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.

A Dimensional Diversity Based Hybrid Multiobjective Evolutionary Algorithm for Optimization Problem

2016 ◽  
Vol 30 (07) ◽  
pp. 1659020 ◽  
Author(s):  
Peng Wang ◽  
Changsheng Zhang ◽  
Bin Zhang ◽  
Tingting Liu ◽  
Jiaxuan Wu
Keyword(s):  
Multiobjective Optimization ◽  
Evolutionary Algorithm ◽  
Optimization Problem ◽  
Optimization Problems ◽  
State Of The Art ◽  
Experimental Results ◽  
Selection Scheme ◽  
Genetic Operator ◽  
Hybrid Evolutionary Algorithm ◽  
Multiobjective Optimization Problems

Multiobjective density driven evolutionary algorithm (MODdEA) has been quite successful in solving multiobjective optimization problems (MOPs). To further improve its performance and address its deficiencies, this paper proposes a hybrid evolutionary algorithm based on dimensional diversity (DD) and firework explosion (FE). DD is defined to reflect the diversity degree of population dimension. Based on DD, a selection scheme is designed to balance diversity and convergence. A hybrid variation based on FE and genetic operator is designed to facilitate diversity of population. The proposed algorithm is tested on 14 tests problems with diverse characteristics and compared with three state-of-the-art designs. Experimental results show that the proposed design is better or at par with the chosen state-of-the-art algorithms for multiobjective optimization.

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.

A New Dominance Method Based on Expanding Dominated Area for Many-Objective Optimization

2019 ◽  
Vol 33 (03) ◽  
pp. 1959008
Author(s):  
Junhua Liu ◽  
Yuping Wang ◽  
Xingyin Wang ◽  
Si Guo ◽  
Xin Sui
Keyword(s):  
Evolutionary Algorithms ◽  
Selection Pressure ◽  
Optimization Problems ◽  
State Of The Art ◽  
Experimental Results ◽  
Benchmark Problems ◽  
Optimal Solutions ◽  
Pareto Dominance ◽  
Global Optimal

The performance of the traditional Pareto-based evolutionary algorithms sharply reduces for many-objective optimization problems, one of the main reasons is that Pareto dominance could not provide sufficient selection pressure to make progress in a given population. To increase the selection pressure toward the global optimal solutions and better maintain the quality of selected solutions, in this paper, a new dominance method based on expanding dominated area is proposed. This dominance method skillfully combines the advantages of two existing popular dominance methods to further expand the dominated area and better maintain the quality of selected solutions. Besides, through dynamically adjusting its parameter with the iteration, our proposed dominance method can timely adjust the selection pressure in the process of evolution. To demonstrate the quality of selected solutions by our proposed dominance method, the experiments on a number of well-known benchmark problems with 5–25 objectives are conducted and compared with that of the four state-of-the-art dominance methods based on expanding dominated area. Experimental results show that the new dominance method not only enhances the selection pressure but also better maintains the quality of selected solutions.

scholarly journals A multipopulation evolutionary framework with Steffensen’s method for dynamic multiobjective optimization problems

2021 ◽  
Author(s):  
Tianyu Liu ◽  
Lei Cao ◽  
Zhu Wang
Keyword(s):  
Multiobjective Optimization ◽  
Optimization Problems ◽  
Population Diversity ◽  
Environment Changes ◽  
Steffensen’S Method ◽  
Diversity Maintenance ◽  
Multiobjective Optimization Problems ◽  
Comprehensive Comparison ◽  
Dynamic Multiobjective Optimization ◽  
Single Objective

AbstractDynamic multiobjective optimization problems (DMOPs) require the evolutionary algorithms that can track the moving Pareto-optimal fronts efficiently. This paper presents a dynamic multiobjective evolutionary framework (DMOEF-MS), which adopts a novel multipopulation structure and Steffensen’s method to solve DMOPs. In DMOEF-MS, only one population deals with the original DMOP, while the others focus on single-objective problems that are generated by the weighted summation of the original DMOP. Then, Steffensen’s method is used to control the evolving process in two ways: prediction and diversity-maintenance. Particularly, the prediction strategy is devised to predict the next promising positions for the individuals that handle single-objective problems, and the diversity-maintenance strategy is used to increase population diversity before the environment changes and reinitialize the multiple populations after the environment changes. This paper gives a comprehensive comparison of DMOEF-MS with some state-of-the-art DMOEAs on 14 DMOPs and the experimental results demonstrate the effectiveness of the proposed algorithm.

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.

Multiobjective Optimization

AI Magazine ◽  
2008 ◽  
Vol 29 (4) ◽  
pp. 47 ◽  
Author(s):  
Matthias Ehrgott
Keyword(s):  
Decision Making ◽  
Combinatorial Optimization ◽  
Multiobjective Optimization ◽  
Real World ◽  
Optimization Problems ◽  
Multiple Objectives ◽  
Combinatorial Optimization Problems ◽  
Multiobjective Optimization Problems ◽  
Single Objective

Using some real world examples I illustrate the important role of multiobjective optimization in decision making and its interface with preference handling. I explain what optimization in the presence of multiple objectives means and discuss some of the most common methods of solving multiobjective optimization problems using transformations to single objective optimisation problems. Finally, I address linear and combinatorial optimization problems with multiple objectives and summarize techniques for solving them. Throughout the article, I refer to the real world examples introduced at the beginning.

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.

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