Local Optimization Problem Research Articles

Genetic Algorithm Based on Opposite Chromosome Multiple Genetic Operations Combined with Task Load Balancing

A collaborative optimization method for task allocation and path planning in multi-UAV execution of multi-objective cooperative inspection tasks is proposed. The method is based on the Opposite Genetic Algorithms (OGA), which combines the actual task completion time with the balance of UAV inspection flight time, fault downtime, and maximum-minimum time load. A Task Balancing Opposite Chromosome Multiple Mutation Operator Genetic Algorithm (TOMGA) is introduced to solve the task load balancing problem by optimizing the task allocation among multiple UAVs with time as the optimization objective. Simulation results demonstrate that, this algorithm can effectively allocate inspection tasks to UAVs and generate initial flight routes. It resolves the issue of task load imbalance, improves the rationality of task allocation, enhances convergence speed, and overcomes the problem of local optima.

Diversified Knowledge Transfer Strategy for Multitasking Particle Swarm Optimization.

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

Two-stage problems of optimal location and distribution of the humanitarian logistics system’s structural subdivisions

Purpose. To ensure the rational organization of the evacuation of people from a region affected by an emergency by developing a mathematical and algorithmic toolkit that will allow for the early distribution of transport and material resources, maximizing coverage of the affected areas while minimizing evacuation time. Methodology. System analysis of evacuation processes; mathematical modeling, the theory of continuous problems of optimal partitioning of sets, non-differentiable optimization. Findings. The object of the study is the two-stage evacuation logistic processes that occur when serving the population of areas affected by emergencies of a natural or technogenic nature. The research considers the possibility of optimally distributing human flows within the transportation system, the structural subdivisions of which are first-stage centers (first aid stations that carry out the reception of citizens from areas affected by the disaster) and second-stage centers (specialized units of the emergency aid system that provide further services to the evacuated population). The proposed mathematical model deals with the problem of optimally partitioning a continuous set with the placement of subset centers and additional connections. Methods for its solution have been described. We demonstrate the versatility of these models, as they can be used to describe logistic evacuation processes, organize assembly points, intermediate locations, evacuation reception points, and those providing primary assistance to the affected population. We calculate the appropriate number of essential products and deliver them from existing warehouses through distribution centers to the affected areas. Originality. As preventive measures to increase the level of population safety during an emergency, we consider the optimal placement of rescue facilities and the zoning of the territory to distribute evacuation traffic. We also address the problem of the optimal distribution of human flows in the transport and logistics system. Practical value. The presented models, methods, and algorithms enable the solution of many practical problems related to the development of preventive measures and the planning of rescue operations to ensure the population’s safety in case of emergencies. The theoretical results obtained are translated into specific recommendations that can be utilized when addressing logistical problems related to the organization of primary evacuation of the population from affected areas and their subsequent transportation to safer locations for further assistance.

Hybrid path planning method for USV using bidirectional A* and improved DWA considering the manoeuvrability and COLREGs

This paper proposes a hybrid dynamic path planning algorithm that integrates global path planning (GPP) and local path planning (LPP). The objective is to effectively address the challenges associated with path planning and collision avoidance for unmanned surface vehicles (USV) in complex environments. The bidirectional A* algorithm is used to search the optimized strategy based on the actual geographical information map for the navigation routes of USV. The Dynamic Window Algorithm (DWA) is employed, and a novel cost function is formulated considering the USV's manoeuvring characteristics, dynamic constraints, and environmental information. The primary purpose is to ensure the compliance of the USV with COLREGs during dynamic obstacle avoidance. It accomplishes this by providing positive reinforcement for achieving the correct turning speed when the USV determines the orientation of an approaching ship. Another evaluation function is introduced to mitigate the problem of local optima in complex environments that the LPP may encounter. The actual work map is used to model the application scenario with the obstacles in the presence of incoming ships, the simulation results show that the proposed algorithm is capable of generating adaptive, collision-free routes while adhering to COLREGs rules.

