We address the Traveling Salesman Problem (TSP), a famous NP-hard combinatorial optimization problem. And we propose a variable strategy reinforced approach, denoted as VSR-LKH, which combines three reinforcement learning methods (Q-learning, Sarsa and Monte Carlo) with the well-known TSP algorithm, called Lin-Kernighan-Helsgaun (LKH). VSR-LKH replaces the inflexible traversal operation in LKH, and lets the program learn to make choice at each search step by reinforcement learning. Experimental results on 111 TSP benchmarks from the TSPLIB with up to 85,900 cities demonstrate the excellent performance of the proposed method.

We address the Budgeted Maximum Coverage Problem (BMCP), which is a natural and more practical extension of the standard 0–1 knapsack problem and the set cover problem. Given m elements with nonnegative weights, n subsets of elements with nonnegative costs, and a total budget, BMCP aims to select some subsets such that the total cost of selected subsets does not exceed the budget, and the total weight of associated elements is maximized. In this paper, we propose a variable depth local search algorithm (VDLS) for the BMCP. VDLS first generates an initial solution by a greedy algorithm, then iteratively improves the solution through a partial depth-first search method, that can improve the solution by simultaneously changing the states (selected or not) of multiple subsets. Such method allows VDLS to explore the solution space widely and deeply, and to yield high-quality solutions. We further propose a neighbor structure to boost the algorithm performance, that is, both subsets have a neighbor relation if they share at least one common associated element. By applying the neighbor structure, VDLS can adjust the selected subsets while losing as few covered elements as possible. Since the existing BMCP benchmarks only have simple structures and small scales, we design 60 new instances with relatively large scales and complex structures to enrich the diversity of the BMCP instances. Experimental results on 30 public instances and 60 new instances we designed demonstrate that VDLS significantly outperforms the existing heuristic and the general CPLEX exact solver.

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Scan registration is a fundamental step for the simultaneous localization and mapping of mobile robot. The accuracy of scan registration is critical for the quality of mapping and the accuracy of robot navigation. During all of the scan registration methods, normal distribution transform is an efficient and wild-using one. But normal distribution transform will lead to the unreasonable interruption when splitting the grid and can’t express the points’ local geometric feature by prefixed grid. In this article, we propose a novel method, composite clustering normal distribution transform, which comprises the density-based clustering and k-means clustering to aggregate the points with similar local distributing feature. It takes singular value decomposition to judge the suitable degree of one cluster for further division. Meanwhile, to avoid the radiating phenomenon of LIDAR in measuring the points’ distance, we propose a method based on trigonometric to measure the internal distance. The clustering method in composite clustering normal distribution transform could ensure the expression of LIDAR’s local distribution and matching accuracy. The experimental result demonstrates that our method is more accurate and more stable than the normal distribution transform and iterative closest point methods.