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Feasibility robust optimization techniques solve optimization problems with uncertain parameters that appear only in their constraint functions. Solving such problems requires finding an optimal solution that is feasible for all realizations of the uncertain parameters. This paper presents a new feasibility robust optimization approach involving uncertain parameters defined on continuous domains without any known probability distributions. The proposed approach integrates a new sampling-based scenario generation scheme with a new scenario reduction approach in order to solve feasibility robust optimization problems. An analysis of the computational cost of the proposed approach was performed to provide worst case bounds on its computational cost. The new proposed approach was applied to three test problems and compared against other scenario-based robust optimization approaches. A test was conducted on one of the test problems to demonstrate that the computational cost of the proposed approach does not significantly increase as additional uncertain parameters are introduced. The results show that the proposed approach converges to a robust solution faster than conventional robust optimization approaches that discretize the uncertain parameters.

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Operating unmanned aerial vehicles (UAVs) over inhabited areas requires mitigating the risk to persons on the ground. Because the risk depends upon the flight path, UAV operators need approaches (techniques) that can find low-risk flight paths between the mission’s start and finish points. In some areas, the flight paths with the lowest risk are excessively long and indirect because the least-populated areas are too remote. Thus, UAV operators are concerned about the tradeoff between risk and flight time. Although there exist approaches for assessing the risks associated with UAV operations, existing risk-based path planning approaches have considered other risk measures (besides the risk to persons on the ground) or simplified the risk assessment calculation. This paper presents a risk assessment technique and bi-objective optimization methods to find low-risk and time (flight path) solutions and computational experiments to evaluate the relative performance of the methods (their computation time and solution quality). The methods were a network optimization approach that constructed a graph for the problem and used that to generate initial solutions that were then improved by a local approach and a greedy approach and a fourth method that did not use the network solutions. The approaches that improved the solutions generated by the network optimization step performed better than the optimization approach that did not use the network solutions.