Active Kriging-based conjugate first-order reliability method for highly efficient structural reliability analysis using resample strategy

Efficient structural reliability analysis method is crucial to solving reliability analysis of complex structural problems. High-computational cost and low-failure probability problems greatly limit the efficiency in structural reliability analysis problems, causing the safety and reliability of the structure to be questioned. In this work, a highly efficient structural reliability analysis method coupling active Kriging algorithm with conjugate first order reliability method (AK-CFORM) is proposed. Specifically, the resample strategy is considered to reduce the number of samples evaluated in each active learning process; the uniform sampling is used to better balance global and local optimal problems; the conjugate map is used to improve the robustness of analytical first order reliability method; and the approximate numerical differential formula is proposed to solve the problems of non-convergence when solving the gradient of the Kriging surrogate model. Finally, three numerical cases and four engineering cases are used to illustrate the effectiveness and robustness of the proposed method. The results show that the proposed AK-CFORM has greater advantages in the number of calling system response and surrogate model with robust and accurate performance.

Optimal Location of Capacitor in a Radial Distribution System Using New Hybrid Method

This paper solves the problem of optimal sizing and locations of capacitors in radial distribution system using a new hybrid method combining a new stability index and a genetic algorithm to improve the loss, voltage and stability planes. The Bus Voltage Stability Index BVSI is used to determine the locations and the genetic algorithm GA to calculate the size. The GA-BVSI analytical-metaheuristic method, compared with existing methods, is more suitable and recommended for operators who are faced with the problem of sizing capacitors to improve the technical performance of their network. Keywords: Optimal sizing and locations; Capacitors; Radial distribution system; New stability index;Hybrid method.

Optimizing Rack Locations in the Mobile-Rack Picking System: A Method of Integrating Rack Heat and Relevance

The flexible movement of racks in the mobile-rack picking system (MRPS) significantly improves the picking efficiency of e-commerce orders with the characteristics of “one order multi–items” and creates a challenging problem of how to place racks in the warehouse. This is because the placement of each rack in the MRPS directly influences the distance that racks need to be moved during order picking, which in turn affects the order picking efficiency. To handle the rack location optimization problem (RLOP), this work introduces a novel idea and methodology, taking into account the heat degree and the relevance degree of racks, to enhance the efficiency of rack placements in the MRPS. Specifically, a two-stage solution strategy is implemented. In stage 1, an integer programming model (Model 1) is developed to determine the heat and relevance degree of racks, and it can be solved quickly by the Gurobi. Stage 2 entails developing a bi-objective integer programming model (Model 2) with the objective to minimize the travel distances of robots in both heavy load and no-load conditions, using the rack heat and relevance degree as inputs. In light of the challenge of decision coupling and the vast solution space in stage 2, we innovatively propose two lower bounds by slacking off the distance between storage locations. A matheuristic algorithm based on Benders decomposition (MABBD) is designed, which utilizes Benders-related rules to reconstruct Model 2, introduces an enhanced cut and an improved optimal cut with RLOP characteristics, and designs the warm start strategy and the master variable fixed strategy. Given the substantial size of real-life problems, the Memetic algorithm (MA) is specifically devised to address them. Instances of varying sizes are also employed to validate the science and efficacy of the model and algorithm.

Learning for Cellular Neural Networks Using the GARPLA Algorithm

The main content of this article is to build a hybrid algorithm between genetic algorithm and Recurrent Perceptron Learning Algorithm to determine the weight set for standard cellular neural networks. In particular, the Recurrent Perceptron Learning Algorithm was announced by Gukzelis in 1998 to determine the weight set for CeNNs, however, the nature of the algorithm built according to LMS learning rules means there is still a possibility of local convergence problems of algorithm. Meanwhile, the genetic algorithm originates from natural selection problems and is capable of determining the local optimal domain of the problem. Therefore, the GARPLA hybrid algorithm will fully determine the optimal weight set for the CeNNs network, reducing potential local optimization problems encountered in the RPLA algorithm.

Optimizing the Probabilistic Neural Network Model with the Improved Manta Ray Foraging Optimization Algorithm to Identify Pressure Fluctuation Signal Features.

