The development of multiagent systems (MASs) has given rise to a new type of traveling salesman problem (TSP), namely the multiagent TSP (MATSP). MATSP aims to find multiple routes with the minimum total cost through the cooperation of intelligent agents. Since the distributed nature of MATSP, it is challenging to solve MATSP effectively in a distributed manner. This article focuses on MATSP and proposes a distributed ant colony system with pheromone transfer (DACS) to solve the problem. First, we formally define MATSP, in which each agent has only partial data and independently makes routing decisions. All agents cooperate to make a consensus on the visiting conflicts caused by the loss of global information. To further consider the balanced workloads of agents, the fairness-aware colored MATSP is further formulated. Second, to solve MATSP in a distributed manner, the proposed DACS allows each agent to run an ant colony optimizer and be responsible for the routing under its jurisdiction. To coordinate these agents to avoid conflicts, a bidding-based cooperation mechanism (BCM) is designed to reach a consensus on the allocation of cities. Agents bid for the accessibilities of cities based on market-based economic theory, owning the ability to adapt to complex environments. Two pheromone transfer strategies are designed to improve efficiency. DACS transfers learned pheromones within the same agent and between different agents. Besides, we conduct extensive experiments in nine datasets to certify the effectiveness of DACS. Experimental results show that DACS is effective and efficient even in complex environments.

Crowdsourcing leverages the collective intelligence of the crowd to collect data and solve complex computational tasks. Driven by this paradigm, data can now be gathered more efficiently and at larger scales, thereby increasing the need for effective dimensionality reduction, which makes feature selection (FS) essential for efficient learning. In this paper, we refer to the problem in which multiple workers in a crowdsourcing environment collect data and concurrently optimize FS as the crowdsourcing feature selection (CFS) problem. In CFS, workers perform FS on local data and upload candidate feature subsets to complete the outsourced task. Nevertheless, the heterogeneity across multiple data sources hinders the formation of a reliable and high-quality consensus solution. To address this issue, we propose a cooperative learning-based Distributed Evolutionary Algorithm for the CFS problem (DEA-CFS). First, we formulate the CFS problem and define the roles of workers and the server, as well as their interactions in a crowdsourcing environment. Second, on the worker side, we design a distributed cooperative learning strategy that refines local solutions and mitigates data heterogeneity through confidence-aware fitness comparison. Third, on the server side, we introduce an adaptive credibility-based aggregation mechanism that aggregates a robust consensus solution. Extensive experiments on 18 datasets with up to 10,000 features demonstrate the efficiency and effectiveness of DEA-CFS. Specifically, compared to four existing distributed baselines, DEA-CFS achieves a superior average rank of 1.16 and obtains the best performance on 15 of the 18 datasets.

Surrogate model-assisted evolutionary algorithm (SAEA) has become a generalized method for expensive optimization problems (EOPs) with high-cost evaluations. However, most existing SAEAs retrain surrogate models frequently during evolutionary iterations. Besides, the quality of sample data directly affects model accuracy, leading to difficulties in finding the optimal solution. To address these challenges, this paper introduces the tree-based broad learning system (TBLS) as the surrogate model into SAEA framework, and a TBLS-assisted optimizer with incremental learning (TBLSO-IF) is proposed. First, an incrementable TBLS is constructed for predicting the quality of the solution, and the model is incrementally updated by expanding the layer nodes when the samples increase. And then effectively avoids the high computational costs of retraining models from scratch and significantly improves the update efficiency of surrogate models. Second, an adaptive sample augmentation (ASA) strategy is designed to generate more samples for updating the TBLS using a variational autoencoder (VAE). Experiments on 15 problems in the CEC2017 benchmark functions show that the proposed TBLSO-IF algorithm is more effective and competitive than the other five state-of-the-art SAEA methods.

