Optimal Attack Against An Area Defense Protecting Many Targets

Abstract

Many separated targets, of only a few differing values, are subject to a simultaneous attack. The area defenses considered have (a) impact point prediction (IPP) and full coordination, or (b) no IPP and full coordination, or (c) no IPP and partial coordination. For a given attack, the defense wishes to allocate its interceptors to maximize the expected total survival value of the targets. For a given attack size, and with knowledge of the defense’s capabilities, the offense seeks a strategy to minimize expected total survival value against best defense. We present algorithms to determine optinial attack and defense strategies and the optimal value of the min-max problem, and we Show how to take computational advantage of the relatively few unique target values. Illustrative computational results are provided.

Résumé:

Beaucoup de cibles séparées, de quelques valeurs différentes, sont exposées a une attaque simultanée. Les defenses aeriennes considérées ont (a) une prédiction des points d’impact et pleine coordination, ou (b) pas de prédiction et pleine coordination, ou (c) pas de prédiction et une coordination partiale. Pour une attaque donnée, la défense veut assigner ses avions d’interception pour maximiser la valeur attendue de survivre des cibles. Pour la grandeur d’une attaque donnee et avec la connaissance des capacités de la défense, l’agression cherche une stratégie pour minimiser la valeur attendue de survivre contre la meilleure défense. Nous présentons des algorithms pour déterminer les attaques optimales et les stratégies défensives et la valeur optimale du probléme minmax. Aussi nous démontrons à prendre l’avantage des calcul de quelques valeurs des cibles. Quelques résultats qui expliquent ces calculs sont aussi données.

Additional information

Notes on contributors

Norman T. O’Meara

Norman O’Meara has served worldwide in a variety of command and staff positions with the United States Army for more than twenty years. He received the B.S. degree from the United States Military Acadeniy (1968), M.S. degrees in Operations Research and Mathematics from Rensselaer Polytechnic Institute (1972) and the D.Sc. degree from The George Washington University (1988). Colonel O’Meara is presently assigned to the Army’s Training and Doctrine Command. His current work involves corps level combat analysis with the RAND Corporation in Santa Monica, Califonia and Washington, DC.

Richard M. Soland

Richard Soland is Professor of Operations Resaerch and Ciairman of the Department of Operations Research in the School of Engineering and Applied Science of George Washington University. He received a B.E.E degree from Rensselaer Polytechnic Institute in 1961 and a Ph.D. i i Mathematics I from the Massachusetts Institute of Technology in 1964. After seven years at Research Analysis Corporation, he held academic posts with The University of Texas at Austin and then Ecole Polytechnique de Montréal; he has been at George Washington University since 1978. He has also held visiting academic positions in Denmark, Finland, France and Venezuela. Dr. Soland is author or coauthor of more than 40 published papers on a variety of operations research subjects, but his current interests are missile exchange problems and multiple criteria decision making. He is a Member of CORS and ORSA and a senior member of IIE and IEEE.