A Novel Angular-Guided Particle Swarm Optimizer for Many-Objective Optimization Problems

Most multiobjective particle swarm optimizers (MOPSOs) often face the challenges of keeping diversity and achieving convergence on tackling many-objective optimization problems (MaOPs), as they usually use the nondominated sorting method or decomposition-based method to select the local or best particles, which is not so effective in high-dimensional objective space. To better solve MaOPs, this paper presents a novel angular-guided particle swarm optimizer (called AGPSO). A novel velocity update strategy is designed in AGPSO, which aims to enhance the search intensity around the particles selected based on their angular distances. Using an external archive, the local best particles are selected from the surrounding particles with the best convergence, while the global best particles are chosen from the top 20% particles with the better convergence among the entire particle swarm. Moreover, an angular-guided archive update strategy is proposed in AGPSO, which maintains a consistent population with balanceable convergence and diversity. To evaluate the performance of AGPSO, the WFG and MaF test suites with 5 to 10 objectives are adopted. The experimental results indicate that AGPSO shows the superior performance over four current MOPSOs (SMPSO, dMOPSO, NMPSO, and MaPSO) and four competitive evolutionary algorithms (VaEA, θ-DEA, MOEA\D-DD, and SPEA2-SDE), when solving most of the test problems used.

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An evolutionary based framework for many-objective optimization problems

Engineering Computations ◽

10.1108/ec-08-2017-0296 ◽

2018 ◽

Vol 35 (4) ◽

pp. 1805-1828 ◽

Cited By ~ 1

Author(s):

Kimia Bazargan Lari ◽

Ali Hamzeh

Keyword(s):

Optimization Problems ◽

State Of The Art ◽

Fitness Function ◽

Population Diversity ◽

Numerical Results ◽

Superior Performance ◽

High Dimensional ◽

Test Problems ◽

Content Type ◽

Objective Space

Purpose Recently, many-objective optimization evolutionary algorithms have been the main issue for researchers in the multi-objective optimization community. To deal with many-objective problems (typically for four or more objectives) some modern frameworks are proposed which have the potential of achieving the finest non-dominated solutions in many-objective spaces. The effectiveness of these algorithms deteriorates greatly as the problem’s dimension increases. Diversity reduction in the objective space is the main reason of this phenomenon. Design/methodology/approach To properly deal with this undesirable situation, this work introduces an indicator-based evolutionary framework that can preserve the population diversity by producing a set of discriminated solutions in high-dimensional objective space. This work attempts to diversify the objective space by proposing a fitness function capable of discriminating the chromosomes in high-dimensional space. The numerical results prove the potential of the proposed method, which had superior performance in most of test problems in comparison with state-of-the-art algorithms. Findings The achieved numerical results empirically prove the superiority of the proposed method to state-of-the-art counterparts in the most test problems of a known artificial benchmark. Originality/value This paper provides a new interpretation and important insights into the many-objective optimization realm by emphasizing on preserving the population diversity.

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A Novel Distributed Quantum-Behaved Particle Swarm Optimization

Journal of Optimization ◽

10.1155/2017/4685923 ◽

2017 ◽

Vol 2017 ◽

pp. 1-9 ◽

Cited By ~ 1

Author(s):

Yangyang Li ◽

Zhenghan Chen ◽

Yang Wang ◽

Licheng Jiao ◽

Yu Xue

Keyword(s):

Big Data ◽

Particle Swarm Optimization ◽

Nonlinear Equation ◽

Optimization Problems ◽

Particle Swarm ◽

Superior Performance ◽

Test Problems ◽

Swarm Optimization ◽

Mapreduce Model ◽

Nonlinear Equation Systems

Quantum-behaved particle swarm optimization (QPSO) is an improved version of particle swarm optimization (PSO) and has shown superior performance on many optimization problems. But for now, it may not always satisfy the situations. Nowadays, problems become larger and more complex, and most serial optimization algorithms cannot deal with the problem or need plenty of computing cost. Fortunately, as an effective model in dealing with problems with big data which need huge computation, MapReduce has been widely used in many areas. In this paper, we implement QPSO on MapReduce model and propose MapReduce quantum-behaved particle swarm optimization (MRQPSO) which achieves parallel and distributed QPSO. Comparisons are made between MRQPSO and QPSO on some test problems and nonlinear equation systems. The results show that MRQPSO could complete computing task with less time. Meanwhile, from the view of optimization performance, MRQPSO outperforms QPSO in many cases.

