John N. Hooker

Learn More
This tutorial describes a logic based approach to formulating and solving pure and mixed integer programming problems It develops logical counterparts for ideas associated with traditional branch and cut methods such as cutting planes facet de ning cuts re laxations etc The motivations for doing this are a to exploit the structure of a wide range of(More)
Benders decomposition uses a strategy of “learning from one’s mistakes.” The aim of this paper is to extend this strategy to a much larger class of problems. The key is to generalize the linear programming dual used in the classical method to an “inference dual.” Solution of the inference dual takes the form of a logical deduction that yields Benders cuts.(More)
The competitive nature of most algorithmic experimentation is a source of problems that are all too familiar to the research community It is hard to make fair comparisons between algorithms and to assemble realistic test problems Competitive testing tells us which algorithm is faster but not why Because it requires polished code it consumes time and energy(More)
The class of Horn clause sets in propositional logic is extended to a larger class for which the satisfiability problem can still be solved by unit resolution in linear time. It is shown that to every arborescence there corresponds a family of extended Horn sets, where ordinary Horn sets correspond to stars with a root at the center. These results derive(More)
We combine mixed integer linear programming (MILP) and constraint programming (CP) to solve an important class of planning and scheduling problems. Tasks are allocated to facilities using MILP and scheduled using CP, and the two are linked via logic-based Benders decomposition. Tasks assigned to a facility may run in parallel subject to resource constraints(More)
Recent experience suggests that branching algorithms are among the most attractive for solving propositional satisfiability problems. A key factor in their success is the rule they use to decide on which variable to branch next. We attempt to explain and improve the performance of branching rules with an empirical model-building approach. One model is based(More)
The typical constraint store transmits a limited amount of information because it consists only of variable domains. We propose a richer constraint store in the form of a limited-width multivalued decision diagram (MDD). It reduces to a traditional domain store when the maximum width is one but allows greater pruning of the search tree for larger widths.(More)
Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and(More)
Recent experience suggests that branching algorithms are among the most attractive for solving propositional satissability problems. A key factor in their success is the rule they use to decide on which variable to branch next. We attempt to explain and improve the performance of branching rules with an empirical model-building approach. One model is based(More)
Given a set of clauses in propositional logic that have been found satis able we wish to check whether satis ability is preserved when the clause set is incremented with a new clause We describe an e cient implementation of the Davis Putnam Loveland algorithm for checking satis ability of the original set We then show how to modify the algorithm for e cient(More)