A novel Dynamic Pareto bi-level Multi-Objective Particle Swarm Optimization (DPb-MOPSO) algorithm

Optimization Problems ◽

Particle Swarm ◽

Search Space ◽

Response Strategy ◽

Pareto Optimal ◽

Distributed Architecture ◽

Swarm Optimization ◽

Multi Objective ◽

Pareto Optimal Set

Distributed architecture-based Particle Swarm Optimization is very useful for static optimization and not yet explored to solve complex dynamic multi-objective optimization problems. This study proposes a novel Dynamic Pareto bi-level Multi-Objective Particle Swarm Optimization (DPb-MOPSO) algorithm with two optimization levels. In the first level, all solutions are optimized in the same search space and the second level is based on a distributed architecture using the Pareto ranking operator for dynamic multi-swarm subdivision. The proposed approach adopts a dynamic handling strategy using a set of detectors to keep track of change in the objective function that is impacted by the problem’s time-varying parameters at each level. To ensure timely adaptation during the optimization process, a dynamic response strategy is considered for the reevaluation of all non-improved solutions, while the worst particles are replaced with a newly generated one. The convergence and diversity performance of the DPb-MOPSO algorithm are proven through Friedman Analysis of Variance, and the Lyapunov theorem is used to prove stability analysis over the Inverted Generational Distance (IGD) and Hypervolume Difference (HVD) metrics. Compared to other evolutionary algorithms, the novel DPb-MOPSO is shown to be most robust for solving complex problems over a range of changes in both the Pareto Optimal Set and Pareto Optimal Front.

DPb-MOPSO: A Novel Dynamic Pareto bi-level Multi-Objective Particle Swarm Optimization Algorithm

10.36227/techrxiv.17207576 ◽

2021 ◽

Author(s):

Ahlem Aboud ◽

Nizar Rokbani ◽

Raja Fdhila ◽

Abdulrahman M. Qahtani ◽

Omar Almutiry ◽

...

Keyword(s):

Environmental Changes ◽

Dynamic Change ◽

Particle Swarm ◽

Search Space ◽

Response Strategy ◽

Parallel Optimization ◽

Pareto Optimal ◽

Swarm Optimization ◽

Particle swarm optimization system based on the distributed architecture has shown its efficiency for static optimization and has not been studied to solve dynamic multiobjective problems (DMOPs). When solving DMOP, tracking the best solutions over time and ensuring good exploitation and exploration are the main challenging tasks. This study proposes a novel Dynamic Pareto bi-level Multi-Objective Particle Swarm Optimization (DPb-MOPSO) algorithm including two parallel optimization levels. At the first level, all solutions are managed in a single search space. When a dynamic change is successfully detected, the Pareto ranking operator is used to enable a multiswarm subdivisions and processing which drives the second level of enhanced exploitation. A dynamic handling strategy based on random detectors is used to track the changes of the objective function due to time-varying parameters. A response strategy consisting in re-evaluate all unimproved solutions and replacing them with newly generated ones is also implemented. Inverted generational distance, mean inverted generational distance, and hypervolume difference metrics are used to assess the DPb-MOPSO performances. All quantitative results are analyzed using Friedman's analysis while the Lyapunov theorem is used for stability analysis. Compared with several multi-objective evolutionary algorithms, the DPb-MOPSO is robust in solving 21 complex problems over a range of changes in both the Pareto optimal set and Pareto optimal front. For 13 UDF and ZJZ functions, DPb-MOPSO can solve 8/13 and 7/13 on IGD and HVD with moderate changes. For the 8 FDA and dMOP benchmarks, DPb-MOPSO was able to resolve 4/8 with severe change on MIGD, and 5/8 for moderate and slight changes. However, for the 3 kind of environmental changes, DPb-MOPSO assumes 4/8 of the solving function on IGD and HVD.

DPb-MOPSO: A Novel Dynamic Pareto bi-level Multi-Objective Particle Swarm Optimization Algorithm

10.36227/techrxiv.13325354.v2 ◽

2022 ◽

Author(s):

Ahlem Aboud ◽

Nizar Rokbani ◽

Raja Fdhila ◽

Abdulrahman M. Qahtani ◽

Omar Almutiry ◽

...

