On Geometric Features with the Discount Effort-Reward Parameter of a Searching Path in the Space to Find a Hidden Target with Minimum Cost

In this paper, we discuss the Slinky-turn-Spiral search path with the discount effort-reward parameter to detect a randomly hidden target in the space. There is a known probability distribution for the target position. The searcher moves from a predetermined location in the searching space. This work allows us to include the discounted effort-reward search as a parameter in the search path model. This parameter has an impact on the search path’s geometric features, including torsion and curvature. We demonstrate that the expected value of the detection cost will be lower for these features’ optimal values.