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Robust Optimization Approach Using Scenario Concepts for Artillery Firing Scheduling Under Uncertainty

Department of Industrial Engineering, Yonsei University 50 Yonsei-ro, Seodaemun-gu, Seoul 03722, Korea
Institute of Defense Acquisition Program, Kwangwoon University, Seoul 01897, Korea
Division of Business Administration, Cheongju University, 298, Daeseong-ro, Cheongwon-gu, Cheongju-si, Chungcheongbuk-do 28503, Korea
Author to whom correspondence should be addressed.
Appl. Sci. 2019, 9(14), 2811;
Received: 5 June 2019 / Revised: 26 June 2019 / Accepted: 12 July 2019 / Published: 14 July 2019
(This article belongs to the Section Applied Industrial Technologies)
PDF [1278 KB, uploaded 14 July 2019]


Real wars involve a considerable number of uncertainties when determining firing scheduling. This study proposes a robust optimization model that considers uncertainties in wars. In this model, parameters that are affected by enemy’s behavior and will, i.e., threats from enemy targets and threat time from enemy targets, are assumed as uncertain parameters. The robust optimization model considering these parameters is an intractable model with semi-infinite constraints. Thus, this study proposes an approach to obtain a solution by reformulating this model into a tractable problem; the approach involves developing a robust optimization model using the scenario concept and finding a solution in that model. Here, the combinations that express uncertain parameters are assumed by scenarios. This approach divides problems into master and subproblems to find a robust solution. A genetic algorithm is utilized in the master problem to overcome the complexity of global searches, thereby obtaining a solution within a reasonable time. In the subproblem, the worst scenarios for any solution are searched to find the robust solution even in cases where all scenarios have been expressed. Numerical experiments are conducted to compare robust and nominal solutions for various uncertainty levels to verify the superiority of the robust solution.
Keywords: robust optimization; artillery firing scheduling; threat time; uncertainty robust optimization; artillery firing scheduling; threat time; uncertainty
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Choi, Y.B.; Yun, H.Y.; Kim, J.; Jin, S.H.; Kim, K.S. Robust Optimization Approach Using Scenario Concepts for Artillery Firing Scheduling Under Uncertainty. Appl. Sci. 2019, 9, 2811.

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