Keyword(s):

Environmental Changes ◽

Dynamic Change ◽

Particle Swarm ◽

Search Space ◽

Response Strategy ◽

Parallel Optimization ◽

Pareto Optimal ◽

Swarm Optimization ◽

Particle swarm optimization system based on the distributed architecture over multiple sub-swarms has shown its efficiency for static optimization and has not been studied to solve dynamic multi-objective problems (DMOPs). When solving DMOP, tracking the best solutions over time and ensuring good exploitation and exploration are the main challenging tasks. This study proposes a novel Dynamic Pareto bi-level Multi-Objective Particle Swarm Optimization (DPb-MOPSO) algorithm including two parallel optimization levels. At the first level, all solutions are managed in a single search space. When a dynamic change is successfully detected in the objective values, the Pareto ranking operator is used to enable a multiple sub-swarm’ subdivisions and processing which drives the second level of enhanced exploitation. A dynamic handling strategy based on random detectors is used to track the changes of the objective function due to time-varying parameters. A response strategy consisting in re-evaluate all unimproved solutions and replacing them with newly generated ones is also implemented. Inverted generational distance, mean inverted generational distance, and hypervolume difference metrics are used to assess the DPb-MOPSO performances. All quantitative results are analyzed using Friedman's analysis of variance while the Lyapunov theorem is used for stability analysis. Compared with several multi-objective evolutionary algorithms, the DPb-MOPSO is robust in solving 21 complex problems over a range of changes in both the Pareto optimal set and Pareto optimal front. For 13 UDF and ZJZ functions, DPb-MOPSO can solve 8/13 and 7/13 on IGD and HVD with moderate changes. For the 8 FDA and dMOP benchmarks, DPb-MOPSO was able to resolve 4/8 with severe change on MIGD, and 5/8 for moderate and slight changes. However, for the 3 kind of environmental changes, DPb-MOPSO assumes 4/8 of the solving function on IGD and HVD metrics.

DPb-MOPSO: A Novel Dynamic Pareto bi-level Multi-Objective Particle Swarm Optimization Algorithm

10.36227/techrxiv.17207576.v1 ◽

2021 ◽

Author(s):

Ahlem Aboud ◽

Nizar Rokbani ◽

Raja Fdhila ◽

Abdulrahman M. Qahtani ◽

Omar Almutiry ◽

...

Keyword(s):

Environmental Changes ◽

Dynamic Change ◽

Particle Swarm ◽

Search Space ◽

Response Strategy ◽

Parallel Optimization ◽

Pareto Optimal ◽

Swarm Optimization ◽

Particle swarm optimization system based on the distributed architecture has shown its efficiency for static optimization and has not been studied to solve dynamic multiobjective problems (DMOPs). When solving DMOP, tracking the best solutions over time and ensuring good exploitation and exploration are the main challenging tasks. This study proposes a novel Dynamic Pareto bi-level Multi-Objective Particle Swarm Optimization (DPb-MOPSO) algorithm including two parallel optimization levels. At the first level, all solutions are managed in a single search space. When a dynamic change is successfully detected, the Pareto ranking operator is used to enable a multiswarm subdivisions and processing which drives the second level of enhanced exploitation. A dynamic handling strategy based on random detectors is used to track the changes of the objective function due to time-varying parameters. A response strategy consisting in re-evaluate all unimproved solutions and replacing them with newly generated ones is also implemented. Inverted generational distance, mean inverted generational distance, and hypervolume difference metrics are used to assess the DPb-MOPSO performances. All quantitative results are analyzed using Friedman's analysis while the Lyapunov theorem is used for stability analysis. Compared with several multi-objective evolutionary algorithms, the DPb-MOPSO is robust in solving 21 complex problems over a range of changes in both the Pareto optimal set and Pareto optimal front. For 13 UDF and ZJZ functions, DPb-MOPSO can solve 8/13 and 7/13 on IGD and HVD with moderate changes. For the 8 FDA and dMOP benchmarks, DPb-MOPSO was able to resolve 4/8 with severe change on MIGD, and 5/8 for moderate and slight changes. However, for the 3 kind of environmental changes, DPb-MOPSO assumes 4/8 of the solving function on IGD and HVD.

A Distributed Multifactorial Particle Swarm Optimization Approach

10.36227/techrxiv.17260040 ◽

2021 ◽

Author(s):

Ahlem Aboud ◽

Nizar Rokbani ◽

Seyedali Mirjalili ◽

Abdulrahman M. Qahtani ◽

Omar Almutiry ◽

...