To improve the identification accuracy of pressure fluctuation signals in the draft tube of hydraulic turbines, this study proposes an improved manta ray foraging optimization (ITMRFO) algorithm to optimize the identification method of a probabilistic neural network (PNN). Specifically, first, discrete wavelet transform was used to extract features from vibration signals, and then, fuzzy c-means algorithm (FCM) clustering was used to automatically classify the collected information. In order to solve the local optimization problem of the manta ray foraging optimization (MRFO) algorithm, four optimization strategies were proposed. These included optimizing the initial population of the MRFO algorithm based on the elite opposition learning algorithm and using adaptive t distribution to replace its chain factor to optimize individual update strategies and other improvement strategies. The ITMRFO algorithm was compared with three algorithms on 23 test functions to verify its superiority. In order to improve the classification accuracy of the probabilistic neural network (PNN) affected by smoothing factors, an improved manta ray foraging optimization (ITMRFO) algorithm was used to optimize them. An ITMRFO-PNN model was established and compared with the PNN and MRFO-PNN models to evaluate their performance in identifying pressure fluctuation signals in turbine draft tubes. The evaluation indicators include confusion matrix, accuracy, precision, recall rate, F1-score, and accuracy and error rate. The experimental results confirm the correctness and effectiveness of the ITMRFO-PNN model, providing a solid theoretical foundation for identifying pressure fluctuation signals in hydraulic turbine draft tubes.

Generative Pre-Trained Transformer-Based Reinforcement Learning for Testing Web Application Firewalls

Web Application Firewalls (WAFs) are widely deployed to protect key web applications against multiple security threats, so it is important to test WAFs regularly to prevent attackers from bypassing them easily. Machine-learning-based black-box WAF testing is gaining more attention, though existing learning-based approaches have strict requirements on the source and scale of payload data and suffer from the local optimum problem, limiting their effectiveness and practical application. We propose GPTFuzzer, a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">practical</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">effective</i> generation-based approach to test WAFs by generating attack payloads token-by-token. Specifically, we fine-tune a Generative Pre-trained Transformer language model with reinforcement learning to make GPTFuzzer have the least restrictions on payload data and thus more applicable in practice, and we use reward modeling and KL-divergence penalty to improve the effectiveness of our approach and mitigate the local optimum issue. We implement GPTFuzzer and evaluate it on two well-known open-source WAFs against three kinds of common attacks. Experimental results show that GPTFuzzer significantly outperforms state-of-the-art approaches, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i.e.</i> ML-Driven and RAT, finding up to 7.8× (3.2× on average) more bypassing payloads within 1,250,000 requests, or finding out all bypassing payloads using up to 8.1× (3.3× on average) fewer requests.

A High-Efficiency and Incentive-Compatible Peer-to-Peer Energy Trading Mechanism

Due to the rapid development of demand response management and distributed energy resources, prosumers are becoming more proactive, which also promotes the emergence of peer-to-peer (P2P) energy trading mechanisms. However, we find that it is quite difficult to simultaneously achieve high computational efficiency, decentralized operations and solution optimality in a P2P energy trading mechanism, which is called the “P2P energy trading trilemma”. In this paper, we first propose a novel negotiation mechanism for P2P energy trading that can maximize social welfare in a decentralized manner and respect physical network constraints. Then, the local optimization problem is transformed into a closed-form alternating update algorithm (AUA), so that the computational efficiency can be greatly improved. Therefore, our proposed mechanism solves the “P2P energy trading trilemma" to a certain extent. Another challenge is that the locational marginal price (LMP)-based market mechanism cannot satisfy the incentive-compatible property. To encourage prosumers to cooperate in a lack-of-trust environment, a novel incentive-compatible mechanism is proposed for P2P energy trading using consensus mechanism inspired by proof of solution (PoSo) and smart contract (SC). Finally, we simulate the functionality of the mechanism in terms of convergence performance, reliability, scalability, computational efficiency, and SC operations.

