Evolutionary Multitasking Research Articles

Improving Evolutionary Multitasking Optimization by Leveraging Inter-Task Gene Similarity and Mirror Transformation

Solving a complex optimization task from scratch can be significantly expensive and/or time-consuming. Common knowledge obtained from different (but possibly related) optimization tasks may help enhance the solving of such tasks. In this regard, evolutionary multitasking optimization (EMTO) has been proposed to improve the solving of multiple optimization tasks simultaneously via knowledge transfer in the evolutionary algorithm framework. The effectiveness of knowledge transfer is crucial for the success of EMTO. Multifactorial evolutionary algorithm (MFEA) is one of the most representative EMTO algorithms, however, it suffers from negative knowledge transfer among the tasks with low correlation. To address this issue, in this study, inter-task gene-similarity-based knowledge transfer and mirror transformation are integrated into MFEA (termed as MFEA-GSMT). In the proposed inter-task gene-similarity-based knowledge transfer, a probabilistic model is used to feature each gene and the Kullback-Leibler divergence is employed to measure the inter-task dimension similarity. Guided by the inter-task gene similarity, a selective crossover is used to reproduce offspring solutions. The proposed inter-task knowledge transfer is based on online gene similarity evaluation, instead of individual similarity, to overcome the imprecise estimation of population distributions in a high-dimensional space with only a small number of samples. The proposed mirror transformation is an extension of opposition-based learning to avoid premature convergence and explore additional promising search areas. Experimental results on both single-objective and multi-objective multi-tasking problems demonstrate the effectiveness and efficiency of the proposed MFEA-GSMT.

Surrogate-Assisted Evolutionary Framework with Adaptive Knowledge Transfer for Multi-Task Optimization

Multi-task optimization is a hot research topic in the field of evolutionary computation. This paper proposes an efficient surrogate-assisted multi-task evolutionary framework (named SaEF-AKT) with adaptive knowledge transfer for multi-task optimization. In the proposed SaEF-AKT, several tasks which are computationally expensive are solved jointly in each generation. Surrogate models are built based on the historical search information of each task to reduce the number of fitness evaluations. To improve the search efficiency, a general similarity measure mechanism and an adaptive knowledge transfer mechanism are proposed, which can help knowledge transfer among the tasks to be solved. The proposed SaEF-AKT is tested on a number of benchmark problems in multi-task optimization scenario and real-world time series regression problems. The experimental results demonstrate that the proposed framework can outperform several state-of-the-art multi-task optimization algorithms.

Evolutionary multi-task optimization with hybrid knowledge transfer strategy

As an emerging research paradigm in the field of evolutionary computation, evolutionary multi-task optimization (EMTO) has received an increasing amount of attention due to its capability in concurrently solving multiple related optimization tasks. In EMTO, without any prior knowledge about the complementarity between different tasks, the task relatedness is mainly captured dynamically through the evolving population. However, how to transfer the knowledge across tasks in accordance with different degrees of relatedness as the search proceeds has received little visibility. To address this issue and further enhance the performance of EMTOs, this paper proposes a hybrid knowledge transfer (HKT) strategy. In HKT, a population distribution-based measurement (PDM) technique is designed to evaluate the task relatedness based on the distribution characteristics of the evolving population, and then a multi-knowledge transfer (MKT) mechanism is employed to conduct multiple strategies of knowledge transfer according to the degree of relatedness between tasks. By incorporating the HKT strategy into EMTO, the resultant algorithmic framework, termed EMTO–HKT, is presented. The experimental results on the single-objective multi-task optimization test suite demonstrate the superiority of EMTO–HKT compared with other state-of-the-art EMTO algorithms.