Keyword(s):

Optimization Problems ◽

Beta Function ◽

Particle Swarm ◽

Search Space ◽

Optimization Approach ◽

Multi Objective Optimization ◽

Swarm Optimization ◽

Multi Objective ◽

New System

Multifactorial Optimization (MFO) and Evolutionary Transfer Optimization (ETO) are new optimization challenging paradigms for which the multi-Objective Particle Swarm Optimization system (MOPSO) may be interesting despite limitations. MOPSO has been widely used in static/dynamic multi-objective optimization problems, while its potentials for multi-task optimization are not completely unveiled. This paper proposes a new Distributed Multifactorial Particle Swarm Optimization algorithm (DMFPSO) for multi-task optimization. This new system has a distributed architecture on a set of sub-swarms that are dynamically constructed based on the number of optimization tasks affected by each particle skill factor. DMFPSO is designed to deal with the issues of handling convergence and diversity concepts separately. DMFPSO uses Beta function to provide two optimized profiles with a dynamic switching behaviour. The first profile, Beta-1, is used for the exploration which aims to explore the search space toward potential solutions, while the second Beta-2 function is used for convergence enhancement. This new system is tested on 36 benchmarks provided by the CEC’2021 Evolutionary Transfer Multi-Objective Optimization Competition. Comparatives with the state-of-the-art methods are done using the Inverted General Distance (IGD) and Mean Inverted General Distance (MIGD) metrics. Based on the MSS metric, this proposal has the best results on most tested problems.

A Distributed Multifactorial Particle Swarm Optimization Approach

10.36227/techrxiv.17260040.v1 ◽

2021 ◽

Author(s):

Ahlem Aboud ◽

Nizar Rokbani ◽

Seyedali Mirjalili ◽

Abdulrahman M. Qahtani ◽

Omar Almutiry ◽

...

Keyword(s):

Optimization Problems ◽

Beta Function ◽

Particle Swarm ◽

Search Space ◽

Optimization Approach ◽

Multi Objective Optimization ◽

Swarm Optimization ◽

Multi Objective ◽

New System

Multifactorial Optimization (MFO) and Evolutionary Transfer Optimization (ETO) are new optimization challenging paradigms for which the multi-Objective Particle Swarm Optimization system (MOPSO) may be interesting despite limitations. MOPSO has been widely used in static/dynamic multi-objective optimization problems, while its potentials for multi-task optimization are not completely unveiled. This paper proposes a new Distributed Multifactorial Particle Swarm Optimization algorithm (DMFPSO) for multi-task optimization. This new system has a distributed architecture on a set of sub-swarms that are dynamically constructed based on the number of optimization tasks affected by each particle skill factor. DMFPSO is designed to deal with the issues of handling convergence and diversity concepts separately. DMFPSO uses Beta function to provide two optimized profiles with a dynamic switching behaviour. The first profile, Beta-1, is used for the exploration which aims to explore the search space toward potential solutions, while the second Beta-2 function is used for convergence enhancement. This new system is tested on 36 benchmarks provided by the CEC’2021 Evolutionary Transfer Multi-Objective Optimization Competition. Comparatives with the state-of-the-art methods are done using the Inverted General Distance (IGD) and Mean Inverted General Distance (MIGD) metrics. Based on the MSS metric, this proposal has the best results on most tested problems.

Movement Strategies for Multi-Objective Particle Swarm Optimization

International Journal of Applied Metaheuristic Computing ◽

10.4018/jamc.2010070105 ◽

2010 ◽

Vol 1 (3) ◽

pp. 59-79 ◽

Cited By ~ 25

Author(s):

S. Nguyen ◽

V. Kachitvichyanukul

Keyword(s):

Optimization Problems ◽

Particle Swarm ◽

Pso Algorithm ◽

Search Space ◽

Movement Behavior ◽

Test Problems ◽

Swarm Optimization ◽

Multi Objective ◽

Movement Strategies

Particle Swarm Optimization (PSO) is one of the most effective metaheuristics algorithms, with many successful real-world applications. The reason for the success of PSO is the movement behavior, which allows the swarm to effectively explore the search space. Unfortunately, the original PSO algorithm is only suitable for single objective optimization problems. In this paper, three movement strategies are discussed for multi-objective PSO (MOPSO) and popular test problems are used to confirm their effectiveness. In addition, these algorithms are also applied to solve the engineering design and portfolio optimization problems. Results show that the algorithms are effective with both direct and indirect encoding schemes.

