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.

Fake account detection is a topical issue when many Online Social Networks encounter several issues caused by the growing number of unethical online activities. This study presents a new Quantum Beta-behaved Multi-Objective Particle Swarm Optimization (QB-MOPSO) algorithm for machine learning based Twitter fake accounts detection. The proposed approach aims to improve the learning process of deep neural networks, random forest, through minimizing simultaneously the feature dimensionality and the classification error rate. The main contribution consists in proposing a quantum beta MOPSO to handle the training phase of neural and deep architectures. The QB-MOPSO is used to perform a multi-objective training of the random forest algorithm. The QB-MOPSO has two optimization profiles: the first one uses a quantum-behaved equation for improving the exploratory behaviour of PSO, while the second one uses a beta function to enhance PSO’s exploitation. An extensive experimental study is carried out using two open Twitter datasets with 1982 and 928 accounts. The new proposal is a random forest QB-MOPSO. Results showed that random forest QB-MOPSO accuracy is about 99.19% and 97.52% accounts on datasets 1 and 2. Comparative analysis of the prosed architecture toward the original architecture showed that the use of QB-MOPSO for learning enhances the random forest algorithm which perform then the original ones.

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.

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.

Dynamic multi-objective optimization problems (DMOPs) and Many-Objective Optimization Problems (MaOPs) are two classes of the optimization filed which have potential applications in engineering. Modified Multi-Objective Evolutionary Algorithms hybrid approaches seem to be suitable to effectively deal with such problems. However, the Crow Search Algorithm has not yet considered for both DMOP and MaOP. This paper proposes a Distributed Bi-behaviorsCrow Search Algorithm (DB-CSA) with two different mechanisms, one corresponding to the search behavior and another to the exploitative behavior with a dynamic switch mechanism. The bi-behaviors CSA chasing profile is defined based on a large Gaussian-like Beta-1 function which ensures diversity enhancement, while the narrow Gaussian Beta-2 function is used to improve the solution tuning and convergence behavior. The DB-CSA approach is developed to solve several types of DMOPs and a set of MaOPs with 2, 3, 5, 7, 8, 10 and 15 objectives. The Inverted General Distance, the Mean Inverted General Distance and the Hypervolume Difference are the main measurement metrics are used to compare the DB-CSA approach to the state-of-the-art MOEAs. All quantitative results are analyzed using the nonparametric Wilcoxon signed rank test with 0.05 significance level which proving the efficiency of the proposed method for solving both 44 DMOPs and MaOPs utilized.