Toward optimizing static target search path planning

Discrete static open-loop target search path planning is known to be a NP (non-deterministic polynomial) - Hard problem, and problem-solving methods proposed so far rely on heuristics with no way to properly assess solution quality for practical size problems. Departing from traditional nonlinear model frameworks, a new integer linear programming (ILP) exact formulation and an approximate problem-solving method are proposed to near-optimally solve the discrete static search path planning problem involving a team of homogeneous agents. Applied to a search and rescue setting, the approach takes advantage of objective function separability to efficiently maximize probability of success. A network representation is exploited to simplify modeling, reduce constraint specification and speed-up problem-solving. The proposed ILP approach rapidly yields near-optimal solutions for realistic problems using parallel processing CPLEX technology, while providing for the first time a robust upper bound on solution quality through Lagrangean programming relaxation. Problems with large time horizons may be efficiently solved through multiple fast subproblem optimizations over receding horizons. Computational results clearly show the value of the approach over various problem instances while comparing performance to a myopic heuristic.