorting Genetic Algorithm-II (NSGA-II) have emerged as most efficient algorithms for solving multi-objective problems in manufacturing processes. The NSGA method applied to a complex manufacturing process, namely plateau honing process, considering multiple objectives, has been detailed with a case study. The chapter concludes by suggesting implementation of evolutionary algorithms in different research areas which hold promise for future applications.

Evolutionary Multi-Objective Optimization for Assignment Problems

2011 ◽  
pp. 364-387
Author(s):  
Mark P. Kleeman ◽  
Gary B. Lamont
Keyword(s):  
Evolutionary Algorithms ◽  
Multiple Objectives ◽  
Multi Objective Optimization ◽  
Assignment Problems ◽  
Multi Objective ◽  
Advantages And Disadvantages ◽  
Single Objective

Assignment problems are used throughout many research disciplines. Most assignment problems in the literature have focused on solving a single objective. This chapter focuses on assignment problems that have multiple objectives that need to be satisfied. In particular, this chapter looks at how multi-objective evolutionary algorithms have been used to solve some of these problems. Additionally, this chapter examines many of the operators that have been utilized to solve assignment problems and discusses some of the advantages and disadvantages of using specific operators.

Multi-Objective Evolutionary Algorithms

2016 ◽  
pp. 301-345
Author(s):  
A. K. Nandi ◽  
K. Deb
Keyword(s):  
Genetic Algorithm ◽  
Evolutionary Algorithms ◽  
Optimization Problem ◽  
Performance Metrics ◽  
Research Work ◽  
Primary Objective ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Mould Material ◽  
Multi Objective

The primary objective in designing appropriate particle reinforced polyurethane composite which will be used as a mould material in soft tooling process is to minimize the cycle time of soft tooling process by providing faster cooling rate during solidification of wax/plastic component. This chapter exemplifies an effective approach to design particle reinforced mould materials by solving the inherent multi-objective optimization problem associated with soft tooling process using evolutionary algorithms. In this chapter, first a brief introduction of multi-objective optimization problem with the key issues is presented. Then, after a short overview on the working procedure of genetic algorithm, a well- established multi-objective evolutionary algorithm, namely NSGA-II along with various performance metrics are described. The inherent multi-objective problem in soft tooling process is demonstrated and subsequently solved using an elitist non-dominated sorting genetic algorithm, NSGA-II. Multi-objective optimization results obtained using NSGA-II are analyzed statistically and validated with real industrial application. Finally the fundamental results of this approach are summarized and various perspectives to the industries along with scopes for future research work are pointed out.

Product form evolutionary design system construction based on neural network model and multi-objective optimization

2020 ◽  
Vol 39 (5) ◽  
pp. 7977-7991
Author(s):  
Yixiang Wu
Keyword(s):  
Functional Relation ◽  
Product Form ◽  
Design System ◽  
Evolutionary Design ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Multi Objective ◽  
Form Design ◽  
Product Form Design ◽  
Single Objective

The product form evolutionary design based on multi-objective optimization can satisfy the complex emotional needs of consumers for product form, but most relevant literatures mainly focus on single-objective optimization or convert multiple-objective optimization into the single objective by weighting method. In order to explore the optimal product form design, we propose a hybrid product form design method based on back propagation neural networks (BP-NN) and non-dominated sorting genetic algorithm-II (NSGA-II) algorithms from the perspective of multi-objective optimization. First, the product form is deconstructed and encoded by morphological analysis method, and then the semantic difference method is used to enable consumers to evaluate product samples under a series of perceptual image vocabularies. Then, the nonlinear complex functional relation between the consumers’ perceptual image and the morphological elements is fitted with the BP-NN. Finally, the trained BP-NN is embedded into the NSGA-II multi-objective evolutionary algorithm to derive the Pareto optimal solution. Based on the hybrid BP-NN and NSGA-II algorithms, a multi-objective optimization based product form evolutionary design system is developed with the electric motorcycle as a case. The system is proved to be feasible and effective, providing theoretical reference and method guidance for the multi-image product form design.

Multi-Objective Optimization Algorithm Based on Gene Expression Programming and Virus Evolution

2011 ◽  
Vol 225-226 ◽  
pp. 372-376
Author(s):  
Wei Hong Wang ◽  
Yan Ye Du ◽  
Qu Li
Keyword(s):  
Gene Expression ◽  
Gene Expression Programming ◽  
Research Direction ◽  
Virus Evolution ◽  
Host Population ◽  
Test Problems ◽  
Local Optimum ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Multi Objective

Evolutionary Multi-objective Optimization (EMO) is a hot research direction nowadays and one of the state-of-the-art evolutionary multi-objective optimization algorithms ——NSGA-II has gain wide attention and application in many fields. Gene Expression Programming (GEP) has a powerful search capability, but falls into local optimum easily. Based on the transformed GEP, NSGA-II and the virus evolution mechanism, a new multi-objective evolutionary algorithm GEP Virus NSGA-II is proposed. With the infection operation of virus population, the diversity of the host population is increased, and it’s much easier to jump out of the local optimum. And this algorithm has got good experimental results on 9 standard test problems.

scholarly journals MOEA/D with Adaptive Weight Adjustment

2014 ◽  
Vol 22 (2) ◽  
pp. 231-264 ◽  
Author(s):  
Yutao Qi ◽  
Xiaoliang Ma ◽  
Fang Liu ◽  
Licheng Jiao ◽  
Jianyong Sun ◽  
...  
Keyword(s):  
Optimal Solution ◽  
Weight Vector ◽  
Test Problems ◽  
Great Success ◽  
Optimal Solutions ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Multi Objective ◽  
Decomposition Scheme ◽  
Adaptive Weight

