Military aircraft mission planning: a generalized vehicle routing model with synchronization and precedence

Abstract

We introduce a military aircraft mission planning problem where a given fleet of aircraft should attack a number of ground targets. Due to the nature of the attack, two aircraft need to rendezvous at the target, that is, they need to be synchronized in both space and time. At the attack, one aircraft is launching a guided weapon, while the other is illuminating the target. Each target is associated with multiple attack and illumination options. Further, there may be precedence constraints between targets, limiting the order of the attacks. The objective is to maximize the outcome of the entire attack, while also minimizing the mission timespan. We give a linear mixed-integer programming model of the problem, which can be characterized as a generalized vehicle routing problem with synchronization and precedence side constraints. Numerical results are presented for problem instances of realistic size.

Military aircraft mission planning

“…We here address a mission planning problem, introduced in Quttineh et al [5], where a fleet of aircraft should attack a number of ground targets, subject to certain restrictions, such as precedence relationship between the target attacks. The planning of such a mission is typically made close to when the mission actually takes place (say, within 24 hours); one important reason for this is that the planning can then be based on the most recent information.…”

“…The time needed for the chain of planning is of the order of several hours. The work presented in [5] and in this paper has been performed in collaboration with an industrial partner.…”

“…The MAMPP and its mathematical model was introduced in Quttineh et al [5], where a thorough description of the problem and model can be found. For the scenario described in Figure 1, the resulting network model contains 110 nodes and 9771 arcs.…”

“…Numerical results in [5] show that standard solver software can manage to solve small-sized problem instances, but even a mid-sized scenario with four targets and two aircraft, without any precedence on the targets, is not solvable to proven optimality within a reasonable time frame (more than three hours). This implies that it is not reasonable to base a decision support system on standard solver software, since the solver in such a system needs to be fast enough to allow interactive use.…”

“…Problem characteristics and results are shown in Table 1, for the choice µ = 0.05 in the objective (which means high priority to expected effects on targets). The problem numbers within brackets are the corresponding problem instances in [5]. We report the best found objective values found by CPLEX after 15 minutes and three hours, respectively, which are used as reference values when evaluating our metaheuristics.…”