Crowdsourcing has become a powerful tool for data collection and problem-solving, harnessing collective intelligence to address complex tasks. Building knowledge bases through such intelligence is gaining attention to enhance cross-domain model performance. As an essential technique for dimensionality reduction, the task of feature selection (FS) also emerges in the context of crowdsourcing, resulting in crowd-sourcing feature selection (CFS). Due to the diversity of workers and the varying quality of data in a crowdsourcing environment, CFS faces challenges such as heterogeneous data reliability and dynamic participation. To tackle these issues, we present Crowd-Fed Evolutionary Transfer Optimization (CFETO), an efficient and crowdsourcing-enhanced framework for feature selection. CFETO comprises a central server and multiple distributed workers: workers perform local data collection and optimization, extracting knowledge from their datasets, while the server integrates this knowledge to build a knowledge base. An evolutionary transfer learning strategy is further employed to harness this knowledge, thereby improving both convergence speed and selection robustness. Experiments on 20 real-world datasets show that CFETO outperforms traditional centralized FS methods approaches, underlining its potential for broader application in complex, distributed crowdsourcing scenarios.

Recent years have witnessed the increasing adoption of unmanned aerial vehicles (UAVs) for power grid inspection, as they gradually replace conventional hazardous manual operations. However, conventional metaheuristics and operations research-based path planning algorithms suffer from long computation times for large-scale problems, thus making them unsuitable for real-time multi-UAV scheduling under flight time and energy consumption uncertainty. To solve the multi-UAV online path planning problem, this paper proposes a multi-agent deep reinforcement learning (MADRL) algorithm that performs online path planning based on real-time environmental and UAV state information, with the goal of minimizing the total travel distance. We employ resource preservation and decision sharing to handle real-time cooperation under travel time uncertainty while preventing resource conflicts. We design a Safety Mask mechanism that constrains dangerous UAV actions to address energy consumption uncertainty. Experiments on instances with 40-400 towers show that our algorithm requires minimal computation time and generates higher-quality solutions compared to other baseline algorithms in large-scale tower scenarios.

The influence maximization (IM) problem in large-scale social networks has attracted great attention. Considering the interactions among multiple online social platforms, the multilayer IM problem poses further challenges ($\rm i.e.,$high-simulation burden and low-optimization quality). To solve these problems, this article proposes a susceptible-exposed-infected1-infected2-infected12-vigilant (SE3IV) model to simulate the information spreading process in multilayer networks. The spreading dynamic is modeled by mean-field equations considering the effect of cross-layer propagation. To optimize the multilayer information maximization modeled by SE3IV, an asynchronous distributed cooperative coevolutionary algorithm (ADCA) is proposed. To improve the efficiency of the algorithm in multilayer networks, the multilayer community detection first decompresses the network into a single layer by dimension-based method. Then, the Louvain method is adopted to decompose the problems into subcomponents with lower dimensionality. The populations with the same size evolve corresponding subcomponents in an asynchronous and distributed way based on the pool model. Besides, an asynchronous communication mechanism is devised to manage the communication among the shared pool. An adaptive seeds regulation strategy is designed to adjust the number of seeds of subcomponents. Numerous experiments on different networks show that ADCA possesses good scalability and efficiency, especially in large-scale networks.

In expensive multi/many-objective optimization problems (EMOPs), the expensive objectives are generally accessed through different simulation tools, leading to different evaluation latencies and unbearable computational time for serial optimization. One promising approach to improve efficiency is to perform simulation and build surrogates separately for each objective in parallel. However, how to improve the model accuracy and select promising candidates without global information are big challenges. To alleviate these problems, this article proposes an asynchronous influence-based SAEA (AIEA) based on the client-server model. Each client approximates an objective and the server takes charge for evolution. To adaptively select promising candidates, the influence degree is introduced in candidate selection, which is calculated in the objective space to judge which candidate has more beneficial influence for evolution. With the selected candidate, the most-uncertain-first strategy is devised in objective selection for asynchronous evaluations and model improvement. To handle incomplete objective values, the nearest neighbor inheritance is adopted for unevaluated objectives. Comprehensive experiments compared with five surrogate-assisted EAs demonstrate the global optimization and scalability of AIEA.

