Collaborative SLAM systems allow resource-constrained robots to offload intensive computation to a central server, making real-time mapping and localization feasible. However, this approach introduces significant communication overhead, which can hinder practical deployment due to the high bandwidth required to transmit sensor data. To address this communication bottleneck in large-scale SLAM systems, we propose a novel bandwidth-optimization strategy that enables efficient collaboration between resource-constrained robots and a powerful central server. This strategy leverages mutual-information theory to select and transmit only the most informative keyframes, significantly reducing redundancy. Additionally, we apply finite-state entropy coding to achieve lossless compression of the selected data. Experiments on the public dataset and real-world scene demonstrate that our approach achieves a substantial 78% reduction in bandwidth usage compared to state-of-the-art centralized multi-robot SLAM methods, while maintaining high-precision localization and mapping performance without introducing significant computational overhead.

This article investigates the robust nonfragile leaderless consensus control issues of nonlinear multiagent systems (MASs) in the presence of controller gain perturbations, external interferences, and switching directed networks. A novel distributed nonfragile consensus controller is first devised. Subsequently, on the basis of the property that an MAS directed network's Laplacian matrix can be broken down into the product of two particular matrices, the conversion from the consensus control issue to the asymptotic stability control issue is achieved via two variable substitutions related to the above property. Additionally, a sufficient condition, which can guarantee the MASs' asymptotic stability, is proposed and proved by Lyapunov stability theory and algebraic graph theory. Finally, the validity of the devised method is demonstrated by a simulation example.

The stochastic resource allocation (SRA) problem, commonly seen in the decision-making of complex systems, is a typical combinatorial optimization challenge that seeks optimality, quickness, as well as generality. Among various SRA algorithms, constructive heuristics (CH) such as greedy algorithms construct feasible solutions by prioritizing optional resource-task allocation pairs based on a predefined evaluation criterion. They are very suitable for real-time decision-making due to their simplicity and low computational complexity. However, relying on a single fixed criterion can impair optimality and generality. To achieve a generalized expression for the criterion, this paper establishes a fuzzy evaluation system that determines the component priorities by leveraging SRA problem features, enabling diversified and flexible solution construction. Furthermore, for the sake of generality, this paper proposes a fuzzy-evaluation-based constructive heuristics generation framework (FCHG), which generates an ensemble of complementary CHs through automatic training. FCHG adopts an adversarial coevolution mechanism, using the SRA instance generator and evolutionary algorithms to realize competition-based coevolution between the SRA instances and CHs. For SRA problem-solving, the CH ensemble obtained by FCHG can construct multiple SRA solutions efficiently, and the best one will serve as the final solution. Comparative experiments against state-of-the-art algorithms, covering instances with varying scales and structural characteristics, demonstrate the comprehensive superiority of the CH ensemble in solving the SRA problem in terms of optimality, quickness, generality, and numerical stability.

This article addresses a novel path planning problem for multiple fixed-wing autonomous aerial vehicles (AAVs) to visit a set of moving targets, originating from AAV cooperative missions such as emergency communication and target surveillance. This problem can be formulated as a multiple Dubins traveling salesman problem with moving targets (mDTSPMT). The key challenge lies in the strong cross-level coupling between target assignment, encounter sequences, and motion-constrained paths for multiple AAVs in the presence of moving targets. To solve mDTSPMT efficiently, we develop an efficient transformation method by sampling the access location and heading of each AAV to visit moving targets, constructing the mDTSPMT roadmap, and transferring it into an asymmetric multiple traveling salesman problem (AMTSP). This transformation allows the use of mature AMTSP solvers while preserving the essential motion and timing constraints of the original problem. However, the performance of the transformation method heavily depends on the quality of the samples. To improve the quality of samples, a hyper-transformation (HT) framework is proposed, which adaptively optimizes AAV sampling, guiding the search toward more promising configurations and enhancing both the solution quality and computational efficiency of the transformation method. Experiments with extensive instances show that the proposed method outperforms four competitive algorithms in generating coordinated and time-efficient Dubins paths for multiple AAVs encountering multiple targets.

The flexible job shop scheduling problem for processing machines and transportation vehicles (FJSP_PT) has garnered significant attention from academia and industry. Due to the inclusion of transportation vehicle scheduling in the scheduling problem of flexible manufacturing systems, solving FJSP_PT becomes more challenging and significantly more practically relevant compared to the flexible job shop scheduling problem. We summarize the assumptions, constraints, objective functions, and benchmarks of FJSP_PT. Then, statistical analysis is conducted on the literature up to 2023, including journals, number of articles published each year, and solution algorithms. We analyze recent literature on FJSP_PT, categorizing it based on algorithms into exact algorithms, heuristic algorithms, meta-heuristic algorithms, and swarm intelligence based algorithms. Finally, the research trends and challenges faced by FJSP_PT are summarized.

It is extremely important to quickly locate the source of a hazardous substance leak in order to reduce damage to life and property. Multi-robot source localization faces challenges in unknown indoor environments, such as navigating through dense environments, encountering large areas without airflow or concentration clues, experiencing frequent changes in robot measurements, and managing clusters of robots in confined spaces. This study proposes a priority-based multi-robot search algorithm to tackle these challenges. The algorithm consists of a priority-based search strategy, an exploration method based on frontier and Voronoi diagram, an airflow tracking method based on Rapidly-exploring Random Trees Star (RRT*), and a multi-robot collaborative method. The algorithm was compared with three other state-of-the-art algorithms in simulated environments, assessing varying team sizes, airflow speeds, and diverse scenarios. The algorithm was also evaluated in real-robots experiments. The evaluation results demonstrate that the algorithm exhibits outstanding performance in both simulated and real-robots experiments.Note to Practitioners—The aim of this study is to propose a multi-robot search algorithm designed to address the challenges encountered in source searching within unknown indoor environments. These challenges include navigating through dense environments, large areas without airflow and concentration clues, frequent changes in robot measurements, and the clusters of robots in confined spaces. This study proposes a priority-based multi-robot search algorithm. The core idea of the algorithm is to enable robots to adopt different search methods depending on their measurements. When lacking valid airflow and concentration measurements, robots engage in spatial exploration using an exploration method based on frontier and Voronoi diagram to increase the likelihood of encountering the plume. When robots are within a plume, they rely on an RRT*-based airflow tracking method to move towards the source. The RRT* also provides robots with reachable navigation goals in environments with dense obstacles. The multi-robot collaborative method operates based on the priority levels assigned to the robots. On one hand, it directs robots towards the global best to reduce search time. On the other hand, robots ignore global bests that are not of a higher priority than their own, preventing the clustering of multiple robots at the same location. The algorithm was compared with three other state-of-the-art algorithms in simulated environments. It was also evaluated in real-robots experiments. The evaluation results show that the algorithm exhibits outstanding performance in both simulated and real-robots experiments. To further aid research in this field, a dataset for multi-robot indoor source searching has been created and made available online to provide a benchmark for related research.

This article investigates the distributed predefined-time (PT) fault-tolerant control for nonlinear multiagent systems (NNMSs) with nonaffine faults. A novel distributed PT control scheme is proposed based on a new PT theorem. The switching functions are introduced into distributed control signals to avoid the singularity problem. The second-order filter technology is designed to solve “explosion of complexity” issues. The newly designed PT compensation signals are utilized to eliminate filter errors. The proposed distributed PT controller based on local information can guarantee that all signals of the closed-loop system are PT bounded, and consensus errors of NNMSs can be enforced to a small region around the origin within a predefined time. Compared with the finite/fixed time, the predefined time is an exact value given in advance, which remains constant regardless of initial states and control parameters. Finally, two comparative simulations are provided to demonstrate the presented strategy.

