A fuzzy-guided adaptive algorithm with hierarchy mechanism for solving dynamic multi-objective optimization 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.

Combining a hybrid prediction strategy and a mutation strategy for dynamic multiobjective optimization

Double-space environmental change detection and response strategy for dynamic multi-objective optimize problem

The importance of dynamic multi-objective optimization problems (DMOPs) is on the rise, in complex systems. DMOPs have several objective functions and constraints that vary over time to be considered simultaneously. As a result, the Pareto optimal solutions (POS) and Pareto front (PF) will also vary with time. The desired algorithm should not only locate the optima but also track the moving optima efficiently. In this paper, we propose a new Cultural Algorithm (CA) based on decomposition (CA/D). The primary objective of the CA/D algorithm is to decompose DMOP into several scalar optimization subproblems and solve simultaneously. The subproblems are optimized utilizing the information shared only by its neighboring problems. The proposed CA/D is evaluated using CEC 2015 optimization benchmark functions. The results show that CA/D outperforms CA, Multi-population CA (MPCA), and MPCA incorporating game strategies (MPCA-GS), particularly in hybrid and composite benchmark problems.

A dynamic multi-objective evolutionary algorithm with variable stepsize and dual prediction strategies

Dynamic multi-objective optimization problem (DMOP) denotes the multi-objective optimization problem which varies over time. As changes in DMOP may exist some patterns which are predictable, to solve DMOP, a number of research efforts have been made to develop evolutionary search with prediction approaches to estimate the changes of the problem. A common practice of existing prediction approaches is to predict the change of Pareto-optimal solutions (POS) based on the historical solutions obtained in the decision space. However, the change of a DMOP may occur in both decision and objective spaces. Prediction only in the decision space thus may not be able to give the proper estimation of the problem change. Taking this cue, in this paper, we propose an evolutionary search with multi-view prediction for solving DMOP. In contrast to existing prediction methods, the proposed approach conducts prediction from the views of both decision and objective spaces. To estimate dynamic changes in DMOP, a kernelized autoencoding model is derived to perform the multi-view prediction in a Reproducing Kernel Hilbert Space (RKHS), which holds a closed-form solution. To examine the performance of the proposed method, comprehensive empirical studies on the commonly used DMOP benchmarks, as well as a real-world case study on the movie recommendation problem, are presented. The obtained experimental results verified the efficacy of the proposed method for solving both benchmark and real-world DMOPs.

Dynamic multi-objective optimization problems (DMOPs) have become a research hotspot in engineering optimization, because their objective functions, constraints, or parameters may change over time, while quickly and accurately tracking the changing Pareto optimal set (POS) during the optimization process. Therefore, solving dynamic multi-objective optimization problems presents great challenges. In recent years, transfer learning has been proved to be one of the effective means to solve dynamic multi-objective optimization problems. However, this paper proposes a new transfer learning method based on clustering difference to solve DMOPs (TCD-DMOEA). Different from the existing methods, it uses the clustering difference strategy to optimize the population quality and reduce the data difference between the target domain and the source domain. On this basis, transfer learning technology is used to accelerate the construction of initialization population. The advantage of the TCD-DMOEA method is that it reduces the possibility of negative transfer and improves the performance of the algorithm by improving the similarity between the source domain and the target domain. Experimental results show that compared with several advanced dynamic multi-objective optimization algorithms based on different benchmark problems, the proposed TCD-DMOEA method can significantly improve the quality of the solution and the convergence speed.

A new prediction strategy for dynamic multi-objective optimization using Gaussian Mixture Model

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.

Cooperative particle swarm optimization with reference-point-based prediction strategy for dynamic multiobjective optimization

A pareto-based evolutionary algorithm using decomposition and truncation for dynamic multi-objective optimization

Dynamic multiobjective optimization problem (DMOP) denotes the multiobjective optimization problem, which contains objectives that may vary over time. Due to the widespread applications of DMOP existed in reality, DMOP has attracted much research attention in the last decade. In this article, we propose to solve DMOPs via an autoencoding evolutionary search. In particular, for tracking the dynamic changes of a given DMOP, an autoencoder is derived to predict the moving of the Pareto-optimal solutions based on the nondominated solutions obtained before the dynamic occurs. This autoencoder can be easily integrated into the existing multiobjective evolutionary algorithms (EAs), for example, NSGA-II, MOEA/D, etc., for solving DMOP. In contrast to the existing approaches, the proposed prediction method holds a closed-form solution, which thus will not bring much computational burden in the iterative evolutionary search process. Furthermore, the proposed prediction of dynamic change is automatically learned from the nondominated solutions found along the dynamic optimization process, which could provide more accurate Pareto-optimal solution prediction. To investigate the performance of the proposed autoencoding evolutionary search for solving DMOP, comprehensive empirical studies have been conducted by comparing three state-of-the-art prediction-based dynamic multiobjective EAs. The results obtained on the commonly used DMOP benchmarks confirmed the efficacy of the proposed method.

Various real-world multiobjective optimization problems are dynamic, requiring evolutionary algorithms (EAs) to be able to rapidly track the moving Pareto front of an optimization problem once an environmental change occurs. To this end, several methods have been developed to predict the new location of the moving Pareto set (PS) so that the population can be reinitialized around the predicted location. In this paper, we present a multidirectional prediction strategy to enhance the performance of EAs in solving a dynamic multiobjective optimization problem (DMOP). To more accurately predict the moving location of the PS, the population is clustered into a number of representative groups by a proposed classification strategy, where the number of clusters is adapted according to the intensity of the environmental change. To examine the performance of the developed algorithm, the proposed prediction strategy is compared with four state-of-the-art prediction methods under the framework of particle swarm optimization as well as five popular EAs for dynamic multiobjective optimization. Our experimental results demonstrate that the proposed algorithm can effectively tackle DMOPs.

A dynamic multiple populations particle swarm optimization algorithm based on decomposition and prediction

Many problems in the real-world have more than one objective, with at least two objectives in conflict with one another. In addition, at least one objective changes over time. These kinds of problems are called dynamic multi-objective optimisation problems (DMOOPs). Studies have shown that both the quantum particle swarm optimisation (QPSO) and charged particle swarm optimisation (CPSO) algorithms perform well in dynamic environments, since they maintain swarm diversity. Therefore, this paper investigates the effect of using either QPSOs or CPSOs in the sub-swarms of the dynamic vector-evaluated particle swarm optimisation (DVEPSO) algorithm. These DVEPSO variations are then compared against the default DVEPSO algorithm that uses gbest PSOs and DVEPSO using heterogeneous PSOs that contain both charged and quantum particles. Furthermore, all of the aforementioned DVEPSO configurations are compared against the dynamic multi-objective optimisation (DMOPSO) algorithm that was the winning algorithm of a comprehensive comparative study of dynamic multi-objective optimisation algorithms. The results indicate that charged and quantum particles improve the performance of DVEPSO, especially for DMOOPs with a deceptive POF and DMOOPs with a non-linear POS.