Deterministic and Robust Optimization Approach for Single Artillery Unit Fire Scheduling Problem

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Abstract
In this study, deterministic and robust optimization models for single artillery unit fire scheduling are developed to minimize the total enemy threat to friendly forces by considering the enemy target threat level, enemy target destruction time, and target firing preparation time simultaneously. Many factors in war environments are uncertain. In particular, it is difficult to evaluate the threat levels of enemy targets definitively. We consider the threat level of an enemy target to be an uncertain parameter and propose a robust optimization model that minimizes the total enemy threat to friendly forces. The robust optimization model represents a semi-infinite problem that has infinitely many constraints. Therefore, we reformulate the robust optimization model into a tractable robust counterpart formulation with a finite number of constraints. In the robust counterpart formulation with cardinality-constrained uncertainty, the conservativeness and robustness of the solution can be adjusted with an uncertainty degree, Γ. Further, numerical experiments are conducted to verify that the robust counterpart formulation with cardinality-constrained uncertainty can be made equivalent to the deterministic optimization model and the robust counterpart formulation with box uncertainty by setting Γ accordingly.

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