Evolutionary Multitasking for Multiobjective Optimization With Subspace Alignment and Adaptive Differential Evolution

Transferable Adaptive Differential Evolution for Many-Task Optimization

The evolutionary multitask optimization (EMTO) algorithm is a promising approach to solve many-task optimization problems (MaTOPs), in which similarity measurement and knowledge transfer (KT) are two key issues. Many existing EMTO algorithms estimate the similarity of population distribution to select a set of similar tasks and then perform KT by simply mixing individuals among the selected tasks. However, these methods may be less effective when the global optima of the tasks greatly differ from each other. Therefore, this article proposes to consider a new kind of similarity, namely, shift invariance, between tasks. The shift invariance is defined that the two tasks are similar after linear shift transformation on both the search space and the objective space. To identify and utilize the shift invariance between tasks, a two-stage transferable adaptive differential evolution (TRADE) algorithm is proposed. In the first evolution stage, a task representation strategy is proposed to represent each task by a vector that embeds the evolution information. Then, a task grouping strategy is proposed to group the similar (i.e., shift invariant) tasks into the same group while the dissimilar tasks into different groups. In the second evolution stage, a novel successful evolution experience transfer method is proposed to adaptively utilize the suitable parameters by transferring successful parameters among similar tasks within the same group. Comprehensive experiments are carried out on two representative MaTOP benchmarks with a total of 16 instances and a real-world application. The comparative results show that the proposed TRADE is superior to some state-of-the-art EMTO algorithms and single-task optimization algorithms.

Multi-objective evolutionary multitasking algorithm based on cross-task transfer solution matching strategy

The superior performance of evolutionary multitasking (EMT) algorithms is largely owing to the potential synergy between tasks. Current EMT algorithms only involve a unidirectional process of transferring individuals from the source task to the target task. This method does not consider the search preference of the target task in the process of finding transferred individuals; therefore, the potential synergy between tasks is not fully utilized. Herein, we propose a bidirectional knowledge transfer method, which refers to the search preference of the target task in the process of finding transferred individuals. These transferred individuals fit the search process well for the target task. In addition, an adaptive strategy for adjusting the intensity of the knowledge transfer is proposed. This method enables the algorithm to adjust the intensity of knowledge transfer independently according to the living conditions of the individuals to be transferred to balance the convergence of the population with the computational intensity of the algorithm. The proposed algorithm is compared with comparison algorithms on 38 multi-objective multitasking optimization benchmarks. Experimental results show that the proposed algorithm is not only outperforming other comparison algorithms in more than 30 benchmarks, but also has considerable convergence efficiency.

Domain Adaptation Multitask Optimization

Multitask optimization (MTO) is a new optimization paradigm that leverages useful information contained in multiple tasks to help solve each other. It attracts increasing attention in recent years and gains significant performance improvements. However, the solutions of distinct tasks usually obey different distributions. To avoid that individuals after intertask learning are not suitable for the original task due to the distribution differences and even impede overall solution efficiency, we propose a novel multitask evolutionary framework that enables knowledge aggregation and online learning among distinct tasks to solve MTO problems. Our proposal designs a domain adaptation-based mapping strategy to reduce the difference across solution domains and find more genetic traits to improve the effectiveness of information interactions. To further improve the algorithm performance, we propose a smart way to divide initial population into different subpopulations and choose suitable individuals to learn. By ranking individuals in target subpopulation, worse-performing individuals can learn from other tasks. The significant advantage of our proposed paradigm over the state of the art is verified via a series of MTO benchmark studies.