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R2-Based Multi/Many-Objective Particle Swarm Optimization

Computational Intelligence and Neuroscience ◽

10.1155/2016/1898527 ◽

2016 ◽

Vol 2016 ◽

pp. 1-10 ◽

Cited By ~ 7

Author(s):

Alan Díaz-Manríquez ◽

Gregorio Toscano ◽

Jose Hugo Barron-Zambrano ◽

Edgar Tello-Leal

Keyword(s):

Particle Swarm Optimization ◽

Optimization Problems ◽

Particle Swarm ◽

Performance Measure ◽

Interaction Process ◽

Test Problems ◽

Pareto Dominance ◽

Swarm Optimization ◽

External Archive ◽

And Performance

We propose to couple theR2performance measure and Particle Swarm Optimization in order to handle multi/many-objective problems. Our proposal shows that through a well-designed interaction process we could maintain the metaheuristic almost inalterable and through theR2performance measure we did not use neither an external archive nor Pareto dominance to guide the search. The proposed approach is validated using several test problems and performance measures commonly adopted in the specialized literature. Results indicate that the proposed algorithm produces results that are competitive with respect to those obtained by four well-known MOEAs. Additionally, we validate our proposal in many-objective optimization problems. In these problems, our approach showed its main strength, since it could outperform another well-known indicator-based MOEA.

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Elite Exploitation: A Combination of Mathematical Concept and EMO Approach for Multi-Objective Decision Making

Symmetry ◽

10.3390/sym13010136 ◽

2021 ◽

Vol 13 (1) ◽

pp. 136

Author(s):

Wenxiao Li ◽

Yushui Geng ◽

Jing Zhao ◽

Kang Zhang ◽

Jianxin Liu

Keyword(s):

Decision Making ◽

Optimization Problems ◽

Hybrid Genetic Algorithm ◽

Decision Makers ◽

Superior Performance ◽

Test Problems ◽

Mathematical Function ◽

Hyperbolic Tangent ◽

Nsga Ii ◽

Multi Objective

This paper explores the combination of a classic mathematical function named “hyperbolic tangent” with a metaheuristic algorithm, and proposes a novel hybrid genetic algorithm called NSGA-II-BnF for multi-objective decision making. Recently, many metaheuristic evolutionary algorithms have been proposed for tackling multi-objective optimization problems (MOPs). These algorithms demonstrate excellent capabilities and offer available solutions to decision makers. However, their convergence performance may be challenged by some MOPs with elaborate Pareto fronts such as CFs, WFGs, and UFs, primarily due to the neglect of diversity. We solve this problem by proposing an algorithm with elite exploitation strategy, which contains two parts: first, we design a biased elite allocation strategy, which allocates computation resources appropriately to elites of the population by crowding distance-based roulette. Second, we propose a self-guided fast individual exploitation approach, which guides elites to generate neighbors by a symmetry exploitation operator, which is based on mathematical hyperbolic tangent function. Furthermore, we designed a mechanism to emphasize the algorithm’s applicability, which allows decision makers to adjust the exploitation intensity with their preferences. We compare our proposed NSGA-II-BnF with four other improved versions of NSGA-II (NSGA-IIconflict, rNSGA-II, RPDNSGA-II, and NSGA-II-SDR) and four competitive and widely-used algorithms (MOEA/D-DE, dMOPSO, SPEA-II, and SMPSO) on 36 test problems (DTLZ1–DTLZ7, WGF1–WFG9, UF1–UF10, and CF1–CF10), and measured using two widely used indicators—inverted generational distance (IGD) and hypervolume (HV). Experiment results demonstrate that NSGA-II-BnF exhibits superior performance to most of the algorithms on all test problems.