Recently, MOEA/D (multi-objective evolutionary algorithm based on decomposition) has achieved great success in the field of evolutionary multi-objective optimization and has attracted a lot of attention. It decomposes a multi-objective optimization problem (MOP) into a set of scalar subproblems using uniformly distributed aggregation weight vectors and provides an excellent general algorithmic framework of evolutionary multi-objective optimization. Generally, the uniformity of weight vectors in MOEA/D can ensure the diversity of the Pareto optimal solutions, however, it cannot work as well when the target MOP has a complex Pareto front (PF; i.e., discontinuous PF or PF with sharp peak or low tail). To remedy this, we propose an improved MOEA/D with adaptive weight vector adjustment (MOEA/D-AWA). According to the analysis of the geometric relationship between the weight vectors and the optimal solutions under the Chebyshev decomposition scheme, a new weight vector initialization method and an adaptive weight vector adjustment strategy are introduced in MOEA/D-AWA. The weights are adjusted periodically so that the weights of subproblems can be redistributed adaptively to obtain better uniformity of solutions. Meanwhile, computing efforts devoted to subproblems with duplicate optimal solution can be saved. Moreover, an external elite population is introduced to help adding new subproblems into real sparse regions rather than pseudo sparse regions of the complex PF, that is, discontinuous regions of the PF. MOEA/D-AWA has been compared with four state of the art MOEAs, namely the original MOEA/D, Adaptive-MOEA/D, [Formula: see text]-MOEA/D, and NSGA-II on 10 widely used test problems, two newly constructed complex problems, and two many-objective problems. Experimental results indicate that MOEA/D-AWA outperforms the benchmark algorithms in terms of the IGD metric, particularly when the PF of the MOP is complex.

Multi-Objective Evolutionary Algorithms

2017 ◽  
pp. 185-229
Author(s):  
A. K. Nandi ◽  
K. Deb
Keyword(s):  
Genetic Algorithm ◽  
Evolutionary Algorithms ◽  
Optimization Problem ◽  
Performance Metrics ◽  
Research Work ◽  
Primary Objective ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Mould Material ◽  
Multi Objective

The primary objective in designing appropriate particle reinforced polyurethane composite which will be used as a mould material in soft tooling process is to minimize the cycle time of soft tooling process by providing faster cooling rate during solidification of wax/plastic component. This chapter exemplifies an effective approach to design particle reinforced mould materials by solving the inherent multi-objective optimization problem associated with soft tooling process using evolutionary algorithms. In this chapter, first a brief introduction of multi-objective optimization problem with the key issues is presented. Then, after a short overview on the working procedure of genetic algorithm, a well- established multi-objective evolutionary algorithm, namely NSGA-II along with various performance metrics are described. The inherent multi-objective problem in soft tooling process is demonstrated and subsequently solved using an elitist non-dominated sorting genetic algorithm, NSGA-II. Multi-objective optimization results obtained using NSGA-II are analyzed statistically and validated with real industrial application. Finally the fundamental results of this approach are summarized and various perspectives to the industries along with scopes for future research work are pointed out.

Multi-Objective Optimization of Parameters for Milling Using Evolutionary Algorithms and Artificial Neural Networks

2019 ◽  
Author(s):  
Amit Banerjee ◽  
Issam Abu-Mahfouz ◽  
AHM Esfakur Rahman
Keyword(s):  
Neural Networks ◽  
Artificial Neural Networks ◽  
Evolutionary Algorithms ◽  
Cost Function ◽  
Machine Learning Algorithms ◽  
Machining Parameters ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Multi Objective ◽  
Artificial Neural

Abstract Model-based design of manufacturing processes have been gaining popularity since the advent of machine learning algorithms such as evolutionary algorithms and artificial neural networks (ANN). The problem of selecting the best machining parameters can be cast an optimization problem given a cost function and by utilizing an input-output connectionist framework using as ANNs. In this paper, we present a comparison of various evolutionary algorithms for parameter optimization of an end-milling operation based on a well-known cost function from literature. We propose a modification to the cost function for milling and include an additional objective of minimizing surface roughness and by using NSGA-II, a multi-objective optimization algorithm. We also present comparison of several population-based evolutionary search algorithms such as variants of particle swarm optimization, differential evolution and NSGA-II.

scholarly journals An Entropy-Based Multiobjective Evolutionary Algorithm with an Enhanced Elite Mechanism

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Yufang Qin ◽  
Junzhong Ji ◽  
Chunnian Liu
Keyword(s):  
Evolutionary Algorithm ◽  
Pareto Front ◽  
Optimization Problem ◽  
State Of The Art ◽  
Early Stage ◽  
Test Problems ◽  
Multiobjective Optimization Problem ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Multi Objective

Multiobjective optimization problem (MOP) is an important and challenging topic in the fields of industrial design and scientific research. Multi-objective evolutionary algorithm (MOEA) has proved to be one of the most efficient algorithms solving the multi-objective optimization. In this paper, we propose an entropy-based multi-objective evolutionary algorithm with an enhanced elite mechanism (E-MOEA), which improves the convergence and diversity of solution set in MOPs effectively. In this algorithm, an enhanced elite mechanism is applied to guide the direction of the evolution of the population. Specifically, it accelerates the population to approach the true Pareto front at the early stage of the evolution process. A strategy based on entropy is used to maintain the diversity of population when the population is near to the Pareto front. The proposed algorithm is executed on widely used test problems, and the simulated results show that the algorithm has better or comparative performances in convergence and diversity of solutions compared with two state-of-the-art evolutionary algorithms: NSGA-II, SPEA2 and the MOSADE.

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