Multi-objective clustering algorithm using particle swarm optimization with crowding distance (MCPSO-CD)

International Journal of Advances in Intelligent Informatics ◽

10.26555/ijain.v6i1.366 ◽

2020 ◽

Vol 6 (1) ◽

pp. 72

Author(s):

Alwatben Batoul Rashed ◽

Hazlina Hamdan ◽

Nurfadhlina Mohd Sharef ◽

Md Nasir Sulaiman ◽

Razali Yaakob ◽

...

Keyword(s):

Clustering Algorithm ◽

Optimization Problems ◽

Particle Swarm ◽

Optimal Solution ◽

Solution Technique ◽

Pareto Optimal ◽

Swarm Optimization ◽

Multi Objective ◽

Crowding Distance

Clustering, an unsupervised method of grouping sets of data, is used as a solution technique in various ﬁelds to divide and restructure data to become more signiﬁcant and transform them into more useful information. Generally, clustering is difﬁcult and complex phenomenon, where the appropriate numbers of clusters are always unknown, comes with a large number of potential solutions, and as well the datasets are unsupervised. These problems can be addressed by the Multi-Objective Particle Swarm Optimization (MOPSO) approach, which is commonly used in addressing optimization problems. However, MOPSO algorithm produces a group of non-dominated solutions which make the selection of an “appropriate” Pareto optimal or non-dominated solution more difficult. According to the literature, crowding distance is one of the most efficient algorithms that was developed based on density measures to treat the problem of selection mechanism for archive updates. In an attempt to address this problem, the clustering-based method that utilizes crowding distance (CD) technique to balance the optimality of the objectives in Pareto optimal solution search is proposed. The approach is based on the dominance concept and crowding distances mechanism to guarantee survival of the best solution. Furthermore, we used the Pareto dominance concept after calculating the value of crowding degree for each solution. The proposed method was evaluated against five clustering approaches that have succeeded in optimization that comprises of K-means Clustering, MCPSO, IMCPSO, Spectral clustering, Birch, and average-link algorithms. The results of the evaluation show that the proposed approach exemplified the state-of-the-art method with significant differences in most of the datasets tested.

Movement Strategies for Multi-Objective Particle Swarm Optimization

Modeling, Analysis, and Applications in Metaheuristic Computing ◽

10.4018/978-1-4666-0270-0.ch008 ◽

2012 ◽

pp. 109-130

Author(s):

S. Nguyen ◽

V. Kachitvichyanukul

Keyword(s):

Optimization Problems ◽

Particle Swarm ◽

Search Space ◽

Movement Behavior ◽

Test Problems ◽

Swarm Optimization ◽

Multi Objective ◽

Movement Strategies ◽

Indirect Encoding

Particle Swarm Optimization (PSO) is one of the most effective metaheuristics algorithms, with many successful real-world applications. The reason for the success of PSO is the movement behavior, which allows the swarm to effectively explore the search space. Unfortunately, the original PSO algorithm is only suitable for single objective optimization problems. In this paper, three movement strategies are discussed for multi-objective PSO (MOPSO) and popular test problems are used to confirm their effectiveness. In addition, these algorithms are also applied to solve the engineering design and portfolio optimization problems. Results show that the algorithms are effective with both direct and indirect encoding schemes.

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

Multi-objective collaborative multidisciplinary design optimization using particle swarm techniques and fuzzy decision making

10.1177/0954406211432981 ◽

2012 ◽

Vol 226 (9) ◽

pp. 2281-2295 ◽

Cited By ~ 5

Author(s):

Mohammad Reza Farmani ◽

Jafar Roshanian ◽

Meisam Babaie ◽

Parviz M Zadeh

Keyword(s):

Design Optimization ◽

Multidisciplinary Design Optimization ◽

Optimization Problems ◽

Particle Swarm ◽

Collaborative Optimization ◽

Multidisciplinary Design ◽

Fuzzy Decision ◽

Swarm Optimization ◽

This article focuses on the efficient multi-objective particle swarm optimization algorithm to solve multidisciplinary design optimization problems. The objective is to extend the formulation of collaborative optimization which has been widely used to solve single-objective optimization problems. To examine the proposed structure, racecar design problem is taken as an example of application for three objective functions. In addition, a fuzzy decision maker is applied to select the best solution along the pareto front based on the defined criteria. The results are compared to the traditional optimization, and collaborative optimization formulations that do not use multi-objective particle swarm optimization. It is shown that the integration of multi-objective particle swarm optimization into collaborative optimization provides an efficient framework for design and analysis of hierarchical multidisciplinary design optimization problems.