Many machinery manufacturings are categorized as multi-mode resource-constrained project scheduling problems which have attracted significant interest in recent years. It has been shown that such problems are non-deterministic polynomial-time-hard. Particle swarm optimization is one of the most commonly used metaheuristic. Multi-mode resourceconstrained project scheduling problems comprise two sub-problems, namely, an activity operating priority and an activity operating mode sub-problems; hence, two particle swarm optimizations are used to solve these two sub-problems. In solving the activity priority sub-problem, a designed global guidance ratio is involved to control the particle's search behavior. Restated, guiding a diversification search at the beginning stage and conducting an intensification search at latter stage are controlled by adjusting the global guidance ratio. The particle swarm optimization combined with the global guidance ratio mechanism is named global guidance ratio-particle swarm optimization herein. Meanwhile, a non-fixed global guidance ratio adjustment is also suggested to further enhance the search performance. Moreover, different communication topologies for balancing the convergence of using global and local topologies are also suggested in global guidance ratio-particle swarm optimization to further improve the search efficiency. The performance of the proposed global guidance ratio-particle swarm optimization scheme is evaluated by solving all the multi-mode resource-constrained project scheduling problem instances in Project Scheduling Problem Library. It is shown that the scheduling solutions are in good agreement with those presented in the literatures. Hence, the effectiveness of the proposed global guidance ratio-particle swarm optimization scheme is confirmed.

A depot location has a significant effect on the transportation cost in vehicle routing problems. This study proposes a hierarchical particle swarm optimization (PSO) including inner and outer layers to obtain the best location to establish a depot and the corresponding optimal vehicle routes using the determined depot location. The inner layer PSO is applied to obtain optimal vehicle routes while the outer layer PSO is to acquire the depot location. A novel particle encoding is suggested for the inner layer PSO, the novel PSO encoding facilitates solving the customer assignment and the visiting order determination simultaneously to greatly lower processing efforts and hence reduce the computation complexity. Meanwhile, a routing balance insertion (RBI) local search is designed to improve the solution quality. The RBI local search moves the nearest customer from the longest route to the shortest route to reduce the travel distance. Vehicle routing problems from an operation research library were tested and an average of 16% total routing distance improvement between having and not having planned the optimal depot locations is obtained. A real world case for finding the new plant location was also conducted and significantly reduced the cost by about 29%.

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The depot locations have a significant effect on the transportation cost in the multi-depot vehicle routing problem. A two-tier particle swarm optimization framework is proposed, in which an external particle swarm optimization and an internal particle swarm optimization are used to determine the optimal depot locations and the optimal multi-depot vehicle routing problem solution, respectively. In the internal particle swarm optimization, a novel particle encoding scheme is used to minimize the computational cost by concurrently allocating the customers to depots, assigning the customers to vehicles, and determining the optimal routing path for each vehicle. The quality of the solutions is enhanced through a designed mutation local search with savings scheme. To verify the effectiveness of the proposed scheme, six standard multi-depot vehicle routing problem instances are tested and compared. It is shown that the use of the external particle swarm optimization scheme to optimize the multi-depot locations reduces the average routing distance obtained by the internal particle swarm optimization by around 13.16% on average. Furthermore, for a real-world case, the proposed two-tier particle swarm optimization scheme reduces the total routing cost by around 18%. Restated, the proposed particle swarm optimization algorithm provides an effective and efficient tool for solving practical multi-depot vehicle routing problems. Notably, the proposed scheme can be used as a reference model for obtaining the optimal locations in a variety of scheduling problems.

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