Evolutionary Multitask Optimization Research Articles

Multi-Objective Automatic Clustering Algorithm Based on Evolutionary Multi-Tasking Optimization

Data mining technology is the process of extracting hidden knowledge and potentially useful information from a large number of incomplete, noisy, and random practical application data. The clustering algorithm based on multi-objective evolution has obvious advantages compared with the traditional single-objective method. In order to further improve the performance of evolutionary multi-objective clustering algorithms, this paper proposes a multi-objective automatic clustering model based on evolutionary multi-task optimization. Based on the multi-objective clustering algorithm that automatically determines the value of k, evolutionary multi-task optimization is introduced to deal with multiple clustering tasks simultaneously. A set of non-dominated solutions for clustering results is obtained by concurrently optimizing the overall deviation and connectivity index. Multi-task adjacency coding based on a locus adjacency graph was designed to encode the clustered data. Additionally, an evolutionary operator based on relevance learning was designed to facilitate the evolution of individuals within the population. It also facilitates information transfer between individuals with different tasks, effectively avoiding negative transfer. Finally, the proposed algorithm was applied to both artificial datasets and UCI datasets for testing. It was then compared with traditional clustering algorithms and other multi-objective clustering algorithms. The results verify the advantages of the proposed algorithm in clustering accuracy and algorithm convergence.

Evolutionary Multitasking Optimization Enhanced by Geodesic Flow Kernel

Evolutionary Multitasking Optimization Enhanced by Geodesic Flow Kernel

Evolutionary Multi-Tasking Optimization for High-Efficiency Time Series Data Clustering

Evolutionary Multi-Tasking Optimization for High-Efficiency Time Series Data Clustering

Diversified Knowledge Transfer Strategy for Multitasking Particle Swarm Optimization.

Evolutionary multitasking optimization (EMTO) has capability of performing a population of individuals together by sharing their intrinsic knowledge. However, the existed methods of EMTO mainly focus on improving its convergence using parallelism knowledge belonging to different tasks. This fact may lead to the problem of local optimization in EMTO due to unexploited knowledge on behalf of the diversity. To address this problem, in this article, a diversified knowledge transfer strategy is proposed for multitasking particle swarm optimization algorithm (DKT-MTPSO). First, according to the state of population evolution, an adaptive task selection mechanism is introduced to manage the source tasks that contribute to the target tasks. Second, a diversified knowledge reasoning strategy is designed to capture the knowledge of convergence, as well as the knowledge associated with diversity. Third, a diversified knowledge transfer method is developed to expand the region of generated solutions guided by acquired knowledge with different transfer patterns so that the search space of tasks can be explored comprehensively, which is favor of EMTO alleviating local optimization. Finally, the performance of the proposed algorithm is evaluated in comparison with some other state-of-the-art EMTO algorithms on multiobjective multitasking benchmark test suits, and the practicality of the algorithm is verified in a real-world application study. The results of experiments demonstrate the superiority of DKT-MTPSO compared to other algorithms.

Constrained Multiobjective Optimization via Multitasking and Knowledge Transfer

Solving constrained multi-objective optimization problems (CMOPs) with various features and challenges via evolutionary algorithms is very popular. Existing methods usually adopt an additional helper problem to simplify and solve them by divide-and-conquer. This paper proposes a new multitasking framework for CMOPs, borrowing the idea of evolutionary multitasking optimization. The main contributions are i) a multitasking framework is proposed, where a CMOP is modeled as a multitasking optimization problem with three tasks. Then, it is solved by constraint-first, constraint-ignored, and constraint-relaxed multi-objective evolutionary algorithms; ii) a knowledge expression and a transfer strategy are devised to transfer the knowledge among the tasks; and iii) based on the proposed framework, a new two-stage algorithm is presented to solve CMOPs. The effectiveness of our approach is validated through experiments on four CMOP benchmark suites and 19 real-world CMOPs.