Distributed optimization has attracted lots of attention in recent years. Thanks to the intrinsic parallelism and great search capacity, evolutionary computation (EC) has the potential for black-box and non-convex distributed optimization. However, due to the decentralization of local objective functions, it is challenging to optimize the global objective function with efficient communication and guaranteed system consensus. To tackle this challenge, we propose a Multi-Agent Swarm Optimization method with adaptive Internal and External learning (MASOIE). In MASOIE, each agent evolves a swarm of particles by internal learning and external learning. Internal learning enables agents to optimize their local objectives, while external learning enables agents to cooperate to achieve a consensus toward the global objective. To improve the consensus ability, we design a special velocity setting of external learning for particle evolution. We provide the theoretical analysis of the system consensus of deterministic MASOIE. To improve communication efficiency, we design an adaptive communication mechanism to adjust the communication interval, enabling agents to explore at the early stage and reach system consensus at the later stage. Empirical studies show that the proposed algorithm achieves stable consensus performance, competitive solution quality and lower communication cost on benchmark functions compared with existing black-box distributed algorithms.

Surrogate-assisted evolutionary algorithms (SAEAs) have achieved effective performance in solving complex data-driven optimization problems. In the Internet of Things environment, the data of many problems are collected and processed in distributed network nodes and cannot be transmitted. As each local node can only access and build surrogate models based on partial data, local models are usually not accurate and even conflicting. To address these challenges, this paper proposes a classifier-ensemble-based surrogate-assisted evolutionary algorithm (CESAEA) with the following features. First, the local nodes in CESAEA train classifiers as surrogate models based on their own data to classify candidates into several levels according to their fitness quality. The classifiers are less sensitive to the partial and biased data than regression models in local nodes. Second, the central node in CESAEA ensembles the local surrogates to form a global classifier with a relaxation condition to guide the evolutionary optimizer to generate promising candidates. The relaxation condition helps to overcome the problem of local model inconsistency. Overall, CESAEA is composed of local classifier construction, global classifier ensemble, classifier-assisted evolutionary optimization and local regression-assisted selection. As only classifiers are allowed to transmit from local nodes to the central node, the mapping relationship between decision vector and objective is hidden and thus data privacy is protected. The experimental results on benchmark functions as well as distributed feature selection problems verify the effectiveness of CESAEA compared to several state-of-the-art approaches.

The emergence of the last-mile delivery by unmanned aerial vehicles (UAVs) has gained widespread attention in both scientific and industrial communities in recent years. The problem can be modeled as a mixed linear integer programming problem to minimize the routing cost to serve all customers and the number of UAV launches. Considering the complexity of the multi-depot, multi-UAV, and multi-customer pickup and delivery integrated scheduling problem, this paper proposes a novel two-stage order-aware adaptive iterative local search metaheuristic algorithm to solve this problem. In the first stage, tasks are assigned to different depots, transforming the complex original problem into multiple single depot scheduling problem. In the second stage, an order-aware adaptive iterative local search (OAILS) metaheuristic is designed to optimize the route planning for each depot's UAVs. In AILS, we propose a novel order-based adaptive operator selection named (OAOS) to select the appropriate operator based on the recent performance of operator and the order relationships of operators. Finally, a series of experiments were conducted to verify the effectiveness of the proposed OAOS and OAILS methods.

Traffic signal control (TSC) problems have received increasing attention with the development of the smart city. Reinforcement learning (RL) models TSC as a Markov decision process and learns the timing relationship of traffic scheduling from massive historical data. Due to the uncertainty and mutability of TSC problems, existing RL methods face bottlenecks in diversity and are easy to be trapped into local optima. To alleviate this predicament, this paper combines evolutionary optimization and RL to propose an evolutionary algorithm-assisted reinforcement learning (EARL-Light) method for TSC problems. EARL-Light is a population-based algorithm, in which one individual represents a policy and a population of individuals are evolved to search for near-optimal policies. The diversified search ability of evolutionary optimization can help the algorithm get rid of local optima for global optimization and the rapid learning based on the gradient of RL can achieve fast convergence. Extensive experiments on seven real-world traffic datasets demonstrates that EARL-Light achieves shorter travel time with fast convergence.