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Improved Particle Swarm Optimizer with Dynamically Adjusted Search Space and Velocity Limits for Global Optimization

International Journal of Artificial Intelligence Tools ◽

10.1142/s0218213015500177 ◽

2015 ◽

Vol 24 (05) ◽

pp. 1550017 ◽

Cited By ~ 1

Author(s):

Aderemi Oluyinka Adewumi ◽

Akugbe Martins Arasomwan

Keyword(s):

Global Optimization ◽

Optimization Problems ◽

Particle Swarm ◽

Pso Algorithm ◽

Search Space ◽

Particle Swarm Optimizer ◽

Search Range ◽

Original Algorithm ◽

Inertia Weight ◽

And Performance

This paper presents an improved particle swarm optimization (PSO) technique for global optimization. Many variants of the technique have been proposed in literature. However, two major things characterize many of these variants namely, static search space and velocity limits, which bound their flexibilities in obtaining optimal solutions for many optimization problems. Furthermore, the problem of premature convergence persists in many variants despite the introduction of additional parameters such as inertia weight and extra computation ability. This paper proposes an improved PSO algorithm without inertia weight. The proposed algorithm dynamically adjusts the search space and velocity limits for the swarm in each iteration by picking the highest and lowest values among all the dimensions of the particles, calculates their absolute values and then uses the higher of the two values to define a new search range and velocity limits for next iteration. The efficiency and performance of the proposed algorithm was shown using popular benchmark global optimization problems with low and high dimensions. Results obtained demonstrate better convergence speed and precision, stability, robustness with better global search ability when compared with six recent variants of the original algorithm.

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Modified Particle Swarm Optimization with Chaotic Initialization Scheme for Unconstrained Optimization Problems

Mekatronika ◽

10.15282/mekatronika.v3i1.7150 ◽

2021 ◽

Vol 3 (1) ◽

pp. 35-43

Author(s):

K. M. Ang ◽

Z. S. Yeap ◽

C. E. Chow ◽

W. Cheng ◽

W. H. Lim

Keyword(s):

Particle Swarm Optimization ◽

Optimization Problems ◽

Experimental Studies ◽

Particle Swarm ◽

Test Problems ◽

Initial Population ◽

Swarm Optimization ◽

Modified Particle Swarm Optimization ◽

Initialization Scheme ◽

Chaotic Initialization

Different variants of particle swarm optimization (PSO) algorithms were introduced in recent years with various improvements to tackle different types of optimization problems more robustly. However, the conventional initialization scheme tends to generate an initial population with relatively inferior solution due to the random guess mechanism. In this paper, a PSO variant known as modified PSO with chaotic initialization scheme is introduced to solve unconstrained global optimization problems more effectively, by generating a more promising initial population. Experimental studies are conducted to assess and compare the optimization performance of the proposed algorithm with four existing well-establised PSO variants using seven test functions. The proposed algorithm is observed to outperform its competitors in solving the selected test problems.

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A Particle Swarm Optimizer for Constrained Multiobjective Optimization

Research Methods ◽

10.4018/978-1-4666-7456-1.ch054 ◽

2015 ◽

pp. 1246-1276

Author(s):

Wen Fung Leong ◽

Yali Wu ◽

Gary G. Yen

Keyword(s):

Multiobjective Optimization ◽

Optimization Problems ◽

Particle Swarm ◽

Optimal Solution ◽

Constraint Handling ◽

Benchmark Problems ◽

Particle Swarm Optimizer ◽

Multiobjective Optimization Problems ◽

Feasible Solutions ◽

Constrained Multiobjective Optimization

Generally, constraint-handling techniques are designed for evolutionary algorithms to solve Constrained Multiobjective Optimization Problems (CMOPs). Most Multiojective Particle Swarm Optimization (MOPSO) designs adopt these existing constraint-handling techniques to deal with CMOPs. In this chapter, the authors present a constrained MOPSO in which the information related to particles' infeasibility and feasibility status is utilized effectively to guide the particles to search for feasible solutions and to improve the quality of the optimal solution found. The updating of personal best archive is based on the particles' Pareto ranks and their constraint violations. The infeasible global best archive is adopted to store infeasible nondominated solutions. The acceleration constants are adjusted depending on the personal bests' and selected global bests' infeasibility and feasibility statuses. The personal bests' feasibility statuses are integrated to estimate the mutation rate in the mutation procedure. The simulation results indicate that the proposed constrained MOPSO is highly competitive in solving selected benchmark problems.