Evolutionary Optimization with Simplified Helper Task for High-dimensional Expensive Multiobjective Problems

In recent years, surrogate-assisted evolutionary algorithms (SAEAs) have been sufficiently studied for tackling computationally expensive multiobjective optimization problems (EMOPs), as they can quickly estimate the qualities of solutions by using surrogate models to substitute for expensive evaluations. However, most existing SAEAs only show promising performance for solving EMOPs with no more than 10 dimensions, and become less efficient for tackling EMOPs with higher dimensionality. Thus, this article proposes a new SAEA with a simplified helper task for tackling high-dimensional EMOPs. In each generation, one simplified task will be generated artificially by using random dimension reduction on the target task (i.e., the target EMOPs). Then, two surrogate models are trained for the helper task and the target task, respectively. Based on the trained surrogate models, evolutionary multitasking optimization is run to solve these two tasks, so that the experiences of solving the helper task can be transferred to speed up the convergence of tackling the target task. Moreover, an effective model management strategy is designed to select new promising samples for training the surrogate models. When compared to five competitive SAEAs on four well-known benchmark suites, the experiments validate the advantages of the proposed algorithm on most test cases.

An adaptive multitasking optimization algorithm based on population distribution.

Evolutionary multitasking optimization (EMTO) handles multiple tasks simultaneously by transferring and sharing valuable knowledge from other relevant tasks. How to effectively identify transferred knowledge and reduce negative knowledge transfer are two key issues in EMTO. Many existing EMTO algorithms treat the elite solutions in tasks as transferred knowledge between tasks. However, these algorithms may not be effective enough when the global optimums of the tasks are far apart. In this paper, we study an adaptive evolutionary multitasking optimization algorithm based on population distribution information to find valuable transferred knowledge and weaken the negative transfer between tasks. In this paper, we first divide each task population into K sub-populations based on the fitness values of the individuals, and then the maximum mean discrepancy (MMD) is utilized to calculate the distribution difference between each sub-population in the source task and the sub-population where the best solution of the target task is located. Among the sub-populations of the source task, the sub-population with the smallest MMD value is selected, and the individuals in it are used as transferred individuals. In this way, the solution chosen for the transfer may be an elite solution or some other solution. In addition, an improved randomized interaction probability is also included in the proposed algorithm to adjust the intensity of inter-task interactions. The experimental results on two multitasking test suites demonstrate that the proposed algorithm achieves high solution accuracy and fast convergence for most problems, especially for problems with low relevance.

Evolutionary Multitask Optimization With Lower Confidence Bound-Based Solution Selection Strategy

Evolutionary Multitask Optimization With Lower Confidence Bound-Based Solution Selection Strategy

Block-Level Knowledge Transfer for Evolutionary Multitask Optimization.

Evolutionary multitask optimization is an emerging research topic that aims to solve multiple tasks simultaneously. A general challenge in solving multitask optimization problems (MTOPs) is how to effectively transfer common knowledge between/among tasks. However, knowledge transfer in existing algorithms generally has two limitations. First, knowledge is only transferred between the aligned dimensions of different tasks rather than between similar or related dimensions. Second, the knowledge transfer among the related dimensions belonging to the same task is ignored. To overcome these two limitations, this article proposes an interesting and efficient idea that divides individuals into multiple blocks and transfers knowledge at the block-level, called the block-level knowledge transfer (BLKT) framework. BLKT divides the individuals of all the tasks into multiple blocks to obtain a block-based population, where each block corresponds to several consecutive dimensions. Similar blocks coming from either the same task or different tasks are grouped into the same cluster to evolve. In this way, BLKT enables the transfer of knowledge between similar dimensions that are originally either aligned or unaligned or belong to either the same task or different tasks, which is more rational. Extensive experiments conducted on CEC17 and CEC22 MTOP benchmarks, a new and more challenging compositive MTOP test suite, and real-world MTOPs all show that the performance of BLKT-based differential evolution (BLKT-DE) is superior to the compared state-of-the-art algorithms. In addition, another interesting finding is that the BLKT-DE is also promising in solving single-task global optimization problems, achieving competitive performance with some state-of-the-art algorithms.

