For low-dimensional multi-objective optimization problems, the existing multi-objective optimization algorithms have been able to ensure the proximity to the optimal front of the problem, and balance the convergence and the diversity of solution sets. However, the uniformity of the solution is ignored in most algorithms. In the multi-objective optimization problem with irregular Pareto front, the more uniform the distribution of solution is, the more the solution can reflect the true distribution of the optimal front of the problem, and the more reasonable the choices provided to decision makers. To improve the uniform distribution of solutions, a new multi-objective optimization algorithm CM-SPEA2 is proposed based on SPEA2 algorithm and the improved individual fitness calculation. In this algorithm, firstly, the initial population is divided into different clusters by means of hierarchical clustering. Next, the original calculation method of messy degree is improved to measure the messy degree of individuals in their clusters, and the individuals with the lowest messy degree are selected as reference points. Then, based on the Manhattan distance between other individuals and the reference point, the operator representing distribution is calculated and the fitness function is improved. Finally, the fitness threshold is set to screen non-dominated individuals near the reference point, so as to indirectly adjust the environmental selection strategy, make the distribution of retained individuals more uniform, thus improving the convergence and diversity. As compared with some similar multi-objective optimization algorithms, the proposed CM-SPEA2 algorithm has certain advantages in solving IMOP, ZDT and VNT test problems.

Automatic guided vehicles (AGVs) are extensively employed in manufacturing workshops for their high degree of automation and flexibility. This paper investigates a limited AGV scheduling problem (LAGVSP) in matrix manufacturing workshops with undirected material flow, aiming to minimize both total task delay time and total task completion time. To address this LAGVSP, a mixed-integer linear programming model is built, and a nondominated sorting genetic algorithm II based on dual population co-evolution (NSGA-IIDPC) is proposed. In NSGA-IIDPC, a single population is divided into a common population and an elite population, and they adopt different evolutionary strategies during the evolution process. The dual population co-evolution mechanism is designed to accelerate the convergence of the non-dominated solution set in the population to the Pareto front through information exchange and competition between the two populations. In addition, to enhance the quality of initial population, a minimum cost function strategy based on load balancing is adopted. Multiple local search operators based on ideal point are proposed to find a better local solution. To improve the global exploration ability of the algorithm, a dual population restart mechanism is adopted. Experimental tests and comparisons with other algorithms are conducted to demonstrate the effectiveness of NSGA-IIDPC in solving the LAGVSP.

Industrial robots are currently applied for ship sub-assembly welding to replace welding workers because of the intelligent production and cost savings. In order to improve the efficiency of the robot system, a digital twin system of welding path planning for the arc welding robot in ship sub-assembly welding is proposed in this manuscript to achieve autonomous planning and generation of the welding path. First, a five-dimensional digital twin model of the dual arc welding robot system is constructed. Then, the system kinematics analysis and calibration are studied for communication realization between the virtual and the actual system. Besides, a topology consisting of three bounding volume hierarchies (BVH) trees is proposed to construct digital twin virtual entities in this system. Based on this topology, algorithms for welding seam extraction and collision detection are presented. Finally, the genetic algorithm and the RRT-Connect algorithm combined with region partitioning (RRT-Connect-RP) are applied for the welding sequence global planning and local jump path planning, respectively. The digital twin system and its path planning application are tested in the actual application scenario. The results show that the system can not only simulate the actual welding operation of the arc welding robot but also realize path planning and real-time control of the robot.