We revisit one of the classical search problems in which a diffusing target encounters a stationary searcher. Under the condition that the searcher’s detection region is much smaller than the search region in which t...We revisit one of the classical search problems in which a diffusing target encounters a stationary searcher. Under the condition that the searcher’s detection region is much smaller than the search region in which the target roams diffusively, we carry out an asymptotic analysis to derive the decay rate of the non-detection probability. We consider two different geometries of the search region: a disk and a square, respectively. We construct a unified asymptotic expression valid for both of these two cases. The unified asymptotic expression shows that the decay rate of the non-detection probability, to the leading order, is proportional to the diffusion constant, is inversely proportional to the search region, and is inversely proportional to the logarithm of the ratio of the search region to the searcher’s detection region. Furthermore, the second term in the unified asymptotic expansion indicates that the decay rate of the non-detection probability for a square region is slightly smaller than that for a disk region of the same area. We also demonstrate that the asymptotic results are in good agreement with numerical solutions.展开更多
文摘We revisit one of the classical search problems in which a diffusing target encounters a stationary searcher. Under the condition that the searcher’s detection region is much smaller than the search region in which the target roams diffusively, we carry out an asymptotic analysis to derive the decay rate of the non-detection probability. We consider two different geometries of the search region: a disk and a square, respectively. We construct a unified asymptotic expression valid for both of these two cases. The unified asymptotic expression shows that the decay rate of the non-detection probability, to the leading order, is proportional to the diffusion constant, is inversely proportional to the search region, and is inversely proportional to the logarithm of the ratio of the search region to the searcher’s detection region. Furthermore, the second term in the unified asymptotic expansion indicates that the decay rate of the non-detection probability for a square region is slightly smaller than that for a disk region of the same area. We also demonstrate that the asymptotic results are in good agreement with numerical solutions.
文摘针对动态武器目标分配(dynamic weapon target assignment,DWTA)问题,提出一种基于进化算法和局部搜索算法的文化基因算法(memetic algorithm,MA)。以最大化目标毁伤为目标,建立考虑能力约束、策略约束、资源约束、拦截可行性约束条件下的DWTA模型;引入虚拟排列进行编码以满足拦截可行性要求,设计将排列转化为实际分配方案的构造方法,给出算法运行过程中对随机事件的处理方法。通过与遗传算法(genetic algorithm,GA)、MA-GLS(memetic algorithm global local search)求解不同测试实例的对比仿真,结果表明,MA算法具有寻优速度快、优化能力强、稳定性好的优点。