Cultural transmission based multi-objective evolution strategy for evolutionary multitasking

In recent years, many efficient evolutionary multitasking (EMT) algorithms have been proposed to solve multi-objective multi-task optimization problems. However, EMT algorithms often face negative transfer problems. In this paper, a novel multi-objective evolution strategy, called CT-EMT-MOES, is proposed based on a cultural transmission theory for solving multi-objective multitask optimization problems. First, two evolutionary operators inspired by cultural transmission theory are proposed. The elite-guided variation strategy can transfer the information from the current Pareto front to all individuals and guide the population to quickly converge. The horizontal cultural transmission strategy can efficiently transfer information from the source task to the target task. Second, to solve the negative transfer problem, an adaptive information transfer strategy is proposed to adaptively adjust the probability of an information transfer. Third, the proposed algorithm can gain a Pareto front with good convergence and diversity by utilizing a smaller population size and fewer computing resources. As a result, the proposed algorithm can effectively utilize the implicit similarity and complementarity between simultaneous optimized tasks to improve the overall convergence efficiency and reduce a negative transfer. Finally, comprehensive experimental results show that the proposed algorithm can achieve a better performance compared with previous state-of-the-art multi-objective EMT algorithms.

Multi-fidelity evolutionary multitasking optimization for hyperspectral endmember extraction

Endmember extraction plays an indispensable role in hyperspectral image processing, which is also an important step to decompose the mixed pixels in spectral unmixing. Most of the existing methods based on the principle of convex geometry and intelligent optimization algorithms have achieved an excellent result, but they also suffer from the influence of outliers and expensive computation respectively. Furthermore, it is difficult to determine the number of endmembers in a hyperspectral image without any prior conditions. In order to alleviate these problems, we propose a multi-fidelity evolutionary multitasking optimization framework for hyperspectral endmember extraction in this article. In the proposed framework, multiple tasks to extract different numbers of endmembers are uniformly coded into a single population, aiming to process these similar tasks simultaneously with the implicit genetic transfer. Accordingly, our proposed algorithm is capable of extracting the best endmember set within a certain range of the number of endmembers without any prior knowledge. In addition, an ensemble surrogate model is firstly built to approximate the high-fidelity fitness with the low-fidelity fitness in endmember extraction, which greatly alleviates the time-consuming problem of individual evaluation. The experimental results on the simulated and the real hyperspectral data demonstrate the effectiveness of the proposed framework. The accuracy and the efficiency of endmember extraction are greatly improved compared with other classic endmember extraction methods.

Multifactorial Particle Swarm Optimization Enhanced by Hybridization With Firefly Algorithm

In recent years, evolutionary multitasking has received attention in the evolutionary computation community. As an evolutionary multifactorial optimization method, multifactorial evolutionary algorithm (MFEA) is proposed to realize evolutionary multitasking. One concept called the skill factor is introduced to assign a preferred task for each individual in MFEA. Then, based on the skill factor, there are some multifactorial optimization solvers including swarm intelligence that have been developed. In this paper, a PSO-FA hybrid model with a model selection mechanism triggered by updating the personal best memory is applied to multifactorial optimization. The skill factor reassignment is introduced in this model to enhance the search capability of the hybrid swarm model. Then numerical experiments are carried out by using nine benchmark problems based on typical multitask situations and by comparing with a simple multifactorial PSO to show the effectiveness of the proposed method.

Explicit Evolutionary Multitasking for Combinatorial Optimization: A Case Study on Capacitated Vehicle Routing Problem.

Recently, evolutionary multitasking (EMT) has been proposed in the field of evolutionary computation as a new search paradigm, for solving multiple optimization tasks simultaneously. By sharing useful traits found along the evolutionary search process across different optimization tasks, the optimization performance on each task could be enhanced. The autoencoding-based EMT is a recently proposed EMT algorithm. In contrast to most existing EMT algorithms, which conduct knowledge transfer across tasks implicitly via crossover, it intends to perform knowledge transfer explicitly among tasks in the form of task solutions, which enables the employment of task-specific search mechanisms for different optimization tasks in EMT. However, the autoencoding-based explicit EMT can only work on continuous optimization problems. It will fail on combinatorial optimization problems, which widely exist in real-world applications, such as scheduling problem, routing problem, and assignment problem. To the best of our knowledge, there is no existing effort working on explicit EMT for combinatorial optimization problems. Taking this cue, in this article, we thus embark on a study toward explicit EMT for combinatorial optimization. In particular, by using vehicle routing as an illustrative combinatorial optimization problem, the proposed explicit EMT algorithm (EEMTA) mainly contains a weighted l1 -norm-regularized learning process for capturing the transfer mapping, and a solution-based knowledge transfer process across vehicle routing problems (VRPs). To evaluate the efficacy of the proposed EEMTA, comprehensive empirical studies have been conducted with the commonly used vehicle routing benchmarks in multitasking environment, against both the state-of-the-art EMT algorithm and the traditional single-task evolutionary solvers. Finally, a real-world combinatorial optimization application, that is, the package delivery problem (PDP), is also presented to further confirm the efficacy of the proposed algorithm.

