A Game Model Based Co-evolutionary Algorithms for Multiobjective Optimization Problems

2006 ◽  
Author(s):  
Gaoping Wang ◽  
Yongji Wang
Keyword(s):  
Evolutionary Algorithms ◽  
Multiobjective Optimization ◽  
Optimization Problems ◽  
Game Model ◽  
Model Based ◽  
Multiobjective Optimization Problems

scholarly journals A Kriging Model-Based Expensive Multiobjective Optimization Algorithm Using R2 Indicator of Expectation Improvement

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Ding Han ◽  
Jianrong Zheng
Keyword(s):  
Multiobjective Optimization ◽  
Optimization Algorithm ◽  
Optimization Problems ◽  
Kriging Model ◽  
Utilization Efficiency ◽  
Function Evaluation ◽  
Good Convergence ◽  
Model Based ◽  
Multiobjective Optimization Problems ◽  
R2 Indicator

Most of the multiobjective optimization problems in engineering involve the evaluation of expensive objectives and constraint functions, for which an approximate model-based multiobjective optimization algorithm is usually employed, but requires a large amount of function evaluation. Aiming at effectively reducing the computation cost, a novel infilling point criterion EIR2 is proposed, whose basic idea is mapping a point in objective space into a set in expectation improvement space and utilizing the R2 indicator of the set to quantify the fitness of the point being selected as an infilling point. This criterion has an analytic form regardless of the number of objectives and demands lower calculation resources. Combining the Kriging model, optimal Latin hypercube sampling, and particle swarm optimization, an algorithm, EIR2-MOEA, is developed for solving expensive multiobjective optimization problems and applied to three sets of standard test functions of varying difficulty and comparing with two other competitive infill point criteria. Results show that EIR2 has higher resource utilization efficiency, and the resulting nondominated solution set possesses good convergence and diversity. By coupling with the average probability of feasibility, the EIR2 criterion is capable of dealing with expensive constrained multiobjective optimization problems and its efficiency is successfully validated in the optimal design of energy storage flywheel.

scholarly journals An MOEA/D-ACO with PBI for Many-Objective Optimization

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Tianbai Ling ◽  
Chen Wang
Keyword(s):  
Evolutionary Algorithms ◽  
Multiobjective Optimization ◽  
Selection Pressure ◽  
Optimization Problems ◽  
State Of The Art ◽  
Experimental Results ◽  
Significant Problem ◽  
Adjustment Method ◽  
Multiobjective Optimization Problems ◽  
Single Objective

Evolutionary algorithms (EAs) are an important instrument for solving the multiobjective optimization problems (MOPs). It has been observed that the combined ant colony (MOEA/D-ACO) based on decomposition is very promising for MOPs. However, as the number of optimization objectives increases, the selection pressure will be released, leading to a significant reduction in the performance of the algorithm. It is a significant problem and challenge in the MOEA/D-ACO to maintain the balance between convergence and diversity in many-objective optimization problems (MaOPs). In the proposed algorithm, an MOEA/D-ACO with the penalty based boundary intersection distance (PBI) method (MOEA/D-ACO-PBI) is intended to solve the MaOPs. PBI decomposes the problems with many single-objective problems, a weighted vector adjustment method based on clustering, and uses different pheromone matrices to solve different single objectives proposed. Then the solutions are constructed and pheromone was updated. Experimental results on both CF1-CF4 and suits of C-DTLZ benchmarks problems demonstrate the superiority of the proposed algorithm in comparison with three state-of-the-art algorithms in terms of both convergence and diversity.

Combining Convergence and Diversity in Evolutionary Multiobjective Optimization

2002 ◽  
Vol 10 (3) ◽  
pp. 263-282 ◽  
Author(s):  
Marco Laumanns ◽  
Lothar Thiele ◽  
Kalyanmoy Deb ◽  
Eckart Zitzler
Keyword(s):  
Evolutionary Algorithms ◽  
Multiobjective Optimization ◽  
Optimization Problems ◽  
Fundamental Problem ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Pareto Optimal Set ◽  
Multiobjective Optimization Problems ◽  
Baseline Algorithm

Over the past few years, the research on evolutionary algorithms has demonstrated their niche in solving multiobjective optimization problems, where the goal is to find a number of Pareto-optimal solutions in a single simulation run. Many studies have depicted different ways evolutionary algorithms can progress towards the Pareto-optimal set with a widely spread distribution of solutions. However, none of the multiobjective evolutionary algorithms (MOEAs) has a proof of convergence to the true Pareto-optimal solutions with a wide diversity among the solutions. In this paper, we discuss why a number of earlier MOEAs do not have such properties. Based on the concept of ɛ-dominance, new archiving strategies are proposed that overcome this fundamental problem and provably lead to MOEAs that have both the desired convergence and distribution properties. A number of modifications to the baseline algorithm are also suggested. The concept of ɛ-dominance introduced in this paper is practical and should make the proposed algorithms useful to researchers and practitioners alike.