The stochastic resource allocation (SRA) problem is widely encountered in complex systems, where the resource may probabilistically fail to complete its assigned task. In practical scenarios, the assignment of resources to tasks should be handled within specified time windows, and the success probability of each assignment changes over time. Such a problem can be represented as the SRA problem with time window (SRA-TW). Both the discrete assignment relationship and the corresponding continuous-valued assignment time are indispensable in the decision scheme of SRA-TW. This mixed-variable nature poses a great challenge for optimization. Based on these requirements, SRA-TW is formulated as a mixed-variable optimization problem (MVOP) with temporal constraints. To solve this problem, an adaptive hybrid algorithm with clustering-based diversity preservation (AHACDP) is proposed. Firstly, a variable-length hybrid encoding method with constructive decoding is proposed for incremental constraint handling. Secondly, a hybrid search mechanism incorporating a matching-similarity-guided adaptive selection method is proposed to balance the search in discrete and continuous subspaces. Then, a clustering-based diversity preservation strategy is developed, facilitating a good distribution of the population. Finally, an SRA-TW instance generator considering various problem features is designed, so as to comprehensively validate the algorithm’s performance. The statistical results over numerous instances demonstrate the superiority ofAHACDPover prevailing algorithms in addressing SRA-TW.

The distributed shape formation (DSF) of swarm robots is to form a specific shape, where each robot autonomously selects and moves to one target position in the desired shape. In this paper, we design some basic behaviors to construct behavior strategies, in which the swap selector and the obstacle avoidance planner are designed to guide robots in mitigating the negative effects of deadlock and collision during the DSF task. We propose a framework based on multi-agent simulation and genetic programming (GP) to automatically discover efficient behavior strategies followed by each robot to achieve DSF efficiently. The framework is distinguished by a centralized optimization of behavior strategies followed by each robot, along with strategy-driven decentralized decision-making and execution processes. In centralized optimization, to find behavior strategies with better generalization regarding shape types, a shape generator is designed to generate diverse training instances for comprehensively evaluating each behavior strategy in multi-agent simulation. Then, GP is used to evolve behavior strategies. In decentralized decision-making and execution, each robot can be guided by the same behavior strategy to form the shape. In terms of DSF completion time, the behavior strategies discovered by GP outperform the state-of-the-art distributed algorithm significantly across all test instances. These strategies can be well applied to different instances beyond the training instances. Through the statistical analysis, we also identify some crucial behaviors for realizing DSF.Note to Practitioners—This paper was motivated by a problem of distributed shape formation (DSF) for swarm robots but it also applies to other complex systems such as distributed task allocation and motion planning of swarm. Existing distributed algorithms (manually designed heuristics) can solve the DSF problem quickly but rely too much on human experience and cannot sufficiently mine the associations between behaviors and states of robots. Evolutionary algorithms are inspired by natural processes such as reproduction, mutation, and natural selection, enabling them to automatically evolve heuristic rules. The evolved heuristic rules possess the ability to adapt to dynamic environments in real time. To the best of our knowledge, while evolutionary algorithms have not been extensively explored in DSF, notable advancements have been achieved in complex systems such as swarm robots and industrial production. Considering that robots need to respond to dynamic states of robots in real time and the tree-structure representation facilitates the construction of associations between the states and behaviors of robots, we employ GP to search the space of heuristic rules instead of directly searching the solution space about the position-robot assignment and motion planning. Computational experiment results show that the DSF completion time by the evolved behavior strategies is remarkably reduced as compared to that of the manually designed the state-of-the-art heuristics in most test instances. In the future, we plan to explore the possibility of enabling robots to dynamically generate shapes that can adapt to complex environments.

The flexible job-shop co-scheduling problem (FJCSP) for processing machines and automated guided vehicles (AGVs) in a flexible manufacturing system (FMS) has attracted more attention with the aim of improving production efficiency. In FMS, AGVs in charge of transporting jobs realize the flexible linkage of operations between different processing machines. The added interdependence between transporting and processing tasks brings more difficulties than the traditional flexible job-shop scheduling problem (FJSP). In this paper, the mathematical model of FJCSP is formulated to minimize the makespan. Considering the feature similarity of FJCSP with FJSP and AGV-routing problem in different cases, a multi-view modeling-based hybrid algorithm consisting of an estimation of distribution algorithm (EDA) and an ant colony optimization (ACO) is proposed. In EDA, a probability model abstracts the information in superior solutions about the operation sequencing and the rule selection for scheduling machines and AGVs. In ACO, a job-path pheromone model and an AGV-path pheromone model are designed to jointly select the job-machine-AGV combination with shorter processing time and transportation time. In the proposed hybrid algorithm, EDA and ACO generate solutions independently and achieve cooperation by sharing elites. An adaptive parameter is designed to regulate the use of the two methods to adapt to the varying demands of multi-view modeling in different cases and search stages. Furthermore, a local search with a three-layer operator based on the critical path method is proposed to balance exploration and exploitation in solution space. Finally, computational experiments involving a case study verified the advantage of the multi-view modeling-based hybrid algorithm in comparison with the state-of-the-art approaches.Note to Practitioners—This paper was motivated by the optimization problem of scheduling machines and automated guided vehicles (AGVs) in flexible manufacturing system (FMS). In FMS with AGVs, the transportation stages for jobs by AGVs significantly impact the overall production efficiency of the FMS and cannot be overlooked. This paper suggested a hybrid evolutionary algorithm using an estimation of distribution algorithm (EDA), an ant colony optimization (ACO) and a local search algorithm based on the critical path method. In the proposed hybrid algorithm, an adaptive parameter is introduced to regulate the utilization of EDA and ACO in generating a new population. This paper presents a mathematical characterization of the scheduling problem and subsequently outlines the step-by-step design of the hybrid algorithm. Computational experiments, including a case study, demonstrate that the hybrid algorithm exhibits adaptability to various instances and outperforms state-of-the-art approaches.

This article investigates the cooperative control of complex nonlinear multiagent systems (CNMASs), in which the agents suffer from nonaffine faults and the control directions of some agents are unknown. A finite-time adaptive control scheme is presented for the CNMASs. A finite-time command filter is designed to solve the "explosion of complexity" issues, overcome chattering issues, and relax the limitations of the filter input. The impact of filter errors is alleviated by an improved error compensation mechanism. Based on piecewise Nussbaum functions, the partially unknown control direction is addressed. The proposed finite-time cooperative control strategy on the basis of local information can ensure that all signals in the closed-loop system are finite-time bounded, and the absolute value of the cooperative control errors can converge to a given upper bound in a finite time. The rapidity and robustness of the proposed method are verified by two comparative simulation examples. A real multirobot cooperative control experiment is used to verify the effectiveness of the presented method.

Hybridization plays a prominent role in bolstering the performance of optimization algorithms (OAs), yet designing efficient hybrid OAs tailored to intricate optimization problems persists as a formidable task. This article introduces a novel top-down methodology for the automated design of hybrid OAs, treating algorithm design as a meta-optimization problem. A general design template for collaboration-based hybrid OAs is developed, integrating a multitude of hybridization strategies for the first time. Besides, a mathematical model is built to formulate the meta-optimization problem of algorithm design. To address the meta-optimization challenge, an improved multifactorial evolutionary algorithm is proposed to automatically design efficient hybrid metaheuristics in a multitasking environment for the given instances with diverse features. To verify the effectiveness of the proposed design methodology, it is applied to the CEC2017 benchmark functions and the binary knapsack problem. Numerical results have demonstrated the feasibility and effectiveness of the proposed methodology for both continuous and combinatorial optimization benchmarks.