AT-MFCGA: An Adaptive Transfer-guided Multifactorial Cellular Genetic Algorithm for Evolutionary Multitasking

• An adaptive and transfer guided metaheuristic is proposed for Evolutionary Multitasking. • Synergies between tasks are analyzed along the search in a dynamic way. • 4 different combinatorial optimization problems have been considered. • 11 multitasking scenarios are solved comprised by 5 to 20 instances. • Proposed AT-MFCGA is compared with MFEA, MFEA-II and MFCGA. Transfer Optimization is an incipient research area dedicated to solving multiple optimization tasks simultaneously. Among the different approaches that can address this problem effectively, Evolutionary Multitasking resorts to concepts from Evolutionary Computation to solve multiple problems within a single search process. In this paper we introduce a novel adaptive metaheuristic algorithm to deal with Evolutionary Multitasking environments coined as Adaptive Transfer-guided Multifactorial Cellular Genetic Algorithm (AT-MFCGA). AT-MFCGA relies on cellular automata to implement mechanisms in order to exchange knowledge among the optimization problems under consideration. Furthermore, our approach is able to explain by itself the synergies among tasks that were encountered and exploited during the search, which helps us to understand interactions between related optimization tasks. A comprehensive experimental setup is designed to assess and compare the performance of AT-MFCGA to that of other renowned Evolutionary Multitasking alternatives (MFEA and MFEA-II). Experiments comprise 11 multitasking scenarios composed of 20 instances of 4 combinatorial optimization problems, yielding the largest discrete multitasking environment solved to date. Results are conclusive in regard to the superior quality of solutions provided by AT-MFCGA with respect to the rest of the methods, which are complemented by a quantitative examination of the genetic transferability among tasks throughout the search process.

Research on Aerodynamic Optimization Method of Multistage Axial Compressor under Multiple Working Conditions Based on Phased Parameterization Strategy

Multistage axial compressor is the key component of aeroengine and gas turbine to realize energy conversion. In order to avoid the “curse of dimensionality” problem in the global optimization process of AL-31F four-stage low-pressure compressor under multiple working conditions, an optimization method based on phased parameterization strategy is proposed. The method uses the idea of “exploration before exploitation” for reference and divides the optimization process into two phases. In the first phase, the traditional parametric modification method based on stacking line is adopted; in the second phase, the full-blade surface parametric modification method with significant low-dimensional characteristics is adopted. Based on the improved artificial bee colony algorithm, a multitask concurrent optimization system is built on the supercomputing platform, and the engineering optimization solution is obtained within 91 hours. The optimization results are as follows: under the condition of meeting the constraints, the adiabatic efficiency is increased by 0.3% and the surge margin is 4.0% at the design speed; the adiabatic efficiency is increased by 0.8% and the surge margin is 2.3% at the off-design speed. These results verify the usefulness and reliability of the optimization method in the field of aerodynamic optimization of a multistage axial flow compressor.