Accelerating Evolutionary Multitasking Optimization With a Generalized GPU-Based Framework

Accelerating Evolutionary Multitasking Optimization With a Generalized GPU-Based Framework

Ensemble Multifactorial Evolution With Biased Skill-Factor Inheritance for Many-Task Optimization

Current years have witnessed an increment in the number of research activities on improving the efficacy of multitasking algorithms for tackling challenging optimization problems. However, current approaches often present two potential problems. Firstly, although tasks may have different characteristics, existing literature usually utilizes only one search operator for all of them. Secondly, while multitasking environments comprise tasks of varying difficulty, previous proposals treat them equally. This paper proposes an algorithm named Ensemble Multifactorial Evolution with Biased Skill Factor Inheritance (EME-BI) for optimizing a large number of tasks simultaneously. In EME-BI, an effective parameter adaptation based on the knowledge transfer quality with Biased Skill-Factor Inheritance mechanism is designed to minimize negative transfer and allocate generated offspring to tasks that need resources. Besides, instead of using only one fixed search operator, EME-BI can automatically select the most appropriate one for each task at each evolutionary stage. Finally, the proposed algorithm is armed with a dynamically adjusted population size to promote exploitation. Empirical studies on various many-task benchmark problems and a real-world problem are conducted to verify the efficiency of EME-BI. The results portrayed that EME-BI achieves highly competitive performance compared to several state-of-the-art algorithms regarding the solution quality, convergence trend, and computation time. This proposal also won first prize at the CEC2021 Competition on Evolutionary Multi-task Optimization, Multi-task single-objective optimization.

Node depth Representation-based Evolutionary Multitasking Optimization for Maximizing the Network Lifetime of Wireless Sensor Networks

Wireless Sensor Networks (WSNs) face challenges related to limited energy resources in sensor nodes, making network lifetime and energy consumption critical considerations. In this paper, we introduce a novel approach to extend network lifetime and reduce energy consumption in WSNs by optimizing network architecture selection. We explore various architecture options, including single-layer and multi-layer networks, to determine the most suitable configuration. Several studies have applied knowledge transfer in evolutionary multitasking optimization to maximize network lifetime, achieving state-of-the-art results for the problem. However, they still have some drawbacks, such as redundant representations, i.e., many genotypes represent the same phenotype, and invalid solution generation. To address these limitations, we propose a new evolutionary multitasking algorithm incorporating efficient encoding to represent tree-structure solutions (network architectures) to the problem. Additionally, we tailor new genetic operators, such as recombination and mutation, to meet the specific requirements of our proposed evolutionary multitasking algorithm. The standout feature of our proposal lies in its ability to consistently generate valid solutions for the problem, which significantly reduces redundancy within the genotype search space and effectively satisfies the problem constraints. Additionally, our multitask evolutionary algorithm facilitates the exploration of various network architectures, harnessing knowledge transfer to enhance optimal performance and reduce computation time compared to single-task methods. We conduct comprehensive experiments on diverse datasets and use statistical tests, e.g., the Wilcoxon signed rank test, to verify the performance of our proposed algorithms. The empirical results demonstrate that our proposed algorithm outperforms existing methods and achieves state-of-the-art results in terms of solution quality, convergence rate, and running time across a wide range of data instances. Specifically, our algorithm provides 49.54% better solution quality on average across all data types compared to the previous state-of-the-art method.

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.

An ensemble knowledge transfer framework for evolutionary multi-task optimization

The cognitive capability of learning from past experiences to resolve relevant tasks at hand is a hallmark of humans. The emerging evolutionary multi-task transfer optimization (EMTO) fashion pursues such intelligent behavior by exploring useful knowledge drawn from solving one task to accelerate the optimization process of other related tasks. However, in practical scenario, knowledge drawn from various task domains may not always benefit the solving process of one another, and source-target domain mismatch is likely to induce notorious negative transfer, which is a critical concern in EMTO. Domain adaption aims to narrow the gap between distinct domains so as to curb negative transfer. Generally, different strategies possess distinct advantages in different situations, no one can dominate others in all cases. Taking this cue, we present a novel bandit-mechanism-based ensemble method to determine the proper domain adaption strategy online in the context of EMTO. Besides, the intensity of cross-task knowledge transfer is adapted according to historical experiences of the population. We carry out extensive experiments to examine the performance of proposed approach, demonstrating its superiority in comparison to state-of-the-art peers in multi-task problem-solving scenario. Our work thus sheds light on a new alternative way for automatic domain adaption for knowledge transfer across problems.