A multi-objective multi-tasking evolutionary algorithm based inverse mapping and adaptive transformation strategy: IM-MFEA

Multi-tasking optimization algorithm attracts much attention because the knowledge transfer between tasks enables the algorithm to process multiple related tasks simultaneously. However, negative knowledge transfer occasionally occurs, which may weaken the performance of the algorithm. To reduce the impact of negative knowledge transfer, a multi-objective multi-tasking optimization algorithm (IM-MFEA) based on inverse model mapping and an objective transformation strategy is proposed. First, correlation analysis is applied in an inverse mapping strategy to improve the accuracy of the inverse mapping model. Then, following the pattern of using the source domain solutions to assist the optimization of the target domain, the adaptive transformation strategy is used to improve the quality of the source domain solution in the objective space. These transformed solutions are reconstructed through the inverse mapping strategy. Finally, these reconstructed source domain solutions are mated with the target domain solutions to generate competitive offspring individuals for the target domain. To verify the effectiveness of the IM-MFEA, comprehensive experiments were conducted on nine multi-objective multi-factorial optimization (MFO) benchmark problems. Empirical results demonstrate that IM-MFEA is superior to other algorithms in 90% of test instances by inverted generational distance (IGD) and hypervolume (HV) value indicators.

A multitask optimization algorithm based on elite individual transfer

Evolutionary multitasking algorithms aim to solve several optimization tasks simultaneously, and they can improve the efficiency of various tasks evolution through the knowledge transfer between different optimization tasks. Evolutionary multitasking algorithms have been applied to various applications and achieved certain results. However, how to transfer knowledge between tasks is still a problem worthy of research. Aiming to improve the positive transfer between tasks and reduce the negative transfer, we propose a single-objective multitask optimization algorithm based on elite individual transfer, namely MSOET. In this paper, whether to execute knowledge transfer between tasks depends on a certain probability. Meanwhile, in order to enhance the effectiveness and the global search ability of the algorithm, the current population and the elite individual in the transfer population are further utilized as the learning sources to construct a Gaussian distribution model, and the offspring is generated by the Gaussian distribution model to achieve knowledge transfer between tasks. We compared the proposed MSOET with ten multitask optimization algorithms, and the experimental results verify the algorithm's excellent performance and strong robustness.

Multiobjective multitasking optimization assisted by multidirectional prediction method

Multiobjective multitasking optimization (MTO) is an emerging research topic in the field of evolutionary computation, which has attracted extensive attention, and many evolutionary multitasking (EMT) algorithms have been proposed. One of the core issues, designing an efficient transfer strategy, has been scarcely explored. Keeping this in mind, this paper is the first attempt to design an efficient transfer strategy based on multidirectional prediction method. Specifically, the population is divided into multiple classes by the binary clustering method, and the representative point of each class is calculated. Then, an effective prediction direction method is developed to generate multiple prediction directions by representative points. Afterward, a mutation strength adaptation method is proposed according to the improvement degree of each class. Finally, the predictive transferred solutions are generated as transfer knowledge by the prediction directions and mutation strengths. By the above process, a multiobjective EMT algorithm based on multidirectional prediction method is presented. Experiments on two MTO test suits indicate that the proposed algorithm is effective and competitive to other state-of-the-art EMT algorithms.

Multi-Task Optimization and Multi-Task Evolutionary Computation in the Past Five Years: A Brief Review

Traditional evolution algorithms tend to start the search from scratch. However, real-world problems seldom exist in isolation and humans effectively manage and execute multiple tasks at the same time. Inspired by this concept, the paradigm of multi-task evolutionary computation (MTEC) has recently emerged as an effective means of facilitating implicit or explicit knowledge transfer across optimization tasks, thereby potentially accelerating convergence and improving the quality of solutions for multi-task optimization problems. An increasing number of works have thus been proposed since 2016. The authors collect the abundant specialized literature related to this novel optimization paradigm that was published in the past five years. The quantity of papers, the nationality of authors, and the important professional publications are analyzed by a statistical method. As a survey on state-of-the-art of research on this topic, this review article covers basic concepts, theoretical foundation, basic implementation approaches of MTEC, related extension issues of MTEC, and typical application fields in science and engineering. In particular, several approaches of chromosome encoding and decoding, intro-population reproduction, inter-population reproduction, and evaluation and selection are reviewed when developing an effective MTEC algorithm. A number of open challenges to date, along with promising directions that can be undertaken to help move it forward in the future, are also discussed according to the current state. The principal purpose is to provide a comprehensive review and examination of MTEC for researchers in this community, as well as promote more practitioners working in the related fields to be involved in this fascinating territory.