This article studies the tracking control of a class of nonlinear systems with input saturation, subject to nonaffine faults and unknown control direction. A fault-tolerant command filtered control (CFC) method based on adaptive neural networks (NNs) is proposed for this kind of nonlinear system. First, the combination of CFC and error compensation overcomes the "explosion of complexity" issue and alleviates the impact of filter errors. Then, a set of radial basis function NNs is constructed to approximate the unknown nonlinear items containing the nonaffine fault function. Additionally, the issue of unknown control direction in the system is effectively resolved by using Nussbaum gain technology. It is proven that the designed controller can ensure that all signals in the closed-loop system are bounded and convergent, and the upper bound of the absolute value of system tracking error is given. Finally, three comparative simulation results are illustrated to show the effectiveness of the proposed method.

Chemical, biological, or radioactive substances may be released in accidents, posing a threat to human life and property. Due to the dense obstacles and specific structures of indoor environments, indoor source searching still faces challenges, such as the initial position of the robot cannot be placed freely, the source may not be in the airflow, and most areas indoors lack concentration and airflow clues. This study proposes an exploration-enhanced search algorithm, enabling the robot to search for a source located downstream of the robot or outside the airflow in an indoor environment with a narrow plume without losing the classic upstream search ability. The algorithm equips the robot with the capability to search for a source in complex indoor environments where measurements frequently change. The algorithm is evaluated in the simulated environment to assess the contributions of its components and its performance under different airflow speeds. The algorithm is also compared with the state-of-the-art algorithms and shows superior performance. The effectiveness of the algorithm is further demonstrated in real-world environments.

This article focuses on the coalition formation (CF) problem in urgent missions, e.g., disaster rescue, where coalition members should reach mission locations quickly. A mathematical model is first constructed to minimize the latest arrival time of coalition members, considering the capability requirements of missions, nonredundant agents in coalitions, etc. Then, incorporating the benefits in both the diversity of random search and the effectiveness of utilizing problem knowledge, a local-search-based heuristic is put forward to solve the CF problem. An initial solution is incrementally constructed by prioritizing agents with shorter movement times for missions with higher-remaining capability requirements. Additionally, two types of neighborhood search operators, namely, the tabu-based one-to-one swap and the destroy and repair operators, are proposed to search the solution space from two perspectives, i.e., “adjustment” and “reconstruction.” To solve the problem effectively and efficiently, the former excludes certain agent-exchange combinations that do not improve the current solution, while the latter consists of multiple heuristic rules extracted from the correlation among different model elements. Experimental results have demonstrated that the proposed method surpasses several advanced methods across various scenarios regarding multiple factors, such as the number of agents, the number of missions, and the demand-supply ratio on capabilities.

The emergence of a robotic mobile fulfillment system (RMFS) provides an automated solution for e-commerce warehousing to improve productivity and reduce labor costs. This article studies the order picking optimization problem in RMFS, which simultaneously decides the assignment of orders and racks to multiple picking stations. Although this problem has been widely studied in recent years, it is still very challenging for existing methods to solve large-scale instances effectively (e.g., more than 200 orders and 500 racks). To overcome this difficulty to meet the real-world needs, we propose a fulfillment-focused simultaneous assignment (FFSA) method. The proposed FFSA comprises two stages: 1) compression and 2) simultaneous assignment. The compression stage employs a hybrid adaptive large neighborhood search (ALNS) strategy to establish a reduced set of critical racks that can fulfill the demand of all orders. In the simultaneous assignment stage, we develop a marginal-return-based assignment with candidate strategy (MRACS) to simultaneously assign orders and critical racks to picking stations. MRACS takes into account three fulfillment-focused measurements to depict the product supply relationship between the demand of orders and the inventory on critical racks. These measurements are further integrated into the effective heuristics with sufficient problem-specific knowledge to obtain a high-quality solution. Experimental results show that our method significantly outperforms representative algorithms on both synthetic data and large-scale real-world data.

Abstract Interactive multiobjective optimization methods have proven promising in solving optimization problems with conflicting objectives since they iteratively incorporate preference information of a decision maker in the search for the most preferred solution. To find the appropriate interactive method for various needs involves analysis of the strengths and weaknesses. However, extensive analysis with human decision makers may be too costly and for that reason, we propose an artificial decision maker to compare a class of popular interactive multiobjective optimization methods, i.e., reference point based methods. Without involving any human decision makers, the artificial decision maker works automatically to interact with different methods to be compared and evaluate the final results. It makes a difference between a learning phase and a decision phase, that is, learns about the problem based on information acquired to identify a region of interest and refines solutions in that region to find a final solution, respectively. We adopt different types of utility functions to evaluation solutions, present corresponding performance indicators and propose two examples of artificial decision makers. A series of experiments on benchmark test problems and a water resources planning problem is conducted to demonstrate how the proposed artificial decision makers can be used to compare reference point based methods.

This article investigates the tracking-oriented robust leaderless time-varying formation (TVF) control problem for unmanned aerial vehicle swarm systems (UAVSSs) with Lipschitz nonlinear dynamics under directed topology, where external disturbances are random and bounded, and communication delays (CDs) are bounded. In this article, a state-feedback control approach is adopted to make sure that a UAVSS forms a desired TVF and follows a specified trajectory when CDs and external disturbances occur. First, a novel PD-like formation control protocol with several unknown parameters and CDs is designed. The protocol contains the information of the local neighborhood status and its differential quantities. Second, the tracking-oriented robust leaderless TVF control problem with Lipschitz dynamics, external disturbances, and CDs is transformed into a problem about asymptotic stability of a lower dimensional closed-loop control system through a special matrix decomposition. Third, a theorem is proposed to determine the unknown parameters of the control protocol and the upper bound of CDs. In the theorem, sufficient conditions for a UAVSS to attain the anticipated TVF and trajectory tracking are obtained. A Lyapunov-Krasovskii (LK) functional is constructed to verify that the error among the practical flight state of UAVs, the anticipant TVF configuration, and tracking trajectory can asymptotically converge to 0. Finally, with the presentation of a simulation case, the effectiveness of the theoretical results is illustrated.

This article studies the fixed-time consensus tracking control of nonlinear multiagent systems (NNMASs) suffering from nonaffine faults. A fixed-time command filter is constructed to solve the “explosion of complexity” issue, and a novel fixed-time error compensation mechanism is designed to eliminate filtering errors. The adaptive fuzzy control technique is introduced to deal with the unknown nonlinear terms containing nonaffine fault functions. A new fixed-time fault-tolerant control scheme based on the modified prescribed performance technology is proposed for the NNMASs, which ensures that the closed-loop system satisfies the practical fixed-time stability. In addition, the consensus tracking errors of the NNMASs converge to a given range within a prescribed performance bound in a fixed time. Finally, comparative simulation results show the effectiveness of the proposed method.