Multiobjective multifactorial immune algorithm for multiobjective multitask optimization problems

Inspired by human brains’ ability to solve multiple tasks simultaneously, evolutionary multitasking is proposed to improve the overall efficiency of optimizing multiple tasks simultaneously by reusing the learned knowledge. The immune algorithm is inspired by the biological immune system that has been proven to be effective in many practical multiobjective optimization problems, with efficient convergence and search efficiency. In this paper, a novel multiobjective multifactorial immune algorithm is proposed with a novel information transfer method to solve multiobjective multitask optimization problems. For each task, information advantageous for this task will be transferred from the others to accelerate convergence through the proposed information transfer method. Finally, the proposed algorithm is compared with the state-of-the-art multiobjective evolutionary multitasking algorithms and the classic multiobjective evolutionary algorithms. The experimental results on the classical multiobjective multitask and the multiobjective many-task test suites demonstrate that the proposed algorithm provides very promising performances.

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.

Evolutionary multitasking network reconstruction from time series with online parameter estimation

Reconstructing the structure of complex networks from time series is beneficial to understanding and controlling the collective dynamics of networked systems. Existing network reconstruction algorithms can only deal with one network reconstruction problem at one time. However, real-world applications typically have multiple network reconstruction tasks and these tasks often relate to each other to certain extent. For the purpose of exploring similar network structure patterns in different tasks, we establish an evolutionary multitasking framework to simultaneously optimize double network reconstruction tasks. In the proposed method, each task is modeled as a single objective problem containing the reconstruction error and the l0-norm of the weight matrix, which takes both the reconstruction error and the structure error into consideration and deals with the NP-hard problem directly. Online parameter learning scheme is employed to learn the parameter automatically controlling the amount of genetic material to exchange, thus avoiding the negative transfer while allowing the useful information pass between tasks. In addition, the least absolute shrinkage and selection operator (LASSO) initialization is employed to further enhance the performance. We apply the evolutionary multitasking framework to reconstruct both synthetic and real networks of evolutionary game, resistor networks, and communication network dynamic models. The experimental results demonstrate that the proposal exhibits competitive performance against state-of-the-arts in terms of all evaluation measures.

Solving Multitask Optimization Problems With Adaptive Knowledge Transfer via Anomaly Detection

Evolutionary multitask optimization (EMTO) has recently attracted widespread attention in the evolutionary computation community, which solves two or more tasks simultaneously to improve the convergence characteristics of tasks when individually optimized. Effective knowledge between tasks is transferred by taking advantage of the parallelism of population-based search. Without any prior knowledge about tasks, it is a challenging problem of how to adaptively transfer effective knowledge between tasks and reduce the impact of negative transfer in EMTO. However, these two issues are rarely studied simultaneously in the existing literature. Besides, in complex many-task environments, the potential relationships among individuals from highly diverse populations associated with tasks directly determine the effectiveness of cross-task knowledge transfer. Keeping those in mind, we propose a multitask evolutionary algorithm based on anomaly detection (MTEA-AD). Specifically, each task is assigned a population and an anomaly detection model. Each anomaly detection model is used to learn the relationship among individuals between the current task and the other tasks online. Individuals that may carry negative knowledge are identified as outliers, and candidate transferred individuals identified by the anomaly detection model are selected to assist the current task, which may carry common knowledge across the current task and other tasks. Furthermore, to realize the adaptive control of the degree of knowledge transfer, the successfully transferred individuals that survive to the next generation through the elitism are used to update the anomaly detection parameter. The fair competition between offspring and candidate transferred individuals can effectively reduce the risk of negative transfer. Finally, the empirical studies on a series of synthetic benchmarks and a practical study are conducted to verify the effectiveness of MTEA-AD. The experimental results demonstrate that our proposal can adaptively adjust the degree of knowledge transfer through the anomaly detection model to achieve highly competitive performance compared to several state-of-the-art EMTO methods.

Cognizant Multitasking in Multiobjective Multifactorial Evolution: MO-MFEA-II.

