Pseudo-Boolean Conditional Optimization Models for a Class of Multiple Traveling Salesmen Problems

We consider knowledge-oriented models, problems, and algorithms for routing traveling salesmen in complex networks. The formalization leads to models of pseudo-Boolean discrete optimization with constraints that take into account the specifics of the multiple traveling salesmen problem. We consider a class of problems that can be represented in the form of pseudo-Boolean optimization models with separable objective functions (monotone, linear) and constraints in the form of disjunctive normal forms (DNFs). We demonstrate the possibility of an approximate synthesis of DNF constraints based on precedent information. The methodology, theoretical principles, and algorithms for solving problems of this class are presented. It is shown that the solution of routing problems can be based on the application of a multiagent approach in combination with clustering of the original problem, pseudo-Boolean optimization algorithms with disjunctive constraints, and metaheuristics.