Multitasking evolutionary algorithm based on adaptive seed transfer for combinatorial problem

Evolutionary computing (EC) is widely used in dealing with combinatorial optimization problems (COP). Traditional EC methods can only solve a single task in a single run, while real-life scenarios often need to solve multiple COPs simultaneously. In recent years, evolutionary multitasking optimization (EMTO) has become an emerging topic in the EC community. And many methods have been designed to deal with multiple COPs concurrently through exchanging knowledge. However, many-task optimization, cross-domain knowledge transfer, and negative transfer are still significant challenges in this field. A new evolutionary multitasking algorithm based on adaptive seed transfer (MTEA-AST) is developed for multitasking COPs in this work. First, a dimension unification strategy is proposed to unify the dimensions of different tasks. And then, an adaptive task selection strategy is designed to capture the similarity between the target task and other online optimization tasks. The calculated similarity is exploited to select suitable source tasks for the target one and determine the transfer strength. Next, a task transfer strategy is established to select seeds from source tasks and correct unsuitable knowledge in seeds to suppress negative transfer. Finally, the experimental results indicate that MTEA-AST can adaptively transfer knowledge in both same-domain and cross-domain many-task environments. And the proposed method shows competitive performance compared to other state-of-the-art EMTOs in experiments consisting of four COPs.

Many-task evolutionary algorithm with adaptive knowledge transfer via density-based clustering

Evolutionary multitask optimization (EMTO) explores how to solve two or more related optimization tasks simultaneously by exploiting useful knowledge of other related tasks while solving one task, with the goal of enhancing the performance of the algorithm in solving each task. There has been a large body of work in the literature on knowledge transfer and reuse. However, when the number of tasks increases to a certain extent, the potential negative knowledge transfer between tasks becomes a great challenge for most multitask evolutionary algorithms. To allay this threat, this study proposes an adaptive knowledge transfer strategy for evolutionary many-task optimization via density-based clustering (AEMaTO-DC). AEMaTO-DC contains an adaptive mating selection mechanism, a correlation task evaluation and selection mechanism and a cluster-based knowledge interaction mechanism between tasks. Specifically, AEMaTO-DC regulates the probability of knowledge transfer by comparing the relative intensity of the intertask evolution rate and intratask evolution rate. In knowledge transfer, AEMaTO-DC selects related tasks by a maximum mean discrepancy metric, and it determines the intensity of intertask interaction by a density-based clustering method. We compare the performance of AEMaTO-DC with several state-of-the-art multitask evolutionary algorithms on a variety of synthetic benchmarks and a real-world multitask optimization problem. The experimental results demonstrate that AEMaTO-DC shows competitive success rates in solving the many-task problems used, and it takes advantage of synergistic relationships among solution processes for the tasks addressed.

A Self-Adaptive Evolutionary Multi-Task Based Constrained Multi-Objective Evolutionary Algorithm

Constrained multi-objective optimization problems (CMOPs) are difficult to solve since they involve the optimization of multiple objectives and the satisfaction of various constraints. Most constrained multi-objective evolutionary algorithms (CMOEAs) are prone to fall into the local optima due to the imbalance between objectives and constraints as well as the poor search ability of the population. To better solve CMOPs, this paper proposes a double-balanced evolutionary multi-task optimization (DBEMTO) algorithm, which evolves two populations to respectively solve the main task (CMOP) and the auxiliary task (MOP extracted from the CMOP). In DBEMTO, three evolutionary strategies are assigned to each population for offspring generation. The three evolutionary strategies include an individual transfer-based inter-task strategy and two intra-task strategies, not only utilizing the information of inter-task but also providing diverse search abilities of intra-task. Moreover, a self-adaptive scheme is developed to self-adaptively employ three strategies, so that the population can balance the information utilization of both intra-task and inter-task. Then, in the environmental selection, the performance of the three strategies is adopted to guide the sharing of the two offspring populations. Compared with several other state-of-the-art CMOEAs, DBEMTO has performed more competitively according to the final results.