Humans have the ability to identify recurring patterns in diverse situations encountered over a lifetime, constantly understanding relationships between tasks and efficiently solving them through knowledge reuse. The capacity of artificial intelligence systems to mimic such cognitive behaviors for effective problem solving is deemed invaluable, particularly when tackling real-world problems where speed and accuracy are critical. Recently, the notion of evolutionary multitasking has been explored as a means of solving multiple optimization tasks simultaneously using a single population of evolving individuals. In the presence of similarities (or even partial overlaps) between high-quality solutions of related optimization problems, the resulting scope for intertask genetic transfer often leads to significant performance speedup-as the cost of re-exploring overlapping regions of the search space is reduced. While multitasking solvers have led to recent success stories, a known shortcoming of existing methods is their inability to adapt the extent of transfer in a principled manner. Thus, in the absence of any prior knowledge about the relationships between optimization functions, a threat of predominantly negative (harmful) transfer prevails. With this in mind, this article presents a realization of a cognizant evolutionary multitasking engine within the domain of multiobjective optimization. Our proposed algorithm learns intertask relationships based on overlaps in the probabilistic search distributions derived from data generated during the course of multitasking-and accordingly adapts the extent of genetic transfers online. The efficacy of the method is substantiated on multiobjective benchmark problems as well as a practical case study of knowledge transfers from low-fidelity optimization tasks to substantially reduce the cost of high-fidelity optimization.

Surrogate-Assisted Evolutionary Multitask Genetic Programming for Dynamic Flexible Job Shop Scheduling

Dynamic flexible job shop scheduling (JSS) is an important combinatorial optimization problem with complex routing and sequencing decisions under dynamic environments. Genetic programming (GP), as a hyperheuristic approach, has been successfully applied to evolve scheduling heuristics for JSS. However, its training process is time consuming, and it faces the retraining problem once the characteristics of job shop scenarios vary. It is known that multitask learning is a promising paradigm for solving multiple tasks simultaneously by sharing knowledge among the tasks. To improve the training efficiency and effectiveness, this article proposes a novel surrogate-assisted evolutionary multitask algorithm via GP to share useful knowledge between different scheduling tasks. Specifically, we employ the phenotypic characterization for measuring the behaviors of scheduling rules and building a surrogate for each task accordingly. The built surrogates are used not only to improve the efficiency of solving each single task but also for knowledge transfer in multitask learning with a large number of promising individuals. The results show that the proposed algorithm can significantly improve the quality of scheduling heuristics for all scenarios. In addition, the proposed algorithm manages to solve multiple tasks collaboratively in terms of the evolved scheduling heuristics for different tasks in a multitask scenario.

Two-stage multi-tasking transform framework for large-scale many-objective optimization problems

Real-world optimization applications in complex systems always contain multiple factors to be optimized, which can be formulated as multi-objective optimization problems. These problems have been solved by many evolutionary algorithms like MOEA/D, NSGA-III, and KnEA. However, when the numbers of decision variables and objectives increase, the computation costs of those mentioned algorithms will be unaffordable. To reduce such high computation cost on large-scale many-objective optimization problems, we proposed a two-stage framework. The first stage of the proposed algorithm combines with a multi-tasking optimization strategy and a bi-directional search strategy, where the original problem is reformulated as a multi-tasking optimization problem in the decision space to enhance the convergence. To improve the diversity, in the second stage, the proposed algorithm applies multi-tasking optimization to a number of sub-problems based on reference points in the objective space. In this paper, to show the effectiveness of the proposed algorithm, we test the algorithm on the DTLZ and LSMOP problems and compare it with existing algorithms, and it outperforms other compared algorithms in most cases and shows disadvantage on both convergence and diversity.

Surrogate-Assisted Evolutionary Multitasking for Expensive Minimax Optimization in Multiple Scenarios

Minimax optimization is a widely-used formulation for robust design in multiple operating or environmental scenarios, where the worst-case performance among multiple scenarios is the optimization objective requiring a large number of quality assessments. Consequently, minimax optimization using evolutionary algorithms becomes prohibitive when each quality assessment involves computationally expensive numerical simulations or costly physical experiments. This work employs evolutionary multitasking optimization and surrogate techniques to address the challenges of the high-dimensional search space and high computation cost of minimax optimization. To this end, finding the worst-case scenario for different candidate solutions is considered as the optimization of multiple problems that can be solved simultaneously using the evolutionary multitasking optimization approach. In order to further speed up the proposed algorithm, a surrogate model in the joint space of the decision and scenario spaces is built to replace part of the expensive function evaluations. A generation-based model management strategy using a statistical hypothesis test is designed to manage the surrogate model. Experimental results on both benchmark problems and an airfoil design application indicate that the proposed algorithm can find satisfactory solutions with a very limited computational budget.

