4. Multiple Assignments

Abstract

Let everyone sweep in front of his own door, and the whole world will be clean. —Johann Wolfgang von Goethe Assigning vehicles to targets with single task tours makes it necessary to solve some multiple-vehicle multiple-target assignment problems in a greedy manner by using strategies such as recalculating the assignments for all vehicles after each vehicle finishes its currently assigned task. This is inefficient and can introduce delays in the system that lead to phenomena such as churning; see Chapter 3, section 3.3.1. Since the required tasks are known a priori, plans can be generated to assign multiple tasks to each vehicle, i.e., multiple task tours. In this chapter we discuss methods of assigning multiple task tours to vehicles. These methods include mixed integer linear programming (MILP), tree search, and genetic algorithms (GAs). 4.1 Mixed Integer Linear Programming The fundamental limitation of the CTAP algorithms presented previously is that all the decision variables are binary. Solutions can be computed very quickly, but only a very limited set of problems can be directly formulated in such a manner. A natural extension is to the MILP, where both integer and real-valued decision variables can be included. The use of MILP allows rigorous inclusion of timing constraints and opens up the possibility of optimal solutions for a much wider range of joint task assignment and scheduling problems. The WASM cooperative control problem will now be solved with a MILP model using a discrete representation of the real world based on nodes that represent discrete start and end positions for segments of a vehicle's path.