Hierarchical path-finding for Navigation Meshes (HNA*)

Path-finding can become an important bottleneck as both the size of the virtual environments and the number of agents navigating them increase. It is important to develop techniques that can be efficiently applied to any environment independently of its abstract representation. In this paper we present a hierarchical NavMesh representation to speed up path-finding. Hierarchical path-finding (HPA*) has been successfully applied to regular grids, but there is a need to extend the benefits of this method to polygonal navigation meshes. As opposed to regular grids, navigation meshes offer representations with higher accuracy regarding the underlying geometry, while containing a smaller number of cells. Therefore, we present a bottom-up method to create a hierarchical representation based on a multilevel k-way partitioning algorithm (MLkP), annotated with sub-paths that can be accessed online by our Hierarchical NavMesh Path-finding algorithm (HNA*). The algorithm benefits from searching in graphs with a much smaller number of cells, thus performing up to 7.7 times faster than traditional A¿ over the initial NavMesh. We present results of HNA* over a variety of scenarios and discuss the benefits of the algorithm together with areas for improvement.Peer ReviewedPostprint (author's final draft

On-line Search History-assisted Restart Strategy for Covariance Matrix Adaptation Evolution Strategy

Restart strategy helps the covariance matrix adaptation evolution strategy (CMA-ES) to increase the probability of finding the global optimum in optimization, while a single run CMA-ES is easy to be trapped in local optima. In this paper, the continuous non-revisiting genetic algorithm (cNrGA) is used to help CMA-ES to achieve multiple restarts from different sub-regions of the search space. The CMA-ES with on-line search history-assisted restart strategy (HR-CMA-ES) is proposed. The entire on-line search history of cNrGA is stored in a binary space partitioning (BSP) tree, which is effective for performing local search. The frequently sampled sub-region is reflected by a deep position in the BSP tree. When leaf nodes are located deeper than a threshold, the corresponding sub-region is considered a region of interest (ROI). In HR-CMA-ES, cNrGA is responsible for global exploration and suggesting ROI for CMA-ES to perform an exploitation within or around the ROI. CMA-ES restarts independently in each suggested ROI. The non-revisiting mechanism of cNrGA avoids to suggest the same ROI for a second time. Experimental results on the CEC 2013 and 2017 benchmark suites show that HR-CMA-ES performs better than both CMA-ES and cNrGA. A positive synergy is observed by the memetic cooperation of the two algorithms.Comment: 8 pages, 9 figure

Enforcing efficient equilibria in network design games via subsidies

The efficient design of networks has been an important engineering task that involves challenging combinatorial optimization problems. Typically, a network designer has to select among several alternatives which links to establish so that the resulting network satisfies a given set of connectivity requirements and the cost of establishing the network links is as low as possible. The Minimum Spanning Tree problem, which is well-understood, is a nice example. In this paper, we consider the natural scenario in which the connectivity requirements are posed by selfish users who have agreed to share the cost of the network to be established according to a well-defined rule. The design proposed by the network designer should now be consistent not only with the connectivity requirements but also with the selfishness of the users. Essentially, the users are players in a so-called network design game and the network designer has to propose a design that is an equilibrium for this game. As it is usually the case when selfishness comes into play, such equilibria may be suboptimal. In this paper, we consider the following question: can the network designer enforce particular designs as equilibria or guarantee that efficient designs are consistent with users' selfishness by appropriately subsidizing some of the network links? In an attempt to understand this question, we formulate corresponding optimization problems and present positive and negative results.Comment: 30 pages, 7 figure