Dedication to Emeritus Professor Theodor StewartDedicated with respect and appreciation to Theo Stewart, one of the forerunners in the international multi-criteria decision analysis (MCDA) arena, on the special occasion of his 70 th birthday. Not only has Theo made a large and significant contribution to the field of MCDA, but he also served the Operations Research Society of South Africa for many years in a number of capacities, amongst them as president of the Society and founding editor of ORiON. We celebrate his considerable impact on Operations Research, both locally and internationally, and especially on the development of MCDA theory and practice. Happy birthday Theo, may you be blessed with many more! Abstract A typical ground-based air defence (GBAD) environment comprises defended assets on the ground which require protection from enemy aircraft entering the defended airspace. Protection against these aircraft is afforded by means of pre-deployed ground-based weapon systems that are assigned to engage these enemy aircraft according to some pre-specified criterion or set of criteria. The conditions under which human operators have to propose assignments of weapon systems to engage these aircraft are severely stressful since time is a critical factor and there is no room for error. Some progress has already been made with respect to the design of computerised threat evaluation and weapon assignment (TEWA) decision support systems (DSSs) within the context of a GBAD system. However, the weapon assignment (WA) component within such a TEWA DSS is typically based on a single criterion (objective). The aim in this paper is to model the WA problem as a multiobjective decision problem. A list of relevant factors (related to objectives) is identified by means of feedback received from a WA questionnaire which was completed by a number of military experts. For illustrative purposes, two objectives, namely the cost of assigning weapon systems for engagement and the accumulated survival probabilities of observed threats as a result of these engagements, were isolated from these factors in order to derive a bi-objective WA model. This model is solved in the context of a simulated, but realistic, GBAD environment by means of an existing multiobjective solution technique called the Nondominated Sorting Genetic Algorithm II.
In a military surface-based air defence environment, a fire control officer typically employs a computerised weapon assignment decision support subsystem to aid him in the assignment of available surface-based weapon systems to engage aerial threats in an attempt to protect defended surface assets -a problem known in the military operations research literature as the weapon assignment problem. In this paper, a tri-objective, dynamic weapon assignment model is proposed by modelling the weapon assignment problem as a multi-objective variation of the celebrated vehicle routing problem with time windows. A multi-objective, evolutionary metaheuristic for solving the vehicle routing problem with time windows is used to solve the model. The workability of this modelling approach is illustrated by solving the model in the context of a simulated, surface-based air defence scenario.
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