Cooperation rules in a trajectory-based centralised cooperative strategy for Dynamic Optimisation Problems

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.

Evolutionary optimization algorithms, including particle swarm optimization (PSO), have been successfully applied in oil industry for production planning and control. Such optimization studies are quite challenging due to large number of decision variables, production scenarios, and subsurface uncertainties. In this work, multi-stage, multi-swarm PSO (MS2PSO) algorithm is proposed to fix certain issues with canonical PSO algorithm such as premature convergence, excessive influence of global best solution, and oscillation. Multiple experiments are conducted using Olympus benchmark to compare the efficacy of algorithms. Results from canonical PSO are first compared with two PSO variations in which hyperparameters are tuned to prioritize exploration in early phase and exploitation in late phase. Firstly, linearly decreasing inertia weight (LDIW-PSO) is used to have greater weight of current particle position during initial iterations, and vice versa. Then, time-varying acceleration coefficients (TVAC-PSO) are used to have greater weight of personal best and lesser weight of global best during the initial iterations, and vice versa. Next, a two-stage multi-swarm PSO (2SPSO) is used where multiple-swarms of the first stage collapse into a single swarm in the second stage. Finally, MS2PSO with multiple stages and multiple swarms is used in which swarms recursively collapse after each stage. Multiple swarm strategy ensures that diversity is retained within the population and multiple modes are explored. Staging ensures that local optima found during initial stage does not lead to premature convergence. Optimization test case comprises of 90 control variables of which 72 are well control related and 18 are well placement related. Swarm intelligence refers to global patterns emerging from simple interactions among population. Algorithmic rules at micro level lead to social interaction at meso level, which then further leads to collective behavior at macro level. It is observed that different algorithm designs have their own benefits and drawbacks. Decreasing inertia weight in LDIW-PSO enables exploration in early stages and convergence around global best in the later stages. TVAC-PSO on the other hand restricts social learning and aids exploration in the early iterations. Social learning component is increased as run progresses, and population moves towards global best. 2SPSO aids in exploring multi-modal objective space, thus preventing premature convergence to a local optima. Swarms collapse into one group in the second stage, and run finally converges towards global best. Multiple swarms and stages in MS2PSO ensure that diversity in population is maintained throughout the run which enables continuous learning, and thus mitigates premature convergence. Both 2SPSO and MS2PSO are found to be helpful for problems with high dimensions and multiple modes where greater degree of exploration is desired. Commercial cloud computing and parallel programming were used to handle high computational workload and reduce run-time from weeks to days. Coefficients of canonical PSO are tuned in LDIW-PSO and TVAC-PSO, which helps in mitigating issues like premature convergence and oscillation. Two-stage PSO (2SPSO) where multiple swarms of first stage collapse into one in second stage, and multi-stage multi-swarm PSO (MS2PSO) where swarms recursively collapse into one are proposed. These algorithms modify the social behavior at meso scale based on number of swarms, number of stages and iterations in each stage.

In the real world, many optimization problems are dynamic. This requires an optimization algorithm to not only find the global optimal solution under a specific environment but also to track the trajectory of the changing optima over dynamic environments. To address this requirement, this paper investigates a clustering particle swarm optimizer (PSO) for dynamic optimization problems. This algorithm employs a hierarchical clustering method to locate and track multiple peaks. A fast local search method is also introduced to search optimal solutions in a promising subregion found by the clustering method. Experimental study is conducted based on the moving peaks benchmark to test the performance of the clustering PSO in comparison with several state-of-the-art algorithms from the literature. The experimental results show the efficiency of the clustering PSO for locating and tracking multiple optima in dynamic environments in comparison with other particle swarm optimization models based on the multiswarm method.

Most optimisation algorithms from the computational intelligence field assume that the search landscape is static. However, this assumption is not valid for many real-world problems. Therefore, there is a need for efficient optimisation algorithms that can track changing optima. A number of variants of particle swarm optimisation (PSO) have been developed for dynamic environments. Recently, the cooperative PSO has been shown to significantly improve performance of PSO in static environments, especially for high-dimensional problems. This paper investigates the performance of a cooperative version of the charged PSO on a benchmark of dynamic optimisation problems. Empirical results show that the cooperative charged PSO is an excellent alternative to track dynamically changing optima.

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.

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.

This paper compares the performance of two variants of the Particle Swarm Optimization (PSO) algorithm; PSO with constriction factor (PSO), and mutative PSO (MPSO) in optimizing Mel Frequency Cepstrum Coefficients (MFCC) parameters. The parameters were used to extract an optimal feature set for classifying healthy and hypothyroid infant cry using Multi-Layer Perceptrons (MLP). Specifically, the PSO variants optimize the number of filter banks and number of cepstrum coefficients in MFCC. Based on the values chosen by both PSO variants, the extracted features were then fed to a MLP classifier, which was trained to discriminate between the healthy and hypothyroid infant cry. Comparisons between the performance of PSO variants showed that MPSO managed to improve the convergence rate by 2.67% compared to PSO.

