A Deterministic Annealing Approach to the Multiple Traveling Salesmen and Related Problems

This paper presents a novel and efficient heuristic framework for approximating the solutions to the multiple traveling salesmen problem (m-TSP) and other variants on the TSP. The approach adopted in this paper is an extension of the Maximum-Entropy-Principle (MEP) and the Deterministic Annealing (DA) algorithm. The framework is presented as a general tool that can be suitably adapted to a number of variants on the basic TSP. Additionally, unlike most other heuristics for the TSP, the framework presented in this paper is independent of the edges defined between any two pairs of nodes. This makes the algorithm particularly suited for variants such as the close-enough traveling salesman problem (CETSP) which are challenging due to added computational complexity. The examples presented in this paper illustrate the effectiveness of this new framework for use in TSP and many variants thereof

Inequality Constraints in Facility Location and Other Similar Optimization Problems: An Entropy Based Approach

In this paper we propose an annealing based framework to incorporate inequality constraints in optimization problems such as facility location, simultaneous facility location with path optimization, and the last mile delivery problem. These inequality constraints are used to model several application specific size and capacity limitations on the corresponding facilities, transportation paths and the service vehicles. We design our algorithms in such a way that it allows to (possibly) violate the constraints during the initial stages of the algorithm, so as to facilitate a thorough exploration of the solution space; as the algorithm proceeds, this violation (controlled through the annealing parameter) is gradually lowered till the solution converges in the feasible region of the optimization problem. We present simulations on various datasets that demonstrate the efficacy of our algorithm