scholarly journals Difficulty Adjustable and Scalable Constrained Multiobjective Test Problem Toolkit

2020 ◽  
Vol 28 (3) ◽  
pp. 339-378 ◽  
Author(s):  
Zhun Fan ◽  
Wenji Li ◽  
Xinye Cai ◽  
Hui Li ◽  
Caimin Wei ◽  
...  
Keyword(s):  
Evolutionary Algorithms ◽  
Multiobjective Optimization ◽  
Real World ◽  
Optimization Problems ◽  
Test Problems ◽  
Nsga Ii ◽  
Multiobjective Problems ◽  
Multiobjective Optimization Problems ◽  
Dominance Principle ◽  
Constrained Multiobjective Optimization

Multiobjective evolutionary algorithms (MOEAs) have progressed significantly in recent decades, but most of them are designed to solve unconstrained multiobjective optimization problems. In fact, many real-world multiobjective problems contain a number of constraints. To promote research on constrained multiobjective optimization, we first propose a problem classification scheme with three primary types of difficulty, which reflect various types of challenges presented by real-world optimization problems, in order to characterize the constraint functions in constrained multiobjective optimization problems (CMOPs). These are feasibility-hardness, convergence-hardness, and diversity-hardness. We then develop a general toolkit to construct difficulty adjustable and scalable CMOPs (DAS-CMOPs, or DAS-CMaOPs when the number of objectives is greater than three) with three types of parameterized constraint functions developed to capture the three proposed types of difficulty. In fact, the combination of the three primary constraint functions with different parameters allows the construction of a large variety of CMOPs, with difficulty that can be defined by a triplet, with each of its parameters specifying the level of one of the types of primary difficulty. Furthermore, the number of objectives in this toolkit can be scaled beyond three. Based on this toolkit, we suggest nine difficulty adjustable and scalable CMOPs and nine CMaOPs, to be called DAS-CMOP1-9 and DAS-CMaOP1-9, respectively. To evaluate the proposed test problems, two popular CMOEAs—MOEA/D-CDP (MOEA/D with constraint dominance principle) and NSGA-II-CDP (NSGA-II with constraint dominance principle) and two popular constrained many-objective evolutionary algorithms (CMaOEAs)—C-MOEA/DD and C-NSGA-III—are used to compare performance on DAS-CMOP1-9 and DAS-CMaOP1-9 with a variety of difficulty triplets, respectively. The experimental results reveal that mechanisms in MOEA/D-CDP may be more effective in solving convergence-hard DAS-CMOPs, while mechanisms of NSGA-II-CDP may be more effective in solving DAS-CMOPs with simultaneous diversity-, feasibility-, and convergence-hardness. Mechanisms in C-NSGA-III may be more effective in solving feasibility-hard CMaOPs, while mechanisms of C-MOEA/DD may be more effective in solving CMaOPs with convergence-hardness. In addition, none of them can solve these problems efficiently, which stimulates us to continue to develop new CMOEAs and CMaOEAs to solve the suggested DAS-CMOPs and DAS-CMaOPs.

scholarly journals A Review of Surrogate Assisted Multiobjective Evolutionary Algorithms

2016 ◽  
Vol 2016 ◽  
pp. 1-14 ◽  
Author(s):  
Alan Díaz-Manríquez ◽  
Gregorio Toscano ◽  
Jose Hugo Barron-Zambrano ◽  
Edgar Tello-Leal
Keyword(s):  
Evolutionary Algorithms ◽  
Multiobjective Optimization ◽  
Pareto Front ◽  
Optimization Problems ◽  
State Of The Art ◽  
Surrogate Models ◽  
Multiobjective Evolutionary Algorithms ◽  
Advantages And Disadvantages ◽  
Multiobjective Optimization Problems ◽  
Computationally Expensive

Multiobjective evolutionary algorithms have incorporated surrogate models in order to reduce the number of required evaluations to approximate the Pareto front of computationally expensive multiobjective optimization problems. Currently, few works have reviewed the state of the art in this topic. However, the existing reviews have focused on classifying the evolutionary multiobjective optimization algorithms with respect to the type of underlying surrogate model. In this paper, we center our focus on classifying multiobjective evolutionary algorithms with respect to their integration with surrogate models. This interaction has led us to classify similar approaches and identify advantages and disadvantages of each class.

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