Particle Swarm Optimization or Differential Evolution—A comparison

Several variants of particle swarm optimization (PSO) have been created to identify various solutions to compli-cated optimization problems. Only a few PSO algorithms exist that can locate and monitor multiple optima in dynamically shifting search landscapes when dealing with dynamic optimization situations. These methods have yet to be thoroughly tested on a large number of dynamic optimization problems. In fact, because there are so many PSO algorithm modifications, it's simple to get stuck in a local optima. To address the aforementioned flaws, this work proposes and evaluates an enhanced version of the multiswarm particle swarm optimization technique (MsPSO) with numerous variations particle swarm optimization published in the literature. Standard tests and indicators provided in the specialized literature are used to verify the effectiveness of the suggested algorithm. Furthermore, on the CEC’ 13 test suite, comparison results between the extended heterogeneous multi swarm PSO algorithm (XMsPSO) and other nine popular PSO show that XMsPSO achieves a very optimistic performance for solving various kinds of problems, contributing to both higher solution accuracy.

Molecular docking is an important tool in screening large libraries of compounds to determine the interactions between potential drugs and the target proteins. The molecular docking problem is how to locate a good conformation to dock a ligand to the large molecule. It can be formulated as a parameter optimization problem consisting of a scoring function and a global optimization method. Many docking methods have been developed with primarily these two parts varying. In this paper, a variety of particle swarm optimization (PSO) variants were introduced to cooperate with the semiempirical free energy force field in AutoDock 4.05. The search ability and the docking accuracy of these methods were evaluated by multiple redocking experiments. The results demonstrate that PSOs were more suitable than Lamarckian genetic algorithm (LGA). Among all of the PSO variants, FIPS takes precedence over others. Compared with the four state-of-art docking methods-GOLD, DOCK, FlexX and AutoDock with LGA, AutoDock cooperated with FIPS is more accurate. Thus, FIPS is an efficient PSO variant which has promising prospects that can be expected in the application to virtual screening.

Dynamic multi-objective evolutionary algorithms (Dynamic MOEAs) use the evolutionary algorithms to solve the dynamic multi-objective optimization problems (DMOPs). It has become one of the hot areas of research. The challenge of DMOPs is that the objective functions, the constraints or the parameters may change over time. This paper tries to provide a comprehensive overview of the related work, which is organized by the common process of Dynamic MOEAs, such as, the detection of change, the maintenance of diversity, the prediction of change, the test problems and the performance metrics. Finally, topics for further research are suggested.

Based on the polar coordination particle swarm optimization (PPSO), this paper presents a novel method for the robot path planning in dynamic environment. It decomposes the task into a global planning stage and a local planning stage. PPSO algorithm can search for the global optimal path based on static obstacles information. When the robot moves along the optimal global path, an on-line real-time path planning strategy is adopted to avoid dynamic obstacles by means of predicting the future positions of moving obstacles. Simulation experiment shows that the method is more efficient than traditional particle swarm optimization (TPSO) and genetic algorithm (GA) for solving path planning problem. The feasibility and high stability of real-time obstacle avoidance strategy are demonstrated in dynamic environment.

Integral-controlled particle swarm optimization (ICPSO) is an effective variant of particle swarm optimization (PSO) aiming to increase the population diversity. Due to the additional accelerator items, the behavior of ICPSO is more complex, and provides more chances to escaping from a local optimum than the standard version of PSO. However, many experimental results show the performance of ICPSO is not always well because of the particles' un-controlled movements. Therefore, a new variant, integral particle swarm optimization with dispersed accelerator information (IPSO-DAI) is designed to improve the computational efficiency. In IPSO-DAI, a predefined predicted velocity index is introduced to guide the moving direction. If the average velocity of one particle is superior to the index value, it will choice a convergent manner, otherwise, a divergent manner is employed. Furthermore, the choice of convergent manner or divergent manner for each particle is associated with its performance to fit different living experiences. Simulation results show the proposed variant is more effective than other three variants of particle swarm optimization especially for multi-modal numerical problems. The IPSO-DAI algorithm is also applied to directing the orbits of discrete chaotic dynamical systems by adding small bounded perturbations, and achieves the best performance among four different variants of PSO.

Particle Swarm Optimization (PSO) is the global optimization technique that inspires many researchers to solve large scale of non-linear optimization problems. For certain complex scenarios, the premature convergence problem of PSO algorithm cannot find global optimum in dynamic environments. In this paper, a new variant motility factor based Cellular Particle Swarm Optimization (m-CPSO) algorithm is proposed which is developed by the migration behavior observed from fibroblast cellular organism to overcome this problem. The proposed m-CPSO algorithm is modeled in two different social best and individual best models. The performance of m-CPSO is tested in the benchmark and real-time data instances and compared with classical PSO. The outcome of experimental results has demonstrated that m-CPSO algorithm produces promising results than classical PSO on all evaluated environments.

This paper introduces the optimization of a quantum control application, the so-called molecular alignment problem, subject to a dynamic environment. Given the relative simplicity of optimized pulse-shapes in the low-intensity variant of the problem, versus the high complexity of the optimized pulse-shapes in the high-intensity case, a dynamic-intensity environment is simulated in a noise-free calculation. Specific evolution strategies, natural candidates for optimization in dynamic environments, are applied to this task. The calculations reveal the evolution of the pulse-shapes and their underlying evolving structures, that allow a complete physical interpretation. The combination of an optimization in a dynamic environment with the examination of the intermediate optimized solutions offers a sharper physics view of the problem, and accomplishes a fruitful interdisciplinary study.