Evolutionary Transfer Optimization - A New Frontier in Evolutionary Computation Research

The evolutionary algorithm (EA) is a nature-inspired population-based search method that works on Darwinian principles of natural selection. Due to its strong search capability and simplicity of implementation, EA has been successfully applied to solve many complex optimization problems, which cannot be easily solved by traditional exact mathematical approaches, such as linear programming, quadratic programming, and convex optimization. Despite its great success, it is worth noting that traditional EA solvers start the search from scratch by assuming zero prior knowledge about the task at hand. However, as problems seldom exist in isolation, solving one problem may yield useful information for solving other related problems. There has been growing interest in conducting research on evolutionary transfer optimization (ETO) in recent years: a paradigm that integrates EA solvers with knowledge learning and transfer across related domains to achieve better optimization efficiency and performance. This paper provides an overview of existing works of ETO based on the type of problems being solved by these methods, which are ETO for Optimization in Uncertain Environment, ETO for Multitask Optimization, ETO for Complex Optimization, ETO for Multi/Many-Objective Optimization, and ETO for Machine Learning Applications. The paper also highlights some of the challenges faced in this emerging research field of computational intelligence and discusses some promising future research directions in ETO. It is hoped that the study presented in this paper can help to inspire the development of more advanced ETO methods and applications.

An Improved Genetic Transmission and Dynamic-Opposite Learning Strategy for Multitasking Optimization

Multi-task evolutionary optimization is a new method proposed in recent years to solve optimization problems. Compared with traditional single-task optimization, the multi-task optimization mechanism based on evolutionary algorithms promotes the evolution of population by sharing the potential similarity and complementarity between different problems, so as to improve the performance and efficiency of solving problems. However, with the evolution of the population, the ability of one task to learn from other tasks may decrease, and the efficiency of knowledge transfer will also decrease. To address this issue and improve the quality of knowledge transfer among the tasks, this article proposes a new genetic transmission strategy and mutation strategy of multi task optimization algorithm, namely DOMLMFEA. In particular, in the genetic process, if two parent individuals are specific to different tasks, one parent individual is mapped to the vicinity of the other parent individual through task space mapping, and high-quality offspring individuals are generated through crossover. In addition, a dynamic opposite mutual learning mutation strategy based on wavelet basis function is introduced to generate promising solutions. It can effectively explore and develop in the unified search space and the subspace of each task, and improve the local search ability of the algorithm and the diversity of solutions. In order to evaluate the performance of DOMLMFEA, this paper tests on classical multi-task optimization problems, and compared with several other state-of-the-art MFEA variants. Numerical and simulation results show the effectiveness of the proposed DOMLMFEA.

Learning Task Relationships in Evolutionary Multitasking for Multiobjective Continuous Optimization.

Multiobjective multifactorial optimization (MO-MFO), rooted in a multitasking environment, is an emerging paradigm wherein multiple distinct multiobjective optimization problems are solved together. This article proposes an evolutionary multitasking algorithm with learning task relationships (LTR) for MO-MFO. In the proposed algorithm, a procedure of LTR is well designed. The decision space of each task is treated as a manifold, and all decision spaces of different tasks are jointly modeled as a joint manifold. Then, through solving a generalized eigenvalue decomposition problem, the joint manifold is projected to a latent space while keeping the necessary features for all tasks and the topology of each manifold. Finally, the task relationships are represented as the joint mapping matrix, which is composed of multiple mapping functions, and they are utilized for information transfer across different decision spaces during the evolutionary process. In the empirical experiments, the performance of the proposed algorithm is verified and compared with several state-of-the-art solvers for MO-MFO on three suites of MO-MFO test problems. Empirical results demonstrate that the proposed algorithm surpasses other competitors on most test instances, and can well tackle complicated MO-MFO problems which involve distinct optimization tasks with heterogeneous decision spaces.