Preferential local search with adaptive weights in evolutionary algorithms for multiobjective optimization problems

2011 ◽  
Author(s):  
J. Bhuvana ◽  
Chandrabose Aravindan
Keyword(s):  
Evolutionary Algorithms ◽  
Multiobjective Optimization ◽  
Local Search ◽  
Optimization Problems ◽  
Adaptive Weights ◽  
Multiobjective Optimization Problems

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.

Approximating the Nondominated Front Using the Pareto Archived Evolution Strategy

2000 ◽  
Vol 8 (2) ◽  
pp. 149-172 ◽  
Author(s):  
Joshua D. Knowles ◽  
David W. Corne
Keyword(s):  
Genetic Algorithm ◽  
Multiobjective Optimization ◽  
Local Search ◽  
Optimization Problems ◽  
Population Based ◽  
Evolution Strategy ◽  
Basic Algorithm ◽  
Pareto Optimal Set ◽  
Candidate Solution ◽  
Multiobjective Optimization Problems

We introduce a simple evolution scheme for multiobjective optimization problems, called the Pareto Archived Evolution Strategy (PAES). We argue that PAES may represent the simplest possible nontrivial algorithm capable of generating diverse solutions in the Pareto optimal set. The algorithm, in its simplest form, is a (1+1) evolution strategy employing local search but using a reference archive of previously found solutions in order to identify the approximate dominance ranking of the current and candidate solution vectors. (1+1)-PAES is intended to be a baseline approach against which more involved methods may be compared. It may also serve well in some real-world applications when local search seems superior to or competitive with population-based methods. We introduce (1+λ) and (μ+λ) variants of PAES as extensions to the basic algorithm. Six variants of PAES are compared to variants of the Niched Pareto Genetic Algorithm and the Nondominated Sorting Genetic Algorithm over a diverse suite of six test functions. Results are analyzed and presented using techniques that reduce the attainment surfaces generated from several optimization runs into a set of univariate distributions. This allows standard statistical analysis to be carried out for comparative purposes. Our results provide strong evidence that PAES performs consistently well on a range of multiobjective optimization tasks.

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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