EABOA: Enhanced adaptive butterfly optimization algorithm for numerical optimization and engineering design problems

The butterfly optimization algorithm (BOA) is a meta-heuristic algorithm that mimics foraging and mating behavior of butterflies. In order to alleviate the problems of slow convergence, local optimum and lack of population diversity of BOA, an enhanced adaptive butterfly optimization algorithm (EABOA) is proposed in this paper. First, a new adaptive fragrance model is designed, which provided a finer fragrance perception way and effectively enhanced the convergence speed and accuracy. Second, Lévy flight with high-frequency short-step jumping and low-frequency long-step walking is adopted to help the algorithm jump out of the local optimum. Third, the dimension learning-based hunting is employed to enhance information exchange by creating neighbors for each butterfly, thus improving the balance between local and global search and maintaining population diversity. In addition, the Fitness-Distance-Constraint (FDC) method is introduced to enhance constraint handling in EABOA (named FDC-EABOA). The proposed EABOA is compared with 8 well-known algorithms and 8 BOA variants in CEC 2022 test suite and the results were statistically analyzed using Friedman, Friedman aligned rank, Wilcoxon signed rank, Quade rank and multiple comparisons, analysis of variance (ANOVA) and range analysis. Finally, EABOA and FDC-EABOA are applied to seven engineering problems (parameter identification of photovoltaic module model, speed reducer design, tension/compression spring design, pressure vessel design, gear train design, welded beam design, SOPWM for 3-level inverters), and metrics such as Improvement Index (IF) and Mean Constraint Violation (MV) confirm that the proposed algorithms are satisfactory. Experimental results and statistical analysis show that the proposed algorithms outperform the comparison algorithms and demonstrate the strong potential for solving numerical optimization and engineering design problems.

A new global optimization for hybrid automaton Identification

System Identification to a hybrid automaton is a complex and flourishing research field involving expertise in both continuous dynamics and discrete event system modeling. Current methodologies for hybrid automaton Identification predominantly rely on a framework centered around the sequential resolution of local signal processing optimization problems. This paper seeks to enhance the existing framework by introducing a novel step designed to address certain limitations inherent in the non-global optimization aspect of a sequential resolution framework. The proposed approach enables each Identification step not only to address its local optimization challenges but also to contribute to the optimization of a global cost function including model distance, sequential fidelity, and automaton structure.

A novel parallel ant colony optimization algorithm for mobile robot path planning.

With the continuous development of mobile robot technology, its application fields are becoming increasingly widespread, and path planning is one of the most important topics in the field of mobile robot research. This paper focused on the study of the path planning problem for mobile robots in a complex environment based on the ant colony optimization (ACO) algorithm. In order to solve the problems of local optimum, susceptibility to deadlocks, and low search efficiency in the traditional ACO algorithm, a novel parallel ACO (PACO) algorithm was proposed. The algorithm constructed a rank-based pheromone updating method to balance exploration space and convergence speed and introduced a hybrid strategy of continuing to work and killing directly to address the problem of deadlocks. Furthermore, in order to efficiently realize the path planning in complex environments, the algorithm first found a better location for decomposing the original problem into two subproblems and then solved them using a parallel programming method-single program multiple data (SPMD)-in MATLAB. In different grid map environments, simulation experiments were carried out. The experimental results showed that on grid maps with scales of 20 $ \times $ 20, 30 $ \times $ 30, and 40 $ \times $ 40 compared to nonparallel ACO algorithms, the proposed PACO algorithm had less loss of solution accuracy but reduced the average total time by 50.71, 46.83 and 46.03%, respectively, demonstrating good solution performance.

Preprint: Global, and local optimization beamforming for broadband sources.

This paper presents an alternative energy function for global optimization (GO) beamforming, tailored to acoustic broadband sources. Given that properties, such as the source location, multipole rotation, or flow conditions, are parameterized over the frequency, a cross spectral matrix-fitting can be performed for all frequencies at once. A numerical analysis shows that the nonlinear energy function for the standard GO problem is equivalent to the source's point spread function (PSF) and contains local minima at the locations of the grating lobes and side lobes. The energy function is improved with the proposed broadband energy, as it averages the PSF. Further, it simplifies the process of identifying sources and reconstructing their spectra from the results. The paper shows that the method is superior on synthetic monopoles compared to standard GO and CLEAN based on source coherence (CLEAN-SC). For real-world data, the results of the proposed method and CLEAN-SC are similar, and outperform standard GO. The main difference is that source assumption violations cause noisy maps for CLEAN-SC and cause wrong spectral estimations of the proposed method. By using reasonable initial values, the GO problem reduces to a local optimization problem with similar results. Further, the proposed method is able to identify synthetic multipoles with different pole amplitudes and unknown pole rotations.

