Abstract: A Markovian-target model based on stochastic differential equations and a path programming model with both searcher’s direction and velocity treated as decision variables are presented for optimal searcher path problem in continuous time and space, and the effect of searcher’s velocity on the detection ability is considered. A genetic algorithm with adaptive mutation is designed by introducing three kinds of control factors, which fulfills the adaptive control of the direction and range of mutation and dynamically regulates the balance between local search and global search. In an example of searching a target with a random escaping direction, an approximate logarithmic spiral path is found. Moreover, the algorithm provides a reasonable and effective search scheme in a path programming problem for a helicopter searching multiple targets. The results indicate that the proposed algorithm has the significant advantages of stability and global optimizing ability in comparison with other methods, and is well suitable for the search path programming problem in continuous time and space.

Key words: operations research, optimal search, continuous time and space, Markovian target, genetic algorithm with adaptive mutation, anti-submarine search