Objective To address the cooperative control problem of multi-tug towing systems characterized by multiple constraints and strong physical coupling, a multi-objective particle swarm optimization (MOPSO) method integrated with a multi-criterion switching strategy is proposed.

Method First, a comprehensive mathematical model of the multi-tug towing system's motion is established. This model fully captures the 3-DOF nonlinear dynamics of both the towed ship and each individual tug. This highly coupled dynamic system is subsequently reformulated as a multi-objective optimization problem. The primary conflicting objectives are carefully defined as: (1) Minimizing the towed ship's pose and velocity tracking errors, (2) Minimizing the tugs' pose and velocity tracking errors—specifically, reducing variance in inter-tug distances and relative orientations—to achieve safe, compact, and coordinated tug formation under diverse conditions. Next, tailored velocity and position update rules for the particle swarm are developed to construct a multi-objective particle swarm optimization (MOPSO) control framework. The velocity update mechanism incorporates an adaptive inertia weight to balance global exploration in early stages and fine local exploitation later. Building upon this MOPSO foundation, a multi-criterion switching strategy is introduced as a core innovation. To prevent the particle swarm from becoming trapped in local optima during the search process, this strategy adopts a fixed-interval switching combined with random selection mechanism: a predefined switching interval is set, and whenever the current iteration count reaches a multiple of this interval, a new evaluation criterion is randomly selected from a predefined set of multiple criteria to guide the subsequent iterations. The predefined criteria for selecting the global best particle from the external archive are as follows: (1) Total Loss Minimization Criterion; (2)Towed Ship Loss Minimization Criterion; (3) Maximum Loss Minimization Criterion; (4) Tug Loss Balancing Criterion. By periodically and randomly switching among these complementary criteria at fixed intervals, the strategy dynamically adjusts the search direction, effectively escapes local attractors, maintains better diversity in the Pareto archive, and ultimately yields a more uniform, well-converged, and globally optimal Pareto front tailored to the complex, coupled dynamics of the multi-tug towing system.

Results Simulation results demonstrate that, compared with the traditional optimal control method, the proposed approach improves the convergence speed by 21.88%, while reducing the towed ship's longitudinal and lateral errors by 43.39% and 48.99%, respectively. The tracking errors of all four tugs are also reduced, resulting in smoother and more compact formation control. Furthermore, compared with the single-criterion method, the proposed multi-criterion switching strategy achieves a more uniform Pareto front distribution, with the solution set closer to the ideal optimal region. The convergence speed is improved by 7.41%, and the longitudinal and lateral errors of the towed ship are reduced by 11.47% and 10.27%, respectively, achieving a better balance among multiple objectives.

Conclusion The proposed method enhances the control accuracy of the towed ship while achieving coordinated control among tugs and optimal balance of overall system performance.