Sensor-Target and Weapon-Target Pairings Based on Auction Algorithm Z. R. BOGDANOWICZ, N. P. COLEMAN Armament Research, Development and Engineering Center (ARDEC) Picatinny, NJ 07806 U.S.A. http://www.pica.army.mil Abstract: - Sensor-target and weapon-target pairings are important activities involved in planning and executing a course-of-action in a modern warfare. The outcome of today’s combat operations may strongly depend on the intelligent usage of available sensors and weapons maximizing their effectiveness. The problem can be considered as an assignment optimization problem in mathematics. This problem is difficult because in the real world it involves many different factors and criteria to consider. We show that for practical sensor- target and weapon-target pairings a well-known auction algorithm should be considered the preferred choice. Key-Words: - Assignment problem, auction algorithm, sensor-target pairing, weapon-target pairing. 1 Introduction Sensor-target and weapon-target (or briefly sensor/weapon-target) pairings are challenging and difficult optimization problems. However, with faster computers and better algorithms it becomes more realistic and practical nowadays. Furthermore, the outcome of today’s modern battles may strongly depend on the intelligent usage of available sensors and weapons maximizing their effectiveness. In general, these pairings consider many input types and the strategies of optimization might vary considerably. Hence, designing a single optimization algorithm for generic input is a hard problem. Efficiency of assigning weapons to targets might depend on the assignment of sensors to these targets, which further complicates this task. Sensor-target and weapon-target pairings, however, can be reduced to an assignment optimization problem, which is well known and studied in mathematics [3], [7-8], [10]. Let b jk be a benefit of assigning weapon j to target k when sensor i is already assigned to target k, i.e., s i ﾆt k . If there exists some other sensor-target pairing s i’ ﾆt k , which implies benefit b’ jk of assigning weapon j to target k with b’ jk ≠ b jk , then such sensor/weapon-target pairing is called dependent. Otherwise sensor/weapon-target pairing is called independent. In this paper we consider both types of problems. In today’s battlefields many types of weapons often rely on supporting sensors. As an example of dependent sensor/weapon-target pairings, lasing of a target by a forward observer can guide a precision weapon to its precise destination. For independent sensor/weapon-target pairing, the weapons might still rely on sensors. For example, there might be just one type of sensor under consideration, and the weapons that rely solely on it. In such a case, any complete sensor-target pairing could result in identical weapon-target benefit matrix. Let’s now consider a two-step approach to the sensor/weapon-target pairing problem. In the first step, a preprocessing algorithm converts all the input information into two benefit matrices A,B, where each a ij in A and each b ij in B represents a benefit of assigning row i to column j. In the second step, an optimization algorithm assigns rows to columns in matrices A,B in such a way that the total benefit is maximized. In this paper we focus on the second step of the above approach. There are a number of optimal algorithms that can solve it and they are well documented – algorithms based on maximum matching in graphs [8], variants of the interior point algorithm [1,9,11], and the auction algorithm [2-7] to name a few. We show that for sensor/weapon- target pairing the auction algorithm should be considered the preferred choice. In addition, we back this up with performance results based on a simple forward auction algorithm implementation in Section 8. 2 Why Auction Algorithm To solve an assignment optimization problem focused on sensors, weapons and targets, we might first consider if it makes sense to use an exact optimization algorithm vs. an approximate heuristic. Since the number of sensors, weapons and targets in Proceedings of the 11th WSEAS International Conference on APPLIED MATHEMATICS, Dallas, Texas, USA, March 22-24, 2007 92