Target tracking has broad applications like disaster relief, and unmanned aerial vehicles (UAVs) have been universally applied in target tracking in recent years. Due to the strong responsiveness to deceptive reward signals and diverse exploration, evolutionary reinforcement learning (ERL) is a more noteworthy option for training UAVs than common reinforcement learning. However, for ERL contains too many neural networks, its training efficiency is not satisfactory enough. To address this shortcoming, this paper proposes an evolutionary reinforcement learning with double replay buffers (ERLDRB) for UAV online target tracking problem. Firstly, considering the energy consumption and the possible delay of feedback signals to the UAV, a more realistic model of UAV online target tracking problem is designed. Then based on the problem formulation, ERLDRB utilizes a double experience replay buffers technique to increase learning efficiency in the training stage, which can better solve real-world UAV online target tracking problem. Simulation results show that ERLDRB outperforms multiple contrasting algorithms on the designed model.

Evolutionary algorithms (EAs), such as the genetic algorithm (GA), offer an elegant way to handle combinatorial optimization problems (COPs). However, limited by expertise and resources, most users lack the capability to implement EAs for solving COPs. An intuitive and promising solution is to outsource evolutionary operations to a cloud server, however, it poses privacy concerns. To this end, this article proposes a novel computing paradigm called evolutionary computation as a service (ECaaS), where a cloud server renders evolutionary computation services for users while ensuring their privacy. Following the concept of ECaaS, this article presents privacy-preserving genetic algorithm (PEGA), a privacy-preserving GA designed specifically for COPs. PEGA enables users, regardless of their domain expertise or resource availability, to outsource COPs to the cloud server that holds a competitive GA and approximates the optimal solution while safeguarding privacy. Notably, PEGA features the following characteristics. First, PEGA empowers users without domain expertise or sufficient resources to solve COPs effectively. Second, PEGA protects the privacy of users by preventing the leakage of optimization problem details. Third, PEGA performs comparably to the conventional GA when approximating the optimal solution. To realize its functionality, we implement PEGA falling in a twin-server architecture and evaluate it on two widely known COPs: 1) the traveling Salesman problem (TSP) and 2) the 0/1 knapsack problem (KP). Particularly, we utilize encryption cryptography to protect users' privacy and carefully design a suite of secure computing protocols to support evolutionary operators of GA on encrypted chromosomes. Privacy analysis demonstrates that PEGA successfully preserves the confidentiality of COP contents. Experimental evaluation results on several TSP datasets and KP datasets reveal that PEGA performs equivalently to the conventional GA in approximating the optimal solution.

Crowdsourcing utilizes the crowd intelligence for pervasive data sensing and processing. When the processing task is a decision-making and optimization problem, the objective is evaluated based on sensed data, which is defined as crowdsourcing-based distributed optimization (CrowdDO). As evolutionary computation (EC) is a powerful technique for black-box and data-driven optimization problems, this paper combines crowdsourcing and EC to propose crowdsourcing-based EC (CrowdEC) for CrowdDO. CrowdEC performs optimization based on a server and a crowd of workers. Once receiving a CrowdDO request, the server posts the problem to workers. Each worker senses its own data and makes local decisions by local EC optimizer. Due to the heterogeneity of worker behaviors and devices, the sensed data are partial with noises, and thus the server needs to coordinate global optimization based on workers information. To avoid the leakage of worker privacy, workers only compare optimization results with adjacent workers and report comparison results to the server. With partial comparison results, the server adopts the competitive ranking to guide workers cooperation and develop the reliability detection to distinguish unreliable workers. A crowdsourcing-based level-based learning swarm optimizer is implemented as an example. Comparison experiments on benchmark testsuites and distributed clustering optimization demonstrate the potential applications of CrowdEC.

