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Full-Text Articles in Social and Behavioral Sciences
Optimal Design Of Truss Structures By Logic-Based Branch And Cut, S. Bollapragada, Omar Ghattas, John Hooker
Optimal Design Of Truss Structures By Logic-Based Branch And Cut, S. Bollapragada, Omar Ghattas, John Hooker
John Hooker
The truss design problem is to find the optimal placement and size of structural bars that can support a given load. The problem is nonlinear and, in the version addressed here, the bars must take certain discrete sizes. It is shown that a logic-based method that dispenses with integer variables and branches directly on logical disjunctions can solve substantially larger problems than mixed integer programming, even though the nonlinearities disappear in the mixed integer model. A primary purpose of the paper is to investigate whether advantages of logic-based branching that have been demonstrated elsewhere for linear problems extend to nonlinear …
Mixed Logical-Linear Programming, John Hooker, M. Osorio
Mixed Logical-Linear Programming, John Hooker, M. Osorio
John Hooker
Mixed logical/linear programming (MLLP) is an extension of mixed integer/linear programming (MILP). It can represent the discrete elements of a problem with logical propositions and provides a more natural modeling framework than MILP. It can also have computational advantages, partly because it eliminates integer variables when they serve no purpose, provides alternatives to the traditional continuous relaxation, and applies logic processing algorithms. This paper surveys previous work and attempts to organize ideas associated with MLLP, some old and some new, into a coherent framework. It articulates potential advantages of MLLP's wider choice of modeling and solution options and illustrates some …
Good And Bad Futures For Constraint Programming (And Operations Research), John Hooker
Good And Bad Futures For Constraint Programming (And Operations Research), John Hooker
John Hooker
Two futures are sketched for constraint programming and operations research. In one, they continue their present emphasis on computational methods. In the other, they are empirical sciences dedicated to prescriptive modeling of human activities, with computation playing an ancillary role. The second future is defended as one in which the two fields, which are at root one field, maintain their vitality and make a more effective contribution to solving the problems of an increasingly complex world.
Simpl: A System For Integrating Optimization Techniques, Ionuţ Aron, John Hooker, Tallys Yunes
Simpl: A System For Integrating Optimization Techniques, Ionuţ Aron, John Hooker, Tallys Yunes
John Hooker
In recent years, the Constraint Programming (CP) and Operations Research (OR) communities have explored the advantages of combining CP and OR techniques to formulate and solve combinatorial optimization problems. These advantages include a more versatile modeling framework and the ability to combine complementary strengths of the two solution technologies. This research has reached a stage at which further development would benefit from a general-purpose modeling and solution system. We introduce here a system for integrated modeling and solution called SIMPL. Our approach is to view CP and OR techniques as special cases of a single method rather than as separate …
A Framework For Integrating Solution Methods, John Hooker
A Framework For Integrating Solution Methods, John Hooker
John Hooker
We describe a modeling framework that integrates mathematical programming (MP), constraint programming (CP) and heuristic methods.
Logic-Based Benders Decomposition, John Hooker, G. Ottosson
Logic-Based Benders Decomposition, John Hooker, G. Ottosson
John Hooker
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. The dual is therefore very different