A Distributed Multiple Populations Framework for Evolutionary Algorithm in Solving Dynamic Optimization Problems

In this paper we propose a self adaptive cluster based Differential Evolution (DE) algorithm to solve the Dynamic Optimization Problems (DOPs). We have enhanced the classical DE to perform better in dynamic environments by a powerful clustering technique. During evolution, the information gained by the particles of different clusters is exchanged by a self adaptive strategy. The information exchange is done by re-clustering, and the cluster number is updated adaptively throughout the optimization process. To detect the environment change a test particle is used. Moreover, to adapt the population in new environment an External Archive is also used. The performance of SACDEEA is evaluated on GDBG benchmark problems and compared with other existing algorithms.KeywordsDifferential EvolutionDynamic Optimization Problem (DOP)Self adaptive clustering

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

Particle Swarm Optimization or Differential Evolution—A comparison

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.

Dynamic optimization problems (DOPs) are problems that change over time and many real-world problems are classified as DOPs. However, most of investigations in this domain are focused on tracking moving optima (TMO) without considering any other objectives which creates a gap between real-world problems and academic research in this area. One of the important optimization objectives in many real-world problems is previous-solution displacement restriction (PSDR) in which successive solutions should not be much different. PSDRs can be categorized as a multi-objective problem in which the first objective is optimality and the second one is minimizing the displacement of consecutive solutions which also can represents switching cost. Moreover, PSDRs are counted as dynamic time-linkage problems (DTPs) because the current chosen solution by the optimizer will change the next search space. In this paper, we propose a new hybrid method based on particle swarm optimization (PSO) for PSDRs based on their characteristics. The experiments are done on moving peaks benchmark (MPB) and the performance of the proposed algorithm alongside two comparison ones are investigated on it.

Modified Differential Evolution with Locality induced Genetic Operators for dynamic optimization

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.

Dynamic multimodal optimization problems (DMMOPs) demand algorithms capable of swiftly locating and tracking multiple optimal solutions over time. The primary challenge lies in controlling the population diversity to facilitate effective exploration, all within the limitation of computational resources between consecutive environmental changes. In this paper, we study the utilization of density information derived from both current and historical populations to enhance exploration. First, for each active sub-population, we construct a density landscape based on the distribution of concurrently active sub-populations, and establish dominance relationships between candidate solutions in the sub-population based on density and fitness values, directing this sub-population towards exploring low-density promising areas. Then, for each converged sub-population, we construct a density landscape based on the distribution of sub-populations that have historically become extinct, guiding the restart of this sub-population in low-density unexploited areas. Finally, we develop a comprehensive framework of density-assisted evolutionary algorithm (DAEA), which encompasses density-assisted search and restart, also combined with initialization. Moreover, we employ prediction and memory strategies to enhance the performance of DAEA in dynamic environments. Notably, the algorithm relies on an external monitor to detect environmental changes and trigger the dynamic response strategy. DAEA is tested on the CEC’2022 dynamic multimodal optimization benchmark suite, and is compared against several state-of-the-art dynamic multimodal optimization algorithms. The experimental results demonstrate the competitiveness of DAEA in handling DMMOPs. Additionally, experimental results from the berth allocation problem further confirm the applicability of DAEA to real-world dynamic multimodal optimization tasks.

Objective: In this paper, an improved hybrid differential evolution (IHDE) algorithm based on differential evolution (DE) algorithm and particle swarm optimization (PSO) has been proposed to solve the optimal power flow (OPF) problem of power system which is a multi-constrained, large-scale and nonlinear optimization problem. Method: In IHDE algorithm, the DE is employed as the main optimizer; and the three factors of PSO, which are inertia, cognition, and society, are used to improve the mutation of DE. Then the learning mechanism and the adaptive control of the parameters are added to the crossover, and the greedy selection considering the value of penalty function is proposed. Furthermore, the replacement mechanism is added to the IHDE for reducing the probability of falling into the local optimum. The performance of this method is tested on the IEEE30-bus and IEEE57-bus systems, and the generator quadratic cost and the transmission real power losses are considered as objective functions. Results: The simulation results demonstrate that IHDE algorithm can solve the OPF problem successfully and obtain the better solution compared with other methods reported in the recent literatures.

This paper presents a hybrid optimization strategy for wideband antenna design that leverages the strengths of both Random Forest (RF) and Differential Evolution (DE) algorithms. The strategy employs DE for iteratively updating antenna parameters and RF for feature selection in the process of antenna performance optimization. Initially, DE is applied to update antenna parameters for a predetermined number of iterations, generating a dataset of antenna performance metrics. This dataset is then used to train an RF model, which identifies the importance of each design variable. Feature selection, guided by the RF-derived importance, is applied to reduce the dimensionality of the search space. DE subsequently continues the optimization process within this reduced parameter space. Validation of this hybrid approach is performed through the design of a wideband slot antenna and compared against standalone DE, Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and Simulated Annealing (SA). Results demonstrate that the proposed strategy significantly accelerates convergence, achieving the target reflection coefficient and gain with substantially fewer iterations than the other methods (reductions of 75.56%, 45%, 42.11%, and 50% compared to DE, GA, SA, and PSO, respectively). Furthermore, the hybrid strategy consistently finds superior solutions exhibiting lower loss values compared to the benchmark algorithms. The method offers a computationally efficient, interpretable, and effective approach to antenna optimization.

