Learning from the Past to Dynamically Improve Search: A Case Study on the MOSP Problem

Abstract

Abstract.This paper presents a study conducted on the minimum number of open stacks problem (MOSP) which occurs in various production environments where an efficient simultaneous utilization of resources (stacks) is needed to achieve a set of tasks. We investigate through this problem how classical lookback reasonings based on explanations could be used to prune the search space and design a new solving technique. Explanations have often been used to design intelligent backtracking mechanisms in Constraint Programming whereas their use in nogood recording schemes has been less investigated. In this paper, we introduce a generalized nogood (embedding explanation mechanisms) for the MOSP that leads to a new solving technique and can provide explanations. The Minimum number of Open Stacks ProblemThe Minimum number of Open Stacks Problem (MOSP) has been recently used to support the IJCAI 2005 constraint modeling challenge [14]. This scheduling problem involves a set of products and a set of customer's orders. Each order requires a specific subset of the products to be completed and sent to the customer. Once an order is started (i.e. its first product is being made) a stack is created for that order. At that time, the order is said to be open. When all products that an order requires have been produced, the stack/order is closed. Because of limited space in the production area, the maximum number of stacks that are used simultaneously, i.e. the number of customer orders that are in simultaneous production, should be minimized.Therefore, a solution for the MOSP is a total ordering of the products describing the production sequence that minimizes the set of simultaneously opened stacks. This problem is known to be NP-hard and is related to well known graph problems such as the minimum path-width or the vertex separation problems.