Surrogate-assisted evolutionary algorithms (SAEAs) have become a popular method to solve data-driven optimization problems (DOPs), which are common in industry. However, with the development of the Internet of Things, data are collected, processed, and stored in a distributed manner, leading a new optimization paradigm for SAEAs. To make SAEAs adapt to these distributed DOPs, this paper employs the edge computing paradigm to develop a platform that provides technical support for SAEAs with distributed structures, named ECdo. Specifically, the platform utilizes KubeEdge, an open-source edge computing framework, to mount the cluster and combines microservice interface design with the containerization strategy to offer a flexible deployment approach for distributed SAEAs. In addition, an efficient and stable internal communication mechanism is designed for the interaction between distributed components within the platform. To demonstrate the application of ECdo, we take the examples of a class of distributed DOPs, in which the objective and constraints are expensive and need to be approximated by accumulated data. These problems are known as distributed and expensive constrained optimization problems (DECOPs). We implement a distributed SAEA on ECdo to address DECOPs in real-world scenarios. Experiments show that the ECdo can provide the expected implementation for distributed SAEAs with good network tolerance under tough network conditions.

Surrogate-assisted evolutionary algorithms (EAs) have been proposed in recent years to solve data-driven optimization problems. Most existing surrogate-assisted EAs are for centralized optimization and do not take into account the challenges brought by the distribution of data at the edge of networks in the era of the Internet of Things. To this end, we propose edge-cloud co-EAs (ECCoEAs) to solve distributed data-driven optimization problems, where data are collected by edge servers. Specifically, we first propose a distributed framework of ECCoEAs, which consists of a communication mechanism, edge model management, and cloud model management. This communication mechanism is to avoid deadlock during the collaboration of edge servers and the cloud server. In edge model management, the edge models are trained based on local historical data and data composed of new solutions generated by co-evolutionary and their real evaluation values. In cloud model management, the black-box prediction functions received from edge models are used to find promising solutions to guide the edge model management. Moreover, two ECCoEAs are implemented, which proves the generality of the framework. To verify the performance of algorithms for distributed data-driven optimization problems, we design a novel benchmark test suite. The performance on the benchmarks and practical distributed clustering problems shows the effectiveness of ECCoEAs.

Expensive optimization problems (EOPs) are common in industry and surrogate-assisted evolutionary algorithms (SAEAs) have been developed for solving them. However, many EOPs have not only expensive objective but also expensive constraints, which are evaluated through distributed ways. We define this kind of EOPs as distributed expensive constrained optimization problems (DECOPs). The distributed characteristic of DECOPs leads to the asynchronous evaluation of both objective and constraints. Though some researchers have studied the asynchronous evaluation of objectives, the asynchronous evaluation of constraints has not gained much attention. Therefore, this article gives a formal formulation of DECOPs and proposes a distributed evolutionary constrained optimization algorithm with on-demand evaluation (DEAOE). DEAOE can adaptively evolve different constraints in an asynchronous way through the on-demand evaluation strategy. The on-demand evaluation works from two aspects to improve the population convergence and diversity. From the aspect of individual selection, a joint sample selection strategy is adopted to determine which candidates are promising. From the aspect of constraint selection, an infeasible-first evaluation strategy is devised to judge which constraints need to be further evolved. Extensive experiments and analyses on benchmark functions and engineering problems demonstrate that DEAOE has better performance and higher efficiency compared to centralized state-of-the-art SAEAs.

Surrogate-assisted evolutionary algorithms (SAEAs) have become a popular tool to solve expensive optimization problems and have been gradually used to deal with expensive constraints. To handle inequality expensive constraints, existing SAEAs need both the information of constraint violation and satisfaction to construct surrogate models for constraints. However, many problems only feedback whether the candidate solution is feasible or how much degree it violates constraints. There is no detailed information of how much degree the candidate satisfies constraints. The performance of most existing SAEAs decreases a lot in solving expensive constrained optimization problems (ECOPs) with such incomplete constraint information. To solve the problem, this article proposes a hybrid regressor and classifier-assisted evolutionary algorithm (HRCEA). HRCEA adopts a radial basis function regression model to approximate the degree of constraint violation. In order to make a more credible prediction, a logistic regression classifier (LRC) is constructed for the offspring rectification. The classifier works in cooperation with the$\alpha $-cut strategy, in which the high confidence level can significantly improve the prediction reliability. Besides, the LRC is built based on the boundary training data selection strategy, which is devised to select samples around feasible boundaries. This strategy is helpful for the LRC to fit the local feasibility structure. Extensive experiments on commonly used benchmark functions in CEC2006 and CEC 2010 demonstrate that HRCEA has satisfactory performance in found results and execution efficiency when solving ECOPs with incomplete constraint information. Furthermore, HRCEA is utilized to solve ceramic formula design optimization problem, which shows its promising application in real-world optimization problems.