An emerging optimisation problem from real-world applications, named the multi-point dynamic aggregation (MPDA) problem, has become an active research of the multi-robot system. This paper focuses on a multi-objective MPDA (MO-MPDA) problem which is to design execution plans of robots for minimising the cost of used robots and maximising the efficiency of task execution. The MOMPDA problem has the issues of conflicting objectives, redundant representation, and variable-length encoding, posing extra challenges to address the MO-MPDA problem effectively. Combining the ∊-constraint method and decomposition mechanisms, a novel multi-objective evolutionary algorithm is proposed. The proposed algorithm selects the efficiency objective as the main objective and converts the cost objective as constraints. Thus, the multi-objective problem is decomposed into a series of scalar constrained optimisation subproblems by assigning each subproblem with an upper bound constraint. All the subproblems are optimised and evolved simultaneously with the transferring knowledge from other sub-problems to solve the MO-MPDA problem parallelly and efficiently. Besides, considering the characteristics of parent individuals, this paper designs a hybrid reproduction mechanism to transmit effective information to offspring individuals for tackling the encoding redundancy and varying-length. Experimental results show that the proposed algorithm significantly outperforms the state-of-the-art algorithms in terms of most-used metrics.

The sparrow search algorithm (SSA) is a recent meta-heuristic optimization approach with the advantages of simplicity and flexibility. However, SSA still faces challenges of premature convergence and imbalance between exploration and exploitation, especially when tackling multimodal optimization problems. Aiming to deal with the above problems, we propose an enhanced variant of SSA called the multi-strategy enhanced sparrow search algorithm (MSSSA) in this paper. First, a chaotic map is introduced to obtain a high-quality initial population for SSA, and the opposition-based learning strategy is employed to increase the population diversity. Then, an adaptive parameter control strategy is designed to accommodate an adequate balance between exploration and exploitation. Finally, a hybrid disturbance mechanism is embedded in the individual update stage to avoid falling into local optima. To validate the effectiveness of the proposed MSSSA, a large number of experiments are implemented, including 40 complex functions from the IEEE CEC2014 and IEEE CEC2019 test suites and 10 classical functions with different dimensions. Experimental results show that the MSSSA achieves competitive performance compared with several state-of-the-art optimization algorithms. The proposed MSSSA is also successfully applied to solve two engineering optimization problems. The results demonstrate the superiority of the MSSSA in addressing practical problems.

Multiagent dynamic task assignment of forest fires is a complicated optimization problem because it requires the consideration of multiple factors, such as the spread speed of fires, firefighting speed of agents, the movement speed of agents, and the number of deployed agents. In this article, we investigate multiagent dynamic task assignment based on a forest fire point model, the objective of which is to minimize task completion time. First, we establish a model for the spread of fire and dynamic task assignments. Second, we prove that the optimal static task assignment always makes all task completion times the same under certain assumptions. Furthermore, we calculate the optimal solution to the static task assignment problem assuming no travel time for the agents, which provides the theoretical basis for the initial deployment and dynamic deployment. Third, we propose a dynamic task assignment scheme based on the global information, which ensures that every reassignment reduces the task completion time and makes all task completion times close to each other. Finally, the simulation is carried out on the MATLAB platform to verify the performance of the proposed dynamic task assignment scheme by comparing with a multistage global auction algorithm. We hope that this work provides insight for decision-makers designing reasonable assignment strategies based on the model and solving assignment optimization problem in different situations.Note to practitioners—The forest firefighting problem considered in this article is a typical multitask and multistage optimization problem. Many searching algorithms for multistage optimization problem are available in the existing literature. However, one of the main challenges is that the time of searching increases exponentially with the number of stages. This work first proves that the tasks are completed in the minimum amount of time, under the constraint of one-shot assignment. This finding helps us to evaluate the gap between the searching algorithm and the optimal solution. In addition, in practice, if the underlying dynamic process can be modeled or partially modeled, then we can predict the behavior of future stages and reduce the searching domain. If a model is available, then we can also adjust the assignment scheme dynamically based on the principle that each adjustment would reduce the total time of tasks completion. In this article, we establish a dynamical fire-spreading model and propose a model-based solution to the multistage optimization problems. The findings in this work can serve as a supplement to the existing optimization algorithms.

This paper addresses a UAV path planning problem for a team of cooperating heterogeneous vehicles composed of one unmanned aerial vehicle (UAV) and multiple unmanned ground vehicles (UGVs). The UGVs are used as mobile actuators and scattered in a large area. To achieve multi-UGV communication and collaboration, the UAV, modeled as a Dubins vehicle, serves as a messenger to fly over the effective communication range of all UGVs to relay information. The curvature-constrained path planning of the messenger UAV is formulated as a Dubins Traveling Salesman Problem with Dynamic Neighborhood (DTSPDN) which is a complex optimization problem involving coupled variables and contains dynamic constraints. We design an effective memetic algorithm to find the shortest route that enables the messenger UAV to visit all moving UGVs. This algorithm combines the genetic algorithm procedure, two kinds of local search operators based on gradient search and uniform sampling respectively, and a gradient-based repair operator to repair the solutions violating dynamic constraints. During the evolutionary process, a special phenomenon may occur that changing some decision variables (i.e., visiting sequence and location) may not affect the evaluation function value, but may alter the feasible region of another decision variable (i.e., visiting time) due to the encounter constraint between the UAV and UGV. To track and utilize the change of the feasible region, a transformation procedure is proposed to change one solution to another with less visiting time by analyzing the encounter pattern between UAV and UGV. The computational results on random instances with different scales demonstrate that the proposed approach can effectively generate better curvature-constrained tours to encounter all moving UGVs when compared to other four competitive algorithms in the literature. Note to Practitioners—This paper studies an emerging path planning problem for a UAV which is used to provide communication service for multiple moving UGVs. These UGVs are required to execute tasks (e.g., firefighting, search and rescue) within a large area. Due to their limited communication capabilities, they may be unable to obtain necessary information from other UGVs. The UAV serves as a messenger to fly over the effective communication range of all moving UGVs to relay information. We propose a novel memetic algorithm to efficiently search for the shortest tour that enables the messenger UAV to visit all moving UGVs. The memetic algorithm combines the parallel global search virtue of genetic algorithm with efficient local search procedure to improve the generated tour. A gradient-based repair procedure is also employed to make sure that the planned tour can guide the UAV to sequentially encounter each moving UGV. Simulations exhibit that the proposed approach can effectively generate high-quality tours for messenger UAV to rapidly visit all UGVs, which assists UGVs to achieve collaboration in large area. In future work, the proposed memetic algorithm will be extended to plan tours for multiple messenger UAVs.

The human-agent collaboration (HAC) is a prospective research topic whose great applications and future scenarios have attracted vast attention. In a broad sense, the HAC system (HACS) can be broken down into six elements: "Man," "Agents," "Goal," "Network," "Environment," and "Tasks." By merging these elements and building a relation graph, this article proposes a systematic analysis framework for HACS, and attempts to make a comprehensive analysis of these elements and their relationships. We coin the abbreviation "MAGNET" to name the framework by stringing together the initials of the above six terms. The framework provides novel insights into analyzing various HAC patterns and integrates different types of HACSs in a unifying way. The presentation of the HACS framework is divided into two parts. This article, part I, presents the systematic analysis framework. Part II proposes a normalized two-stage top-level design procedure for designing an HACS from the perspective of MAGNET.

The human-agent collaboration (HAC) is a prospective research topic, whose great applications and future scenarios have attracted vast attention. It is very important to understand the design process of the HAC system (HACS). Inspired by the systematic analysis framework presented in Part I of this dual publication, this article proposes a normalized two-phase procedure, namely, GET-MAN, for the top-level design of HACS from the perspective of system engineering. The two-phase design procedure can produce a coherent and well-running HACS by sophisticatedly and properly determining the six elements of the HACS and their influences. In the verification phase of GET-MAN, by applying the formalized HACS framework proposed in Part I, a formal model can be constructed to look ahead (predict) and back (explain) at potential faults in the candidate HACS. An example of the HACS design for target searching is employed to illustrate the use of the GET-MAN design procedure. The potential challenges and future research directions are discussed in the light of the GET-MAN design procedure. The systematic analysis framework, Part I, as well as the GET-MAN design procedure, Part II, can serve as common guidance and reference for analyzing and developing various HACSs.

