The Closed-Loop Layout Problem (CLLP) is an NP-hard mixed optimization problem, in which an optimal placement order of facilities is found along adjustable rectangle loop with the objection of minimizing the total transport cost of material flow between facilities. In most of the existing methods, meta-heuristic algorithm was used to find the optimal order for the placement of facilities, and enumeration method was applied to find the optimal size of the rectangle loop, which causes extremely low efficiency. To solve this problem, a Hybrid Population-Based Incremental Learning (HPBIL) algorithm was proposed for solving CLLP. In the algorithm, the Discrete Population-Based Incremental Learning (DPBIL) operator and Continuous PBIL (CPBIL) operator were used separately to search the optimal placement order of facilities and the size of rectangle loop at the same time, which improved the efficiency of search. Furthermore, a local search algorithm was designed to optimize some good solutions in each iteration, enhancing the refinement ability. Simulation experiments were carried out on 13 CLLP instances. The results show that HPBIL algorithm finds the best new optimal layouts on 9 instances, and is significantly superior to the algorithms to be compared on the optimization ability for CLLP.

When solving the optimal solutions of 0-1 Knapsack Problems (KPs), the traditional Genetic Algorithm (GA) has insufficient local refinement ability and the simple local search algorithm has limited global exploration ability. Aiming at these problems, two algorithms were integrated to the Hybrid Greedy Genetic Algorithm (HGGA). Under the GA global search framework, local search module was added, and the traditional repair operator based only on item value density was improved, the greedy hybrid option based on item value was added, so as to accelerate the optimization process. In HGGA, the population was led to carry out fine search in the excellent solution space of evolution, and the classical operators of GA were relied on to expand the global search space, so as to achieve a good balance between the refinement ability and the development ability of the algorithm. HGGA was tested on three sets of data. The results show that in the first set of 15 test cases, HGGA is able to find the optimal solution on 12 cases, with a success rate of 80%; on the second small-scale dataset, the performance of HGGA is obviously better than those of other similar GA and other meta-heuristic algorithms; on the third large-scale dataset, HGGA is more stable and efficient than other meta-heuristic algorithms.