Knowledge guided Bayesian classification for dynamic multi-objective optimization

Dynamic multiobjective optimization problems (DMOPs) bring more challenges for multiobjective evolutionary algorithm (MOEA) due to its time-varying characteristic. To handle this kind of DMOPs, this paper presents a dynamic MOEA with multiple response strategies based on linear environment detection, called DMOEA-LEM. In this approach, different types of environmental changes are estimated and then the corresponding response strategies are activated to generate an efficient initial population for the new environment. DMOEA-LEM not only detects whether the environmental changes but also estimates the types of linear changes so that different prediction models can be selected to initialize the population when the environmental changes. To study the performance of DMOEA-LEM, a large number of test DMOPs are adopted and the experiments validate the advantages of our algorithm when compared to three state-of-the-art dynamic MOEAs.

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

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.

Many real-world optimization problems have dynamic multiple objectives and constrains, such problems are called dynamic multi-objective optimization problems (DMOPs). Although many dynamic multi-objective evolutionary algorithms (DMOEAs) have been proposed to solve DMOPs, how to effectively track the optimal solutions in dynamic environments is still a major challenge for dynamic multi-objective optimization. Two classical DMOEAs, population prediction strategy (PPS) and transfer learning based DMOEA (Tr-DMOEA) are validated to have great performance because they integrate machine learning mechanism for optimization. However, there are still some disadvantages in both algorithms. In this paper, we propose a combined algorithm to make up the respective disadvantages of PPS and Tr-DMOEA. Our algorithm retains the prediction method of PPS considering sufficient historical information. Then, we improve the prediction strategy in Tr-DMOEA to further modify the solutions provided by PPS. These modified solutions finally construct the initial population for optimization in the new environment. The experiment results indicate that our algorithm has the overall best performance comparing with PPS and Tr-DMOEA on the test problems.

A dynamic multi-objective optimization evolutionary algorithm for complex environmental changes

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

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) remain a challenge to be settled, because of conflicting objective functions change over time. In recent years, transfer learning has been proven to be a kind of effective approach in solving DMOPs. In this paper, a novel transfer learning based dynamic multi-objective optimization algorithm (DMOA) is proposed called regression transfer learning prediction based DMOA (RTLP-DMOA). The algorithm aims to generate an excellent initial population to accelerate the evolutionary process and improve the evolutionary performance in solving DMOPs. When an environmental change is detected, a regression transfer learning prediction model is constructed by reusing the historical population, which can predict objective values. Then, with the assistance of this prediction model, some high-quality solutions with better predicted objective values are selected as the initial population, which can improve the performance of the evolutionary process. We compare the proposed algorithm with three state-of-the-art algorithms on benchmark functions. Experimental results indicate that the proposed algorithm can significantly enhance the performance of static multi-objective optimization algorithms and is competitive in convergence and diversity.

Dynamic multiobjective optimization problems (DMOPs) aim to optimize multiple (often conflicting) objectives that are changing over time. Recently, there are a number of promising algorithms proposed based on transfer learning methods to solve DMOPs. However, it is very challenging to reduce the negative effect in transfer learning and find more effective transferred solutions. To fill this research gap, this article proposes a clustering-based transfer (CBT) learning method to solve DMOPs. When the environment changes, two novel operations (clustering-based selection (CBS) and CBT) are used to guide knowledge transfer. Specifically, CBS aims to find a population with nondominated solutions and dominated solutions as the training data for the new environment. Then, CBT further collects the previous Pareto-optimal solutions and some noise solutions as the training data for the previous environment. Two training data sets from different environments are, respectively, divided into multiple clusters and transfer learning is conducted on two similar clusters with high probability to reduce the negative effect, which can train an accurate prediction model to identify the promising solutions for the new environment. Empirical studies have been conducted on 14 benchmark DMOPs and one real-life path planning problem of unmanned air/ground vehicles, which validate the effectiveness of our proposed method. Especially, our method can significantly reduce negative transfer on 12 out of 14 cases when compared with direct transfer learning.

The main challenge in handling dynamic multi-objective optimization problems lies in the need for algorithms to accurately track Pareto-optimal solutions in constantly changing environments. Most existing predictionbased dynamic multi-objective evolutionary algorithms (DMOEAs) conduct prediction either in the decision space or the objective space alone, or apply the same prediction model to both spaces. However, such approaches may fail to fully capture the distinct change patterns of each space, especially under nonlinear and complex environmental dynamics, thereby limiting the effectiveness of these algorithms. Furthermore, when sampling methods are used to help the algorithm generate populations in new environments, a large number of sampled individuals can impose a significant computational burden due to the increased number of function evaluations. To address these limitations, this paper proposes a dynamic multi-objective evolutionary algorithm, namely DS-DMOEA, which efficiently adapts to environmental changes through a dual-space prediction strategy and a surrogate-based sampling strategy. The dual-space prediction strategy captures dynamic changes by employing a weight vector-based method in the objective space and a geodesic flow kernel method in the decision space. Simultaneously, the surrogate-based sampling strategy generates a high-quality sampling population by training surrogate models with information from similar historical environments. The predicted and sampled populations are then combined to form an initial population well-suited for the new environment. DS-DMOEA has been tested against nine state-of-the-art DMOEAs on 19 benchmark problems with three types of environmental change patterns. The experimental results validate the effectiveness of the proposed algorithm.

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.

Immune Generalized Differential Evolution for dynamic multi-objective environments: An empirical study

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.

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.