Multipoint dynamic aggregation is a meaningful optimization problem due to its important real-world applications, such as post-disaster relief, medical resource scheduling, and bushfire elimination. The problem aims to design the optimal plan for a set of robots to execute geographically distributed tasks. Unlike the majority of scheduling and routing problems, the tasks in this problem can be executed by multiple robots collaboratively. Meanwhile, the demand of each task changes over time at an incremental rate and is affected by the abilities of the robots executing it. This poses extra challenges to the problem, as it has to consider complex coupled relationships among robots and tasks. To effectively solve the problem, this article develops a new metaheuristic algorithm, called adaptive coordination ant colony optimization (ACO). We develop a novel coordinated solution construction process using multiple ants and pheromone matrices (each robot/ant forages a path according to its own pheromone matrix) to effectively handle the collaborations between robots. We also propose adaptive heuristic information based on domain knowledge to promote efficiency, a pheromone-based repair mechanism to tackle the tight constraints of the problem, and an elaborate local search to enhance the exploitation ability of the algorithm. The experimental results show that the proposed adaptive coordination ACO significantly outperforms the state-of-the-art methods in terms of both effectiveness and efficiency.

The multipoint dynamic aggregation (MPDA) problem of the multirobot system is of great significance for its real-world applications such as bush fire elimination. The problem is to design the optimal plan for a set of heterogeneous robots to complete some geographically distributed tasks collaboratively. In this article, we consider the dynamic version of the problem, where new tasks keep appearing after the robots are dispatched from the depot. The dynamic MPDA problem is a complicated optimization problem due to several characteristics, such as the collaboration of robots, the accumulative task demand, the relationships among robots and tasks, and the unpredictable task arrivals. In this article, a new model of the problem considering these characteristics is proposed. To solve the problem, we develop a new genetic programming hyperheuristic (GPHH) method to evolve reactive coordination strategies (RCSs), which can guide the robots to make decisions in real time. The proposed GPHH method contains a newly designed effective RCS heuristic template to generate the execution plan for the robots according to a GP tree. A new terminal set of features related to both robots and tasks and a cluster filter that assigns the robots to urgent tasks are designed. The experimental results show that the proposed GPHH significantly outperformed the state-of-the-art methods. Through further analysis, useful insights such as how to distribute and coordinate robots to execute different types of tasks are discovered.

Existing techniques on dealing with uncertain optimization problems (UOPs) mostly rely on the preference information of decision makers (DMs) or the knowledge involved in probability distributions on uncertainties. Actually, accurate preferences and distribution information of uncertainties are hard to obtain due to the lack of knowledge. Besides, it is risky to make assumptions on this information to handle uncertainties when DMs do not have sufficient knowledge about the problem. This article attempts to treat UOPs in an a posteriori manner and proposes a subproblem co-solving evolutionary algorithm (EA) for UOPs, namely, S-CoEA. It decomposes a UOP into a series of correlated subproblems by using the proposed decomposition strategy embedded with an original ordered weighted-sum (OWS) operator. These subproblems are formulated in different aggregation forms of sampled function values and represent different preferences on uncertainties. They are co-solved in parallel by using information from neighboring subproblems. The sampling strategy is used to gather the distribution information of uncertain functions and alleviate the detrimental effects of uncertainties. A sample-updating scheme based on historical information is presented to further improve the performance of S-CoEA. The proposed S-CoEA is compared with two state-of-the-art competitors, including the EA with the exponential sampling method (E-sampling) and the population-controlled covariance matrix self-adaptation evolution strategy (pcCMSA-ES). Numerical experiments are conducted on a series of test instances with various characteristics and different strength levels of uncertainties. Experimental results show that S-CoEA outperforms or performs competitively against competitors in the majority of 26 continuous test instances and four test cases of discrete redundancy allocation problems.

This article investigates the joint allocation problem of stochastic resources (JASRs), which is widely found in complex systems. A general mathematical model for joint allocation of multiple heterogeneous stochastic resources is built, capturing the interdependencies between resources, quantity constraints, capability constraints, and strategy constraints of resources. An adaptive memetic algorithm (MA) is proposed for JASR, and the multipermutation encoding method is developed to denote assignment schemes of different resources. Multiple permutation-based operators are employed in the mutation and local search process under the genetic evolution framework and learning framework, respectively. Besides, a hybrid initialization method and an adaptive replacement strategy are put forward. Moreover, a restart strategy is developed to rebuild the population to maintain the genetic diversity. Twenty-five random test instances are produced to validate the effectiveness of the proposed MA. The results of computational experiments and the Wilcoxon rank-sum test demonstrate that these JASR instances can be well handled by the proposed adaptive MA, and the proposed MA is able to provide remarkably better decision schemes for the majority of the test instances than the prevailing solution methods.

Time-varying formation (TVF) and trajectory tracking$H_{\infty }$control problem of multiagent systems (MASs) subject to communication delays and external disturbances under the directed communication topology is studied. This article’s objective is for all agents to attain the desired TVF and track the pregiven formation center trajectory simultaneously. First, a distributed TVF and trajectory tracking control protocol employing neighborhood interaction information is developed in the presence of communication delays. Second, since the Laplacian matrix of a graph can be decomposed into the product of two specific matrices, the TVF and trajectory tracking$H_{\infty }$control problem is converted into the lower dimension asymptotic stability problem of a closed-loop system by applying an appropriate variable conversion. Third, a Lyapunov–Krasovskii functional is constructed to analyze the stability of MASs. Sufficient conditions are obtained in the form of linear matrix inequalities (LMIs) to ensure the completion of the TVF and formation center trajectory tracking of MASs. In the meantime, the maximum allowable communication delay can be calculated by the LMIs. Finally, the results of numerical simulations are presented to verify the validity of the approach this article proposes.

A mixed-integer programming (MIP) problem contains not only constraints but also integer restrictions. Integer restrictions divide the feasible region defined by constraints into multiple discontinuous feasible parts with different sizes. Several popular methods (e.g., rounding and truncation) have been proposed to deal with integer restrictions. Although it is easy for these methods to generate an integer, they tend to converge to an integer which is located in a feasible part with a big size. If the optimal solution is not in this feasible part, they are very likely to converge to a local optimal solution due to the loss of diversity of the population. To overcome this shortcoming, a biobjective optimization-based two-phase method is proposed in this article. In the first phase, a measure function is designed to compute the degree that a solution violates integer restrictions. By employing this measure function as the second objective function and removing integer restrictions, a MIP problem is transformed into a constrained biobjective optimization problem (CBOP). It can be proven that the Pareto optimal solution of the transformed CBOP which satisfies integer restrictions is the optimal solution of the original MIP problem. To solve the transformed CBOP, a new comparison rule is designed. After the first phase, the population can approach the Pareto optimal solution which satisfies integer restrictions. Then, the second phase is implemented to enhance the convergence precision and obtain the optimal solution. In addition, we design 12 test problems to verify the effectiveness of the proposed method. The results demonstrate that the proposed method shows better performance against five state-of-the-art evolutionary algorithms for MIP.