Global path planning is a challenging issue in the filed of mobile robotics due to its complexity and the nature of non-deterministic polynomial-time hard (NP-hard). Particle swarm optimization (PSO) has gained increasing popularity in global path planning due to its simplicity and high convergence speed. However, since the basic PSO has difficulties balancing exploration and exploitation, and suffers from stagnation, its efficiency in solving global path planning may be restricted. Aiming at overcoming these drawbacks and solving the global path planning problem efficiently, this paper proposes a hybrid PSO algorithm that hybridizes PSO and differential evolution (DE) algorithms. To dynamically adjust the exploration and exploitation abilities of the hybrid PSO, a novel PSO, the nonlinear time-varying PSO (NTVPSO), is proposed for updating the velocities and positions of particles in the hybrid PSO. In an attempt to avoid stagnation, a modified DE, the ranking-based self-adaptive DE (RBSADE), is developed to evolve the personal best experience of particles in the hybrid PSO. The proposed algorithm is compared with four state-of-the-art evolutionary algorithms. Simulation results show that the proposed algorithm is highly competitive in terms of path optimality and can be considered as a vital alternative for solving global path planning.

Classification has been widely studied due to its practical applications. Feature selection aims to improve the classification accuracy by selecting a small feature subset from the original full feature set. However, identification of relevant features is not trivial due to the large search space. Particle swarm optimisation (PSO) is an efficient meta-heuristic algorithm which has shown to be promising in feature selection. However, traditional PSO uses its personal best experience and its historical best experience to determine its search direction, but this learning strategy may limit its performance for feature selection due to the premature convergence. Therefore, the potential of PSO needs to be further explored. In this paper, a new evolutionary learning algorithm termed hybridising PSO with differential evolution (HPSO-DE) is proposed to develop new feature selection methods. In HPSO-DE, differential evolution is applied to breed promising and efficient exemplars for PSO to guide its search, which is expected to not only preserve the diversity of the population but also guide particles to fly to promising areas. HPSO-DE is compared with three classic PSO variants and five traditional feature selection methods on 15 classification problems. The results show that the proposed algorithm can effectively achieve a higher classification accuracy with a smaller feature subset than the compared methods.

When facing dynamic optimization problems the goal is no longer to find the extrema, but to track their progression through the space as closely as possible. Over these kind of over changing, complex and ubiquitous real-world problems, the explorative-exploitive subtle counterbalance character of our current state-of-the-art search algorithms should be biased towards an increased explorative behavior. While counterproductive in classic problems, the main and obvious reason of using it in severe dynamic problems is simple: while we engage ourselves in exploiting the extrema, the extrema moves elsewhere. In order to tackle this subtle compromise, we propose a novel algorithm for optimization in dynamic binary landscapes, stressing the role of negative feedback mechanisms. The Binary Ant Algorithm (BAA) mimics some aspects of social insects' behavior. Like Ant Colony Optimization (ACO), BAA acts by building pheromone maps over a graph of possible trails representing pseudo-solutions of increasing quality to a specific optimization problem. Main differences rely on the way this search space is represented and provided to the colony in order to explore/exploit it, while and more important, we enrol in providing strong evaporation to the problem-habitat. By a process of pheromone reinforcement and evaporation the artificial insect's trails over the graph converge to regions near the ideal solution of the optimization problem. Over each generation, positive feedbacks made available by pheromone reinforcement consolidate the best solutions found so far, while enhanced negative feedbacks given by the evaporation mechanism provided the system with population diversity and fast self-adaptive characteristics, allowing BAA to be particularly suitable for severe complex dynamic optimization problems. Experiments made with some well known test functions frequently used in the Evolutionary Algorithms' research field illustrate the efficiency of the proposed method. BAA was also compared with other algorithms, proving to be more able to track fast moving extrema on several test problems.

In this paper, the performance of some evolutionary algorithms on grinding process optimization of silicon carbide (SiC) is investigated. The grinding of SiC is not an easy task due to its low fracture toughness, therefore making the material sensitive to cracking. The efficient grinding involves the optimal selection of operating parameters to maximize the material removal rate (MRR) while maintaining the required surface finish and limiting surface damage. In this work, optimization based on the available model has been carried out to obtain optimum parameters for silicon carbide grinding via three prominent evolutionary algorithms. They are particle swarm optimization (PSO), differential evolution (DE) and genetic algorithm (GA). The objective of this optimization process is to maximize the MRR, subject to surface finish and damage constraints of the grinding process. Numerical results show that PSO is comparatively superior in comparison with DE and GA algorithms for grinding process optimization in terms of its accuracy and convergent capability

In the present paper, a dynamic optimization problem regarding grade transitions in bulk poly(propylene) polymerization processes is formulated and solved for the first time. Initially, a detailed dynamic process model is presented and implemented, comprising mass and energy balances, some of the polymer properties (such as the melting flow index and the xylene solubles) and regulatory control loops. Additionally, the effects of cocatalyst and electron donor on the propagation rate constant are taken into account. Then, the dynamic optimization problem is formulated and an evolutionary algorithm is used to solve the resulting nonlinear programming problem. It is shown that there is significant coupling among the manipulated variables and the controlled performance and polymer property variables, which adds complexity to the grade transition problem and demands the simultaneous manipulation of multiple variables during transitions. Despite the inherent open‐loop unstable nature of the analyzed process, it is shown that smooth grade transition trajectories can be accomplished through proper adjustment of the objective function weights. Finally, it is shown that the obtained optimum trajectories can significantly diminish the transition time, which can be of paramount importance for the plant economics.