Transfer Learning Based on Clustering Difference for Dynamic Multi-Objective Optimization

Many real-world optimization problems involve multiple objectives, constraints, and parameters that may change over time. These problems are often called dynamic multiobjective optimization problems (DMOPs). The difficulty in solving DMOPs is the need to track the changing Pareto-optimal front efficiently and accurately. It is known that transfer learning (TL)-based methods have the advantage of reusing experiences obtained from past computational processes to improve the quality of current solutions. However, existing TL-based methods are generally computationally intensive and thus time consuming. This article proposes a new memory-driven manifold TL-based evolutionary algorithm for dynamic multiobjective optimization (MMTL-DMOEA). The method combines the mechanism of memory to preserve the best individuals from the past with the feature of manifold TL to predict the optimal individuals at the new instance during the evolution. The elites of these individuals obtained from both past experience and future prediction will then constitute as the initial population in the optimization process. This strategy significantly improves the quality of solutions at the initial stage and reduces the computational cost required in existing methods. Different benchmark problems are used to validate the proposed algorithm and the simulation results are compared with state-of-the-art dynamic multiobjective optimization algorithms (DMOAs). The results show that our approach is capable of improving the computational speed by two orders of magnitude while achieving a better quality of solutions than existing methods.

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.

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

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.

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.

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.

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

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

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

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

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.

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.

Performance measures for dynamic multi-objective optimisation algorithms