Minimizing the expected time to detect a randomly located lost target using 3-dimensional search technique

Abstract

This paper considers a new model in search theory to find a randomly located target in the 3-dimensional space. An approximation algorithm that facilitates searching procedures for searchers or robots is presented. The expected time to detect the target is also proved. The statistical analysis by calculating the optimal search strategy which minimizes the time to detect the target, assuming trivariate standard normal distribution is provided, and the technique by flowcharts is designed as well. The effectiveness of this strategy is illustrated by introducing an application from real world.

Keywords:

• 3-D Search
• search theory
• trivariate standard normal distributions
• expected time
• lost black box
• 3-D search algorithm
• optimal search¹