An adaptive neuro-fuzzy with nonlinear PID controller design for electric vehicles

In this work, an adaptive neuro-fuzzy (ANF) with a nonlinear proportional integral derivative (NLPID) controller (ANF-NLPID) has been proposed to solve the speed-tracking problem in electric vehicles (EVs) with brushless DC motor (BLDC). The ANF-NLPID controller eliminates the external disturbances caused by environmental or internal issues and uncertainties caused by parameter variations that lead to insufficient speed-tracking performance and increased energy consumption in EVs. An improved particle swarm optimization based on the chaos theory (IPSO-CT) algorithm is introduced to obtain the parameters of the fuzzy logic controller membership function and nonlinear PID controller and present the optimal performance for the EV. Employing the chaos technique with PSO helps to prevent the system from being trapped in the local minimum or optimum problem. The performance of the IPSO-CT algorithm is tested using a numerical comparison with other existing works. The outstanding performance of the ANF-NLPID controller has been evaluated by measuring the speed-tracking performance for the new European driving cycle (NEDC) and circular trajectories. Three case studies have been presented based on measuring the ANF-NLPID controller performance without disturbances, with disturbances, with disturbances, and uncertainties effects, respectively. Furthermore, the ANF-NLPID controller has been employed in different EV models to study the performance of this type of controller. Each of the three cases includes other existing works along with the ANF-NLPID controller to provide an insightful comparison using statistical functions to obtain each controller’s overall objective function value. The other existing works are fuzzy fractional order PID (Fuzzy FOPID), fuzzy integer order PID (Fuzzy IOPID), and integer order PID (IOPID) controllers. A sensitivity analysis has been conducted to test the proposed controller’s ability to present high speed-tracking performance while changing the disturbances and uncertainty rates. The results demonstrate that the ANF-NLPID controller is superior in speed-tracking control regulation for the new European cycle drive (NEDC) and circular speed trajectories and overcomes the external disturbances and uncertainties problem with low error results. In the end, the results reveal that the ANF-NLPID controller is more efficient than the fuzzy FOPID, fuzzy IOPID, and IOPID controllers in each case.

MODEL OF TRANSPORT SAFETY ASSESSMENT IN MULTIMODAL TRANSPORTATION SYSTEMS

In this paper methods, criteria and models of safety assessment of multimodal transportation systems are investigated. Today, new types of transportation systems are formed – multimodal transportation systems, which may be defined as the result of the synthesis of several transport systems, where different modes of transport are effectively interact. The need for such systems was formed due to the peculiarities of each mode of transport, its technological and technical characteristics, which restrain the ability to compete and promote transport interaction. In this context, the problem of transport safety assess of multimodal freight transportations becomes highly important. An analysis of modern scientific researches on topic of transport safety is conducted. Unfortunately, the considered approaches to transport safety have a set of disadvantages if the complex systems are considered in form of, for example, combined, multimodal or intermodal transportations: the problem of local optimum; the problem of safety management in case of transport company is not the actual infrastructure owner; the problem of unifying estimates for several modes of transport, and so on. The system’s safety depends on its integrity and sustainable development, which is directly dependent on the objective conditions of its formation, development and operation. At the same time, the state of safety is directly dependent on subjective factors, the purpose of which is to ensure security, i.e., to preserve the integrity and maintain sustainable development and optimal functioning of the system. Thus, there is a conditional field of protection of transport system objects, which provides counteraction to a set of existing or perceived threats. In this context, modelling the transport safety assessment of multimodal freight is relevant and requires appropriate scientific developments. In the research, methods of mathematical modelling of transport systems were used in order to develop methodological approach that could be potentially used in improving the multimodal freight transportation safety. A methodical approach to safety assessment on the example of multimodal transportation, which takes into account the drawbacks of existing studies, is proposed. The practical application of developed model was demonstrated on the existing system of multimodal transportation. The developed safety assessment method may be potentially used both to assess the transportation route safety level and as key factor in optimal transportation route designing.