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An Adaptive Multi-Swarm Competition Particle Swarm Optimizer for Large-Scale Optimization

Mathematics ◽

10.3390/math7060521 ◽

2019 ◽

Vol 7 (6) ◽

pp. 521 ◽

Cited By ~ 6

Author(s):

Fanrong Kong ◽

Jianhui Jiang ◽

Yan Huang

Keyword(s):

Large Scale ◽

Optimization Problems ◽

Particle Swarm ◽

The Other ◽

Large Scale Optimization ◽

Particle Swarm Optimizer ◽

Competition Mechanism ◽

Benchmark Suite ◽

Scale Optimization ◽

The One

As a powerful tool in optimization, particle swarm optimizers have been widely applied to many different optimization areas and drawn much attention. However, for large-scale optimization problems, the algorithms exhibit poor ability to pursue satisfactory results due to the lack of ability in diversity maintenance. In this paper, an adaptive multi-swarm particle swarm optimizer is proposed, which adaptively divides a swarm into several sub-swarms and a competition mechanism is employed to select exemplars. In this way, on the one hand, the diversity of exemplars increases, which helps the swarm preserve the exploitation ability. On the other hand, the number of sub-swarms adaptively changes from a large value to a small value, which helps the algorithm make a suitable balance between exploitation and exploration. By employing several peer algorithms, we conducted comparisons to validate the proposed algorithm on a large-scale optimization benchmark suite of CEC 2013. The experiments results demonstrate the proposed algorithm is effective and competitive to address large-scale optimization problems.

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An Entropy-Assisted Particle Swarm Optimizer for Large-Scale Optimization Problem

Mathematics ◽

10.3390/math7050414 ◽

2019 ◽

Vol 7 (5) ◽

pp. 414 ◽

Cited By ~ 3

Author(s):

Weian Guo ◽

Lei Zhu ◽

Lei Wang ◽

Qidi Wu ◽

Fanrong Kong

Keyword(s):

Large Scale ◽

Optimization Problems ◽

Particle Swarm ◽

Large Scale Optimization ◽

Particle Swarm Optimizer ◽

Fitness Evaluation ◽

Diversity Maintenance ◽

Entropy Measurement ◽

Benchmark Suite ◽

Scale Optimization

Diversity maintenance is crucial for particle swarm optimizer’s (PSO) performance. However, the update mechanism for particles in the conventional PSO is poor in the performance of diversity maintenance, which usually results in a premature convergence or a stagnation of exploration in the searching space. To help particle swarm optimization enhance the ability in diversity maintenance, many works have proposed to adjust the distances among particles. However, such operators will result in a situation where the diversity maintenance and fitness evaluation are conducted in the same distance-based space. Therefore, it also brings a new challenge in trade-off between convergence speed and diversity preserving. In this paper, a novel PSO is proposed that employs competitive strategy and entropy measurement to manage convergence operator and diversity maintenance respectively. The proposed algorithm was applied to the large-scale optimization benchmark suite on CEC 2013 and the results demonstrate the proposed algorithm is feasible and competitive to address large scale optimization problems.

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A Culture-Based Particle Swarm Optimization Framework for Dynamic, Constrained Multi-Objective Optimization

International Journal of Swarm Intelligence Research ◽

10.4018/jsir.2012010101 ◽

2012 ◽

Vol 3 (1) ◽

pp. 1-29 ◽

Cited By ~ 4

Author(s):

Ashwin A. Kadkol ◽

Gary G. Yen

Keyword(s):

Particle Swarm Optimization ◽

Transfer Functions ◽

Optimization Problems ◽

Particle Swarm ◽

Parameter Tuning ◽

Cultural Algorithms ◽

Swarm Optimization ◽

Objective Space ◽

Computationally Intensive ◽

Available Information

Real-world optimization problems are often dynamic, multiple objective in nature with various constraints and uncertainties. This work proposes solving such problems by systematic segmentation via heuristic information accumulated through Cultural Algorithms. The problem is tackled by maintaining 1) feasible and infeasible best solutions and their fitness and constraint violations in the Situational Space, 2) objective space bounds for the search in the Normative Space, 3) objective space crowding information in the Topographic Space, and 4) function sensitivity and relocation offsets (to reuse available information on optima upon change of environments) in the Historical Space of a cultural framework. The information is used to vary the flight parameters of the Particle Swarm Optimization, to generate newer individuals and to better track dynamic and multiple optima with constraints. The proposed algorithm is validated on three numerical optimization problems. As a practical application case study that is computationally intensive and complex, parameter tuning of a PID (Proportional–Integral–Derivative) controller for plants with transfer functions that vary with time and imposed with robust optimization criteria has been used to demonstrate the effectiveness and efficiency of the proposed design.

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