A Multi-objective Time-Linkage Approach for Dynamic Optimization Problems with Previous-Solution Displacement Restriction

Many real world problems are dynamic and multi-objective, which requires an optimisation algorithm to be able to continuously track the changing Pareto optimal set (POS) and Pareto optimal front (POF) over time. In this paper, a new variant of particle swarm optimisation (PSO) has been specifically designed by adaptively switching from competitive model to cooperative model to track for both POS and POF. In the proposed method, the competition is used to explore the search space, while the cooperation is applied to exploit the search space. The dynamic multi-objective functions are constructed to test the performance of the proposed algorithm. Both theoretical analysis and the numerical experiment have shown that the proposed algorithm is an excellent alternative for solving the dynamic multi-objective optimisation problems. Finally, the proposed method has been applied to the tuning of the parameters of PID controller for dynamic system in which a satisfactory control is obtained.

A novel hybrid adaptive collaborative approach based on particle swarm optimization and local search for dynamic optimization problems

A dual-population multi operators harmony search algorithm for dynamic optimization problems

Optimization issues are often defined statically, assuming constant environmental conditions.However, in many real-world scenarios, problem environments are dynamic and continuously changing.Thus we need optimization algorithms that could solves those issues in dynamic environments as well.Dynamic optimization problems are change(s) that may occur through the time.Such environments are characterized by uncertainty, temporal changes, and structural complexities, which makes the optimization process a significant challenge.In addressing these challenges, evolutionary algorithms have emerged as one of the most effective approaches for solving dynamic optimization problems (DOPs).Among these algorithms, the Imperialist Competitive Algorithm (ICA), designed based on swarm intelligence and competition among imperialist countries, has garnered considerable attention due to its capability in solving static optimization issues.In this research, Imperialist Competitive Algorithms, inspired by the historical and political processes of colonization and assimilation, have been known as one of the efficient evolutionary algorithms.These algorithms face numerous challenges when dealing with dynamic problems , including reduced population diversity, performance degradation in conditions of rapid environmental changes, and limitations in optimal convergence.These cases indicate the need to develop improved and more adaptable versions of these algorithms.Using concepts such as memory, population clustering, and repulsion mechanisms, this algorithm has been able to maintain population diversity at all stages while increasing the speed of convergence in the face of environmental changes.The key feature of the proposed algorithm is the use of memory to store previous optimal solutions, a clustering mechanism to manage population diversity, and repulsion to prevent unnecessary accumulation of solutions in specific regions.Nevertheless, ICA exhibits poor performance in dynamic environments because it lacks mechanisms to maintain diversity, quick adaptation to environmental changes, and new optima track.This study presents an improved version of ICA aimed at overcoming these limitations.The proposed algorithm incorporates a combination of a memory mechanism and a clustering strategy to enhance its adaptability to environmental changes and preserve diversity within the population.The memory mechanism stores information about previous optima and utilizes it under appropriate conditions to accelerate the optimization process.forclustering method is used for clustering.Clustering in the proposed method ensures that diversity is maintained for the population during the execution of the algorithm.In this study, our goal is to solve problems that change the environment in a global way.That means, the fitness of all points in the environment changes.By testing just one point in the environment and comparing the fitness obtained with its previously stored value, we can detect a change in the environment.On the other hand, the clustering strategy, particularly the k-means technique, to maintain maintain population diversity and prevents the convergence of solutions to specific regions.Together, these two components create a balance between exploration and exploitation, thereby improving the algorithm's performance in dynamic environments.To evaluate the performance of the proposed algorithm, the Moving Peaks Benchmark (MPB) was used as a standard metric.Due to its capability to simulate complex and diverse changes in dynamic environmentsparticularly in Branke's second scenario-MPB is one of the most recognized tools for assessing the performance of dynamic optimization algorithms.The proposed algorithm was evaluated alongside advanced algorithms such as FTmPSO (TMO), RAmQSO-s4, RmNAFSA-s4, TFTmPSO, RFTmPSO, mQSO10 (5+5q), FMSO, CellularPSO, Multi-SwarmPSO, mCPSO, AmQSO*, FTMPSO, almPSO, and CDEPSA.Experimental results demonstrated that the proposed algorithm outperformed other methods in areas such as convergence speed, adaptability to environmental changes, and population diversity preservation.A key feature of the proposed algorithm is its ability to retain identified optima even after environmental changes.Additionally, the use of the k-means clustering technique has ensured that the algorithm effectively avoids excessive focus on specific regions and maintains population diversity while facing complex environmental changes.Another advantage of this algorithm is its scalability in handling dynamic optimization issues with high dimensions and complexities.These findings indicate that the proposed algorithm is not only effective in laboratory settings but also suitable for real-world applications with fast and dynamic changes.