Constraint handling is a core part when using surrogate-assisted evolutionary algorithms (SAEAs) to solve expensive constrained optimization problems (ECOPs). However, most existing SAEAs for ECOPs train a surrogate for each constraint. With the number of constraints increasing, the training burden of surrogates becomes heavy and the efficiency of the algorithm is greatly reduced. To solve this issue, this article proposes an efficient two-stage surrogate-assisted differential evolution (eToSA-DE) algorithm to handle expensive inequality constraints. eToSA-DE trains one surrogate for the degree of constraint violation and the type of the surrogate varies during the evolution process. In the first stage when there are only a few feasible individuals, a Gaussian process regression model is trained to fit the degree of constraint violation. In the second stage when more feasible individuals are accumulated, a support vector machine classification model is trained to classify whether candidates are feasible. Both types of surrogates are constructed by individuals which are chosen by the boundary training data selection strategy. These selected individuals are located around the feasible boundaries and helpful for the surrogate to approximate the feasibility structure. Besides, a feasible exploration strategy is devised to search for promising areas. To alleviate the error caused by the regression model, a nearest neighbor rectification is adopted to modify the prediction results. Extensive experiments on benchmark test functions and two formulated engineering optimization problems demonstrate that the proposed method can get satisfactory optimization results and significantly improve the efficiency of the algorithm.

One essential issue in surrogate-assisted evolutionary algorithms (SAEAs) is how to evaluate solutions and find candidates for evolution, without resorting to the calculation of the computational-expensive real objective function. While most studies use regression models as surrogate models for SAEAs, some recent work propose to use classification models for single-objective expensive optimization, as classification models are more stable and much easier to train with limited available data. However, for multi-objective expensive optimization problems, it is more challenging to classify the solutions into different levels according to their quality, and thus the use of classification-based surrogate models for multi-objective SAEAs has not been explored in-depth. To this end, in this paper we propose a classification-assisted level-based learning swarm optimizer for expensive multi-objective optimization. First, a preference relationship among individuals taking both Pareto dominance and crowding distance into account is defined to divide the whole population into different quality levels. Then, a classification model is trained as the surrogate. In addition, a selection strategy is devised in decision space to acquire solutions on the sparse part on the Pareto front. Experimental results validate the superiority and efficiency of the proposed algorithm on benchmark test functions.

Surrogate-assisted evolutionary algorithms (SAEAs) have become one popular method to solve complex and computationally expensive optimization problems. However, most existing SAEAs suffer from performance degradation with the dimensionality increasing. To solve this issue, this article proposes a classifier-assisted level-based learning swarm optimizer on the basis of the level-based learning swarm optimizer (LLSO) and the gradient boosting classifier (GBC) to improve the robustness and scalability of SAEAs. Particularly, the level-based learning strategy in LLSO has a tight correspondence with the classification characteristic by setting the number of levels in LLSO to be the same as the number of classes in GBC. Together, the classification results feedback the distribution of promising candidates to accelerate the evolution of the optimizer, while the evolved population helps to improve the accuracy of the classifier. To select informative and valuable candidates for real evaluations, we devise an${L}1$-exploitation strategy to extensively exploit promising areas. Then, the candidate selection is conducted between the predicted${L}1$offspring and the already real-evaluated${L}1$individuals based on their Euclidean distances. Extensive experiments on commonly used benchmark functions demonstrate that the proposed optimizer can achieve competitive or better performance with a very small training dataset compared with three state-of-the-art SAEAs.