Enhancing the Robustness of Networks Against Multiple Damage Models Using a Multifactorial Evolutionary Algorithm

Networked systems widely exist in the modern society, and these systems are always operated in the presence of attacks and errors. The robustness of a network indicates its tolerance against potential damages, which is crucial for the network’s normal functionalities. Damage models including malicious attacks and cascading failures have been considered in previous studies. And the mitigation on these two destructive damages has attracted increasing attention, both single-objective and multiobjective optimization techniques are proposed to enhance the robustness of networks. The main weakness of these methods is that the obtained results can only handle one type of damages, either malicious attacks or cascading failures. In this way, multiple independent realizations are evitable to acquire robust candidates against different damages, which omits the inherent complementarities between the optimization of different objectives. Also, the design of networks with comprehensive robustness (CR) against both the two destructive damages is still pendent. For improving the efficiency in optimizing networks considering multiple damage models, in this article, evolutionary multitasking optimization is introduced into the optimization of network robustness. A multifactorial evolutionary algorithm (MFEA) for enhancing the CR of networks, called MFEACR, has been proposed. The algorithm is equipped with several dedicated genetic operators to find networks with robust structures against malicious attacks and cascading failures; meanwhile, the synergy between the optimization of the two objectives is exploited to improve the computational efficiency. Empirical studies demonstrate the competitive performance of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\rm MFEA}_{{\rm CR}}$</tex-math> </inline-formula> over existing methods; the efficiency enhancement is remarkable via the simultaneous optimization of multiple objectives.

Network Collaborative Pruning Method for Hyperspectral Image Classification Based on Evolutionary Multi-Task Optimization

Neural network models for hyperspectral images classification are complex and therefore difficult to deploy directly onto mobile platforms. Neural network model compression methods can effectively optimize the storage space and inference time of the model while maintaining the accuracy. Although automated pruning methods can avoid designing pruning rules, they face the problem of search efficiency when optimizing complex networks. In this paper, a network collaborative pruning method is proposed for hyperspectral image classification based on evolutionary multi-task optimization. The proposed method allows classification networks to perform the model pruning task on multiple hyperspectral images simultaneously. Knowledge (the important local sparse structure of the network) is automatically searched and updated by using knowledge transfer between different tasks. The self-adaptive knowledge transfer strategy based on historical information and dormancy mechanism is designed to avoid possible negative transfer and unnecessary consumption of computing resources. The pruned networks can achieve high classification accuracy on hyperspectral data with limited labeled samples. Experiments on multiple hyperspectral images show that the proposed method can effectively realize the compression of the network model and the classification of hyperspectral images.

Multi-task evolutionary optimization of multi-echelon location routing problems via a hierarchical fuzzy graph

Multi-echelon location-routing problems (ME-LRPs) deal with determining the location of facilities and the routes of vehicles on multi-echelon routing tasks. Since the assignment relationship in multi-echelon routing tasks is uncertain and varying, ME-LRPs are very challenging to solve, especially when the number of the echelons increases. In this study, the ME-LRP is formulated as a hierarchical fuzzy graph, in which high-order fuzzy sets are constructed to represent the uncertain assignment relationship as different routing tasks and cross-task operators are used for routing task selection. Then, an evolutionary multi-tasking optimization algorithm is designed to simultaneously solve the multiple routing tasks. To alleviate negative transfer between the different routing tasks, multi-echelon assignment information is considered together with associated routing task selection in multi-tasking evolution optimization. The experimental results on multi-echelon routing benchmark problems demonstrate the competitiveness of the proposed method.