The distributed optimal consensus based on an event-triggered scheme for Euler-Lagrange (EL) multiagent systems is investigated in this article. The objective is to minimize the global cost function in a distributed manner while achieving consensus, where the local cost function of each agent is only known by itself. First, the distributed optimization algorithms based on the event-triggered scheme are proposed to achieve optimal consensus as well as reduce communication costs for the EL multiagent systems when the model parameters are available. Second, when the model parameters are unavailable, the tracking controllers are developed to solve the optimization problem for the EL multiagent systems. Then, the distributed optimization problem for EL systems can be transformed into the tracking problem for double-integrator multiagent systems. With the proposed algorithms, global optimization can be achieved with the exponential convergence rate. Finally, a simulation example is presented to illustrate the effectiveness of the proposed method.

Multi-Point Dynamic Aggregation (MPDA) is a novel task model to determine task allocation for a multi-robot system. In an MPDA scenario, several robots with different abilities aim to complete a set of tasks cooperatively. The demand of each task is time varying. It increases over time at a certain rate (e.g. the bush fire in Australia). When a robot executes a task, the demand of the task decreases at another certain rate, depending on the robot's ability. In this paper, the objective is to design a task plan for minimising the maximal completed time of all tasks. But coupling cooperative and time-varying characteristics of MPDA brings great challenges to modelling, decoding, and optimisation. In this paper, a multi-permutation encoding is used to represent every robot's visiting sequence of tasks, and an implicit decoding strategy with heuristic rules is designed to simplify the problem from a hybrid variable optimisation to a multi-permutation optimisation. Memetic algorithms for the task allocation of MPDA with two local search methods are designed: equality one-step local search with a better exploration ability and elite multi-step local search with a better exploitation ability. Computational experiments show that the proposed decoding method leads to a better performance given the same computational time budget. Experimental results also show that the proposed memetic algorithms outperform the state-of-the-art method in solving the task planning problems of MPDA.

This paper addresses a UAV path planning problem for a team of cooperating heterogeneous vehicles composed of one unmanned aerial vehicle (UAV) and multiple unmanned ground vehicles (UGVs). The UGVs are used as mobile actuators and scattered in a large area. To achieve multi-UGV communication and collaboration, the UAV serves as a messenger to fly all UGVs to transmit information. The path planning of messenger UAV is formulated as a Dynamic Dubins Traveling Salesman Problem with Neighborhood (DDTSPN). A novel memetic algorithm is proposed to find the shortest route enabling the UAV to fly over all requested UGVs. In the memetic algorithm, the combination of genetic algorithm and local search is employed to find a high-quality solution in a reasonable time, and a gradient-based repair strategy is used to repair the individuals violating dynamic constraints. The calculation results on both small and large instances show that the proposed method can generate high-quality solutions as compared with the state-of-the-art algorithms.

As a cutting-edge branch of unmanned aerial vehicle (UAV) technology, the cooperation of a group of UAVs has attracted increasing attention from both civil and military sectors, due to its remarkable merits in functionality and flexibility for accomplishing complex extensive tasks, e.g., search and rescue, fire-fighting, reconnaissance, and surveillance. Cooperative path planning (CPP) is a key problem for a UAV group in executing tasks collectively. In this paper, an attempt is made to perform a comprehensive review of the research on CPP for UAV groups. First, a generalized optimization framework of CPP problems is proposed from the viewpoint of three key elements, i.e., task, UAV group, and environment, as a basis for a comprehensive classification of different types of CPP problems. By following the proposed framework, a taxonomy for the classification of existing CPP problems is proposed to describe different kinds of CPPs in a unified way. Then, a review and a statistical analysis are presented based on the taxonomy, emphasizing the coordinative elements in the existing CPP research. In addition, a collection of challenging CPP problems are provided to highlight future research directions.

Over the last few decades, the decomposition-based multiobjective evolutionary algorithms (DMOEAs) have became one of the mainstreams for multiobjective optimization. However, there is not too much research on applying DMOEAs to uncertain problems until now. Usually, the uncertainty is modeled as additive noise in the objective space, which is the case this paper concentrates on. This paper first carries out experiments to examine the impact of noisy environments on DMOEAs. Then, four noise-handling techniques based upon the analyses of empirical results are proposed. First, a Pareto-based nadir point estimation strategy is put forward to provide a good normalization of each objective. Next, we introduce two adaptive sampling strategies that vary the number of samples used per solution based on the differences among neighboring solutions and their variance to control the tradeoff between exploration and exploitation. Finally, a mixed objective evaluation strategy and a mixed repair mechanism are proposed to alleviate the effects of noise and remedy the loss of diversity in the decision space, respectively. These features are embedded in two popular DMOEAs (i.e., MOEA/D and DMOEA- [Formula: see text]), and DMOEAs with these features are called noise-tolerant DMOEAs (NT-DMOEAs). NT-DMOEAs are compared with their various variants and four noise-tolerant multiobjective algorithms, including the improved NSGA-II, the classical algorithm Bayesian (1+1)-ES (BES), and the state-of-the-art algorithms MOP-EA and rolling tide evolutionary algorithm to show the superiority of proposed features on 17 benchmark problems with different strength levels of noise. Experimental studies demonstrate that two NT-DMOEAs, especially NT-DMOEA- [Formula: see text], show remarkable advantages over competitors in the majority of test instances.

To address the large-scale and time-consuming multiple agile earth observation satellite (multi-AEOS) scheduling problems, this article proposes a data-driven parallel scheduling approach, which is composed of a probability prediction model, a task assignment strategy, and a parallel scheduling manner. In this approach, given the historical data of satellite scheduling, a prediction model is trained based on the cooperative neuro-evolution of augmenting topologies (C-NEAT) to predict the probabilities that a task will be fulfilled by different satellites. Driven by the probability prediction model, an assignment strategy is adopted for dividing the multi-AEOS scheduling problem into several single-AEOS scheduling subproblems, which can adaptively assign each task to the satellite with the highest predicted probability and greatly decrease the problem size. In a parallel manner, the single-AEOS scheduling subproblems are optimized, respectively, leading to an acceleration in the optimization efficiency of the original problem. Computational experiments indicate that the proposed approach presents better overall performance than other state-of-the-art methods within a very limited scheduling time. As the two main components of the proposed approach, the prediction model based on C-NEAT and the task assignment strategy also outperform other models with traditional training algorithms and inadaptive assignment strategies, respectively.

In this paper, a mathematical model for the joint allocation of two heterogeneous stochastic resources (namely, sensors and actuators) is presented, addressing the interdependencies between sensors and actuators, the resource constraints, the capability constraints as well as the strategy constraints. A heuristic initialized memetic algorithm (MA) is proposed to solve the joint allocation problem about stochastic resources (JASR). The integer-based dual-permutation encoding method is adopted and several permutation-based operators are involved in the process of crossover, mutation and local search. Besides, a hybrid initialization method is employed to maintain a balance between exploration and exploitation. For the performance evaluation, we build a general Monte Carlo simulation based JASR framework. Furthermore, we employ an extension of the state-of-the-art algorithm Swt_opt, MRBCH and BMA as competitors. Computational results show that the proposed MA performs very well in solving JASR instances of different scales, and it can generate better assignment schemes in most cases than its competitors in limited time.

The multi-robot coverage motion planning (MCMP) problem in which every reachable area must be covered is common in multi-robot systems. To deal with the MCMP problem, we propose an efficient, complete, and off-line algorithm, named the “auction-based spanning tree coverage (A-STC)” algorithm. First, the configuration space is divided into mega cells whose size is twice the minimum coverage range of a robot. Based on connection relationships among mega cells, a graph structure can be obtained. A robot that circumnavigates a spanning tree of the graph can generate a coverage trajectory. Then, the proposed algorithm adopts an auction mechanism to construct one spanning tree for each robot. In this mechanism, an auctioneer robot chooses a suitable vertex of the graph as an auction item from neighboring vertexes of its spanning tree by heuristic rules. A bidder robot submits a proper bid to the auctioneer according to the auction vertexes’ relationships with the spanning tree of the robot and the estimated length of its trajectory. The estimated length is calculated based on vertexes and edges in the spanning tree. The bidder with the highest bid is selected as a winner to reduce the makespan of the coverage task. After auction processes, acceptable coverage trajectories can be planned rapidly. Computational experiments validate the effectiveness of the proposed MCMP algorithm and the method for estimating trajectory lengths. The proposed algorithm is also compared with the state-of-the-art algorithms. The comparative results show that the A-STC algorithm has apparent advantages in terms of the running time and the makespan for large crowded configuration spaces.

In network-centric warfare, the interconnections among various combat resources enable an advanced operational pattern of cooperative engagement. The operational effectiveness and outcome strongly depends on the reasonable utilization of available sensors and weapons. In this paper, a mathematical model for the coallocation of sensors and weapons is built, taking into account the interdependencies between weapons and sensors, the resource constraints, the capability constraints, as well as the strategy constraints. A marginal-return-based constructive heuristic (MRBCH) is proposed to solve the formulated sensor-weapon-target assignment (S-WTA) problem. MRBCH exploits the marginal return of each sensor-weapon-target triplet and dynamically updates the threat value of all targets. It relies only on simple lookup operations to choose each assignment triplet, thus resulting in very low computational complexity. For performance evaluation, we build a general Monte Carlo simulation-based S-WTA framework. Furthermore, we employ a random sampling method and an extension of the state-of-the-art algorithm Swt_opt as competitors. The computational results show that MRBCH consistently performs very well in solving S-WTA instances of different scales, and it can generate assignment schemes much more efficiently than its competitors.

Multi-Point Dynamic Aggregation (MPDA) is a novel task model for describing the process of multiple robots performing time-variant tasks. In the MPDA problem, several task points are located in different places and their states change over time. Multiple robots aggregate to these task points and execute the tasks cooperatively to make the states of all the task points change to zero. The task planning of MPDA is a typical NP-hard combinatorial optimization problem. Estimation of Distribution Algorithms (EDA) are evolutionary techniques based on probabilistic models. In this paper, a permutation-based EDA is proposed to solve the task planning problems in MPDA. The algorithm uses K-means clustering to update its probabilistic model which follows the multi-modal Gaussian distribution. Experimental results show that the proposed algorithm outperforms other compared methods in solving the task planning problems of MPDA.

Interactive multiobjective optimization (IMO) methods aim at supporting human decision makers (DMs) to find their most preferred solutions in solving multiobjective optimization problems. Due to the subjectivity of human DMs, human fatigue, or other limiting factors, it is hard to design experiments involving human DMs to evaluate and compare IMO methods. In this paper, we propose a framework of a virtual-DM library consisting of a variety of virtual DMs which reflect characteristics of different types of human DMs. The virtual-DM library is used to replace human DMs to interact with IMO methods. The virtual DMs in the library can express different types of preference information and their most preferred solutions are known. When interacting with an IMO method, the library can select an appropriate virtual DM to provide preference information that the method asks for based on solutions offered by the method. Four types of hybrid virtual DMs are constructed to emulate human DMs with different personalities and dynamically changing preference structures. They can be used to test the ability of IMO methods to adapt to different human DMs and capture DMs' preferences. The usage of these four types of virtual DMs are demonstrated by comparing two IMO algorithms.

The weapon target assignment (WTA) problem is a fundamental problem arising in defense-related applications of operations research. The multi-stage weapon target assignment (MWTA) problem is the basis of the dynamic weapon target assignment (DWTA) problem which commonly exists in practice. The MWTA problem considered in this paper is formulated as a multi-objective constrained combinatorial optimization problem with two competing objectives. Apart from maximizing the damage to hostile targets, this paper follows the principle of minimizing the ammunition consumption. Decomposition and Pareto dominance both are efficient and prevailing strategies for solving multi-objective optimization problems. Three competitive multi-objective optimizers: DMOEA-εC, NSGA-II, and MOEA/D-AWA are adopted to solve multi-objective MWTA problems efficiently. Then comparison studies among DMOEA-εC, NSGA-II, and MOEA/D-AWA on solving three different-scale MWTA instances are done. Three common used performance metrics are used to evaluate the performance of each algorithm. Numerical results demonstrate that NSGA-II performs best on small-scale and medium-scale instances compared with DMOEA-εC and MOEA/D-AWA, while DMOEA-εC shows advantages over the other two algorithms on solving the large-scale instance.

The navigation relayed by multiple stations (NRMS) is an advanced cooperative navigation technology which relies on multiple different stations to sequentially guide a vehicle to its destination. This paper addresses the optimal path planning problem for the vehicle navigated by the NRMS technology (OPP-V-NRMS) which is a challenging hierarchical mixed-variable constrained optimization problem involving two coupling levels. To solve OPP-V-NRMS, we present two decoupling methods: the accurate method and the approximation method. The accurate method performs path planning for all possible arrangements, which is accurate but time-consuming. The approximation method only selects a few arrangements for path planning, which achieves a better tradeoff between solution quality and computational cost. In both decoupling methods, a differential evolution based (DE-based) path planning algorithm is proposed for path planning. Comparative experiments show that both methods can find a feasible and high-quality path for the vehicle while the approximation method brings about much lower computational cost.

The problem of flocking of second-order multiagent systems with connectivity preservation is investigated in this paper. First, for estimating the algebraic connectivity as well as the corresponding eigenvector, a new decentralized inverse power iteration scheme is formulated. Then, based on the estimation of the algebraic connectivity, a set of distributed gradient-based flocking control protocols is built with a new class of generalized hybrid potential fields which could guarantee collision avoidance, desired distance stabilization, and the connectivity of the underlying communication network simultaneously. What is important is that the proposed control scheme allows the existing edges to be broken without violation of connectivity constraints, and thus yields more flexibility of motions and reduces the communication cost for the multiagent system. In the end, nontrivial comparative simulations and experimental results are performed to demonstrate the effectiveness of the theoretical results and highlight the advantages of the proposed estimation scheme and control algorithm.

Decomposition is an efficient and prevailing strategy for solving multiobjective optimization problems (MOPs). Its success has been witnessed by the multiobjective evolutionary algorithm MOEA/D and its variants. In decomposition-based methods, an MOP is decomposed into a number of scalar subproblems by using various scalarizing functions. Most decomposition schemes adopt the weighting method to construct scalarizing functions. In this paper, another classical generation method in the field of mathematical programming, that is the e-constraint method, is adopted for the multiobjective optimization. It selects one of the objectives as the main objective and converts other objectives into constraints. We incorporate the e-constraint method into the decomposition strategy and propose a new decomposition-based multiobjective evolutionary algorithm with the e-constraint framework (DMOEA-εC). It decomposes an MOP into a series of scalar constrained optimization subproblems by assigning each subproblem with an upper bound vector. These subproblems are optimized simultaneously by using information from neighboring subproblems. Besides, a main objective alternation strategy, a solution-to-subproblem matching procedure, and a subproblem-to-solution matching procedure are proposed to strike a balance between convergence and diversity. DMOEA-εC is compared with a number of state-of-theart multiobjective evolutionary algorithms. Experimental studies demonstrate that DMOEA-εC outperforms or performs competitively against these algorithms on the majority of 34 continuous benchmark problems, and it also shows obvious advantages in solving multiobjective 0-1 knapsack problems.

The weapon target assignment (WTA) problem is a fundamental problem arising in defense-related applications of operations research. And the multi-stage weapon target assignment (MWTA) problem is the basis of dynamic weapon target assignment (DWTA) problems which commonly exist in practice. The MWTA problem considered in this paper is with uncertainties, namely the uncertain MWTA (UMWTA) problem, and is formulated into a multi-objective constrained combinatorial optimization problem with two competing objectives. Apart from maximizing damage to hostile targets, this paper follows the principle of minimizing ammunition consumption under the assumption that each element of the kill probability matrix follows four different probability distributions. In order to tackle the two challenges, i.e., multi-objective and the uncertainty, the multi-objective evolutionary algorithm based on decomposition with adaptive weight adjustment (MOEA/D-AWA) and the Max-Min robust operator are adopted to solve the problem efficiently. Then comparison studies between the MOEA/D-AWA and a single objective solver used for a relaxed formulation on solving both certain and uncertain instances of two different scaled MWTA problems which include four uncertain scenarios are conducted. Numerical results show that MOEA/D-AWA outperforms the single objective solver on solving both certain and uncertain multi-objective MWTA problems discussed in this paper. Comparisons between the results of the certain and uncertain formulation also indicate the necessity of the robust formulation of practical problems.

The coordination between unmanned aerial vehicles (UAVs) and unmanned ground vehicles (UGVs) is a proactive research topic whose great value of application has attracted vast attention. This paper outlines the motivations for studying the cooperative control of UAVs and UGVs, and attempts to make a comprehensive investigation and analysis on recent research in this field. First, a taxonomy for classification of existing unmanned aerial and ground vehicles systems (UAGVSs) is proposed, and a generalized optimization framework is developed to allow the decision-making problems for different types of UAGVSs to be described in a unified way. By following the proposed taxonomy, we show how different types of UAGVSs can be built to realize the goal of a common task, that is target tracking, and how optimization problems can be formulated for a UAGVS to perform specific tasks. This paper presents an optimization perspective to model and analyze different types of UAGVSs, and serves as a guidance and reference for developing UAGVSs.

The weapon target assignment (WTA) problem is a fundamental problem arising in defense-related applications of operations research, and the multi-stage weapon target assignment (MWTA) problem is the basis of dynamic weapon target assignment (DWTA) problems which commonly exist in practice. The MWTA problem considered in this paper is formulated into a multi-objective constrained combinatorial optimization problem with two competing objectives. Apart from maximizing damage to hostile targets, this paper follows the principle of minimizing ammunition consumption under the consideration of resource constraints, feasibility constraints and fire transfer constraints. In order to tackle the two challenges, two types of multi-objective optimizers: NSGA-II (domination-based) and MOEA/D (decomposition-based) enhanced with an adaptive mechanism are adopted to achieve efficient problem solving. Then a comparison study between adaptive NSGA-II (ANSGA-II) and adaptive MOEA/D (AMOEA/D) on solving instances of three scales MWTA problems is done, and four performance metrics are used to evaluate each algorithm. Numerical results show that ANSGA-II outperforms AMOEA/D on solving multi-objective MWTA problems discussed in this paper, and the adaptive mechanism definitely enhances performances of both algorithms.

Differential evolution (DE) and particle swarm optimization (PSO) are two formidable population-based optimizers (POs) that follow different philosophies and paradigms, which are successfully and widely applied in scientific and engineering research. The hybridization between DE and PSO represents a promising way to create more powerful optimizers, especially for specific problem solving. In the past decade, numerous hybrids of DE and PSO have emerged with diverse design ideas from many researchers. This paper attempts to comprehensively review the existing hybrids based on DE and PSO with the goal of collection of different ideas to build a systematic taxonomy of hybridization strategies. Taking into account five hybridization factors, i.e., the relationship between parent optimizers, hybridization level, operating order (OO), type of information transfer (TIT), and type of transferred information (TTI), we propose several classification mechanisms and a versatile taxonomy to differentiate and analyze various hybridization strategies. A large number of hybrids, which include the hybrids of DE and PSO and several other representative hybrids, are categorized according to the taxonomy. The taxonomy can be utilized not only as a tool to identify different hybridization strategies, but also as a reference to design hybrid optimizers. The tradeoff between exploration and exploitation regarding hybridization design is discussed and highlighted. Based on the taxonomy proposed, this paper also indicates several promising lines of research that are worthy of devotion in future.

In this paper, we propose an efficient rule-based heuristic to solve asset-based dynamic weapon-target assignment (DWTA) problems. The main idea of the proposed heuristic is to utilize the domain knowledge of DWTA problems to directly achieve weapon assignment, without large number of function evaluations. We update the saturation states of constraints in the assignment process to guarantee the feasibility of generated solutions. For the purpose of testing the performance of the proposed heuristic, we build a general Monte Carlo simulation-based DWTA framework. For comparison, we also employ a Monte Carlo method (MCM) to make DWTA decisions in different defense scenarios. From simulations with DWTA instances under different scales, the heuristic has obvious advantages over the MCM with regard to solution quality and computation time. The proposed method can solve large-scale DWTA problems (e.g., those including 100 weapons, 100 targets, and four defense stages) within only a few seconds.

The dynamic weapon-target assignment (DWTA) problem is a typical constrained combinatorial optimization problem with the objective of maximizing the total value of surviving assets threatened by hostile targets through all defense stages. A generic asset-based DWTA model is established, especially for the warfare scenario of force coordination, to formulate this problem. Four categories of constraints, involving capability constraints, strategy constraints, resource constraints (i.e., ammunition constraints), and engagement feasibility constraints, are taken into account in the DWTA model. The concept of virtual permutation (VP) is proposed to facilitate the generation of feasible decisions. A construction procedure (CP) converts VPs into feasible DWTA decisions. With constraint satisfaction guaranteed by the synergy of VPs and the CP, an elaborate local search (LS) operator, namely move-to-head operator, is constructed to avoid repeatedly generating the same decisions. The operator is integrated into two tabu search (TS) algorithms to solve DWTA problems. Comparative experiments involving a random sampling method, an LS method, a hybrid genetic algorithm, a hybrid ant-colony optimization algorithm, and our TS algorithms show that the proposed TS heuristics for DWTA outperform their competitors in most test cases and they are competent for high-quality real-time DWTA decision makings.

Global optimization process can often be divided into two subprocesses: exploration and exploitation. The tradeoff between exploration and exploitation (T:Er&Ei) is crucial in search and optimization, having a great effect on global optimization performance, e.g., accuracy and convergence speed of optimization algorithms. In this paper, definitions of exploration and exploitation are first given based on information correlation among samplings. Then, some general indicators of optimization hardness are presented to characterize problem difficulties. By analyzing a typical contraction-based three-stage optimization process,Optimal Contraction Theoremis presented to show thatT:Er&Eidepends on the optimization hardness of problems to be optimized.T:Er&Eiwill gradually lean toward exploration as optimization hardness increases. In the case of great optimization hardness, exploration-dominated optimizers outperform exploitation-dominated optimizers. In particular, random sampling will become an outstanding optimizer when optimization hardness reaches a certain degree. Besides, the optimal number of contraction stages increases with optimization hardness. In an optimal contraction way, the whole sampling cost is evenly distributed in all contraction stages, and each contraction takes the same contracting ratio. Furthermore, the characterization of optimization hardness is discussed in detail. The experiments with several typical global optimization algorithms used to optimize three groups of test problems validate the correctness of the conclusions made byT:Er&Eianalysis.