Optimal en-route charging station locations for electric vehicles with heterogeneous range anxiety

This paper addresses a new optimal charging station location problem for intercity highway networks where electric vehicles are of heterogeneous driving ranges and usually need to be charged multiple times in their long-haul trips. Driving range heterogeneity can be measured in practice by sampling the driving population under a variety of physical, environmental and psychological conditions and is characterized in this study by a continuous distribution of some appropriate forms. The behavioral assumption underlying this problem is that all individual drivers choose their optimal route-and-charge choices if they can make a trip by driving an electric vehicle or cancel their trips or switch to other transportation modes if they cannot. By explicitly taking into account the impact of limited driving ranges on both route and trip/mode choices, we constructed a mixed integer linear programming model for formulating the charging station location problem, the goal of which is to maximize the networkwide travel efficiency and preference subject to a limited infrastructure investment budget. To tackle this integer programming model, we developed a branch-and-bound algorithm and a neighborhood search heuristic, in both of which a multi-criterion label-correcting algorithm is embedded for deriving the underlying route-and-charge flow pattern. For justifying the effectiveness and efficiency of the proposed algorithms, a synthetic network and two real-world networks are employed as numerical examples. The computational results obtained from the numerical analysis show that the heuristic is capable of obtaining optimal solutions in most test scenarios and is much more computationally efficient than the branch-and-bound algorithm, with a computing time that is only about one tenth of the latter.

PV/Hydrogen DC microgrid control using distributed economic model predictive control

The integration of hydrogen energy into a photovoltaic-dominated microgrid is now becoming a promising approach to improve the photoconversion efficiency and enhance the operating reliability. However, the energy management and power regulation of the Photovoltaic/Hydrogen DC microgrid face challenges due to the intermittency of photovoltaic (PV) power generation and the randomness of load. In this paper, a distributed economic model predictive control (DEMPC) scheme is developed for a PV/Hydrogen DC microgrid, which integrates the energy management, economic optimization, and power regulation into one optimal control framework. Based on the developed distributed converter-based mathematical model, three local controllers are designed to achieve the economic targets of PV subsystem, alkaline electrolyzer subsystem, and proton exchange membrane fuel cell subsystem respectively, which cooperate with each other through the communication network to realize the power supply–demand balance, DC bus voltage stability, and economic optimization. A mixed integer nonlinear programming algorithm utilizing the finite converter switching states is embedded into the DEMPC to solve the non-convex local optimization problems efficiently. The effectiveness and superiority of the proposed DEMPC scheme are verified by simulations under varying irradiance and load conditions, indicating that the DEMPC can achieve a comparable overall dynamic economic performance with a significantly reduced computation burden and power oscillation, compared to the centralized economic model predictive control (CEMPC).

Autonomous collision avoidance method for MASSs based on precise potential field modelling and COLREGs constraints in complex sailing environments

Autonomous collision avoidance (CA) for maritime autonomous surface ships (MASSs) in complex navigational environments requires accurate environment modelling and efficient CA algorithms. This study proposes a fast construction method for complex environmental potential field models applicable to vector charts. It accurately represents all complex static obstacles, including concave polygons, and dynamically adjusts the range of influence of a potential field according to its danger level. For dynamic ships, a dynamic obstacle modelling method, based on the quaternion ship domain, is designed to highlight the uncertain motion characteristics of ships. Based on the coupled modelling of dynamic and static obstacles, the virtual potential field of target ships, constrained by the International Regulations for Preventing Collisions at Sea (COLREGs), was constructed. By combining the first-order Nomoto model and optimal field prediction strategy, an optimal CA path, satisfying ship dynamics and COLREGs constraints, was realised, and the local optimal problem of the traditional artificial potential field method was solved. Simulation results show that the proposed method accomplishes fast and accurate modelling of complex environments and realises autonomous path planning and real-time multivessel CA tasks for MASSs in complex water considering the COLREGs constraints. Thus, the proposed method can be implemented in actual ships.