Privacy-Preserving Local Search for the Traveling Salesman Problem

In this chapter, we specifically examine distributed traveling salesman problems in which the cost function is defined by information distributed among two or more parties. Moreover, the information is desired to be kept private from others. As intuitive situations in which distributed private information appears in combinatorial optimization problems, we take problems in supply chain management (SCM) as examples. In SCM, the delivery route decision, the production scheduling and the procurement planning are fundamental problems. Solving these problems contributes to improvement of the correspondence speed to the customer and shortening the cycle time(Vollmann, 2005; Handfield & Nichols, 1999). In the process of forming the delivery route decision and production schedule decision, the combinatorial optimization plays an important role. When the SCM is developed between two or more enterprises, information related to the stock, the production schedule, and the demand forecast must be shared among enterprises. Electronic Data Interchange (EDI), the standardized data exchange format over the network, is often used to support convenient and prompt information sharing1. Information sharing apparently enhances the SCM availability; however, all information related to the problem resolution must be disclosed to all participants to lay the basis for global optimization. Such information is often highly confidential and its disclosurewould be impossible in many cases. As more concrete examples, two scenarios are presented. These scenarios pose situations that appear to be unsolvable unless private information is shared. Scenario 1: Let there be a server EA that manages a route-optimization service and a user EB who tries to use this service. The user’s objective is to find the optimal route that visits points F1, ...,Fn chosen by himself. The user, however, does not like to reveal the list of visiting points to the server. The server manages a matrix of cost for traveling between any two points. The server does not like to reveal the cost matrix to the user, either. How can the user learn the optimal route without mutually revelation of private information? Note that this problem is obviously solved as the Traveling Salesman Problem (TSP) if either of traveling cost or visiting points is shared. As more complicated examples, a multi-party situation is described next. Scenario 2: Let there be two shipping companies EA and EB in two regionsA and B. Client EC requests that EA deliver freight to point F A 1 , ...,Fn in region A and also requests EB to deliver