The particle swarm optimization (PSO) algorithm has successfully been applied to dynamic optimization problems with very competitive results. One of its best performing variants is the one based on the atomic model, with quantum and trajectory particles. However, there is no precise knowledge on how these particles contribute to the global behavior of the swarms during the optimization process. This work analyzes several aspects of each type of particle, including the best combination of them for different scenarios, and how many times do they contribute to the swarm’s best. Results show that, for the Moving Peaks Benchmark (MPB), a higher number of trajectory particles than quantum particles is the best strategy. Quantum particles are most helpful immediately after a change in the environment has occurred, while trajectory particles lead the optimization in the final stages. Suggestions on how to use this knowledge for future developments are also provided.KeywordsParticle Swarm OptimizationTrajectory ParticleParticle PropertyQuantum ParticleDynamic Optimization ProblemThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Dynamic multiobjective optimization problem (DMOP) is a class of complex dynamic optimization problem (DOP), its widely exists in many real-world problems. Firstly, an core estimation of distribution model which used to approximately estimate the Pareto solution in the next environment is given, when a change in the environment is detected, the algorithm uses the collected information from the previous searching environments to predict the location of the Pareto solution in the next environment. Furthermore, a dynamic multiobjective optimization evolutionary algorithm with core estimation of distribution is proposed. The computer simulations are made on two dynamic multiobjective optimization problems, and the results indicate the proposed algorithm is effective.

In recent years, there has been a growing interest in the study of particle swarm optimization (PSO) in dynamic environments. This paper presents a new PSO model, called PSO with composite particles (PSO-CP), to address dynamic optimization problems. PSO-CP partitions the swarm into a set of composite particles based on their similarity using a "worst first" principle. Inspired by the composite particle phenomenon in physics, the elementary members in each composite particle interact via a velocity-anisotropic reflection scheme to integrate valuable information for effectively and rapidly finding the promising optima in the search space. Each composite particle maintains the diversity by a scattering operator. In addition, an integral movement strategy is introduced to promote the swarm diversity. Experiments on a typical dynamic test benchmark problem provide a guideline for setting the involved parameters and show that PSO-CP is efficient in comparison with several state-of-the-art PSO algorithms for dynamic optimization problems.

Brain Storm Optimization (BSO), which is an effective swarm intelligence method inspired by the human brainstorming process, has shown promising results in solving static optimization problems. However, The search spaces of many real-world problems change over time, in which the original BSO and its variants are not able to cope with. This paper extends BSO as an adaptive multi-population based algorithm, i.e., mBSO, to solve dynamic optimization problems (DOPs). Firstly, a modified BSO, which uses new update mechanisms independent from the maximum number of iterations and objective space grouping method, is proposed. Then, the modified BSO is embedded in a multi-population framework. Several mechanisms such as convergence detection, exclusion, and re-diversification are employed to address the challenging issues of DOPs. The moving peaks benchmark (MPB) is used to evaluate the performance of mBSO along with comparison with other state-of-the-art methods. The outcome indicates the efficiency of the proposed mBSO in locating optima and tracking them after environmental changes.

Optimisation in dynamic environments is a very active and important area which tackles problems that change with time (as most real-world problems do). The possibility to use a new centralised cooperative strategy based on trajectory methods (tabu search) for solving Dynamic Optimisation Problems (DOPs) was previously introduced showing good results against state of the art methods like the Particle Swarm Optimisation (PSO) variant with multiple swarms and different types of particles. The analysis of this previous work are further extended here by exploring more possibilities for the cooperation rules used in the strategy. The results show that different classes of cooperation can lead to quite different results, some of them greatly outperforming the previous ones.

Quantum particles-enhanced multiple Harris Hawks swarms for dynamic optimization problems

The exclusion operator is a key component in separating the search territory of each population in multi-population optimisation algorithms for unconstraint continues dynamic optimisation problems (DOPs) with the aim of maintaining the overall diversity of the population and avoiding redundant search. Although extensively used by the researchers, the role of exclusion has been barely studied in detail. Therefore, in this paper, we solely study the role of exclusion as a part of multi-population methods in DOPs. For this purpose, a comprehensive review of the various exclusion strategies reported in the literature is provided. Four strategies are also introduced to reduce the shortcomings of exclusion operator. Experimental results show that proposed strategies compared to other schemes such as reinitialized midpoint check, hill-valley detection with three checkpoints, and merging information of collided populations have the same or even higher ability to improve the performance of the multi-swarm PSO algorithms in moving peaks benchmark.

Adaptive genetic algorithms applied to dynamic multiobjective problems

In the last years, there has been a large growth in the research of computational techniques inspired in nature. This area, named Bioinspired Computing, has provided biologically motivated solutions for several real world problems. Among Bioinspired Computing techniques, one can mention Artificial Neural Networks (ANN), Evolutionary Algorithms (EA), Artificial Immune Systems (AIS) and Ant Colony Optimization (ACO). ACO is a meta-heuristic based on the structure and behavior of ant colonies. It has been successfully applied to several optimization problems. Several real world optimization problems may change the configuration of its search space with time. These problems are known as dynamic optimization problems. This chapter presents the main concepts of ACO and show how it can be applied to solve real optimization problems on dynamic environments. As a case study, it will be illustrated how ACO can be applied to process scheduling problems. The chapter starts describing how real ants forage for food, environmental modifications related to this activity (for example, the blockage of a path) and the effects of these modifications in the colony. After, a brief review of previous works on Ant Colony Optimization is presented. For computer simulations, the activities of an ant colony may be modeled as a graph. After modeling the problem of foraging for food (as a graph), the goal (finding the shortest path at a given moment) is defined and the mechanism to solve the problem is presented. The need to model an on-line problem as a graph, the goal of finding the shortest path and the mechanisms adopted for solving the problem (an adapted version of the AntSystem) are detailed. Before ACO is applied to the process scheduling problem, the problem is analyzed and modeled using a graph representation. Next, simulation results obtained in a set of experiments are presented, which are validated by results obtained in a real implementation. Important issues related with the use of ACO for process scheduling, like parameter adjustments, are discussed. In the conclusion of this chapter, we point out a few future directions for ACO researches. The use of computational techniques inspired in nature has become very frequent in the last years. This area, named Bioinspired Computing, provides efficient biologically motivated

Aiming to dynamic optimization problems (DOPs), this paper develops a novel general distributed multiple populations (DMP) framework for evolutionary algorithms (EAs). DMP employs six strategies designed in three levels (i.e., population-level, subpopulation-level, and individual-level) to deal with different kinds of DOPs. First, the population-level subpopulation division estimation strategy in initialization phase rationally divides the whole population into several subpopulations to explore distinct subareas of search space sufficiently. Then, during the steady evolutionary process, diversity preservation in individual-level and population-level accelerates the responsiveness of the whole population to a new landscape, while subpopulation-level self-learning of elitist individuals promotes the exploitation of promising areas. Moreover, in subpopulation-level, the archive quality assurance technique avoids repeat exploring the same peaks by storing the locations of different peaks with low redundancy. When landscape variation occurs, in population-level, historical information containing excellent evolutionary pattern is recorded to guide the population evolution better in the new environment. DMP framework is easy to implement in various EAs due to its well generality and independence about operators and parameters of the embedded algorithm. Four DMP-EAs are accomplished in this paper whose basic algorithms are particle swarm optimization (PSO) and differential evolution (DE) with different settings. The performance of the four proposed DMP-EAs is evaluated on all the widely used complex DOP benchmarks from CEC 2009. The testing results indicate that the DMP-EAs generally significantly outperform many state-of-the-art dynamic EAs (DEAs) on most of DOP benchmarks.

Many of optimization problems possess dynamic characteristics. Introducing strategies to maintain population diversity plays a key role in Dynamic Optimization Problems (DOPs), thus making the balance of exploration ability and the exploitation ability of the proposed algorithm. In this study, a crowding based differential evolution, combined with self-adaptive control parameters (CaDE)was proposed. Our proposed method adopts crowding with the least individual within a predefined neighborhood radius, and the control parameters are self-adaptive during the evolution process. For comparative analysis, several schemes incorporated with differential evolution are tested on a widely used moving peaks benchmark (MPB). Performance of the proposed algorithm is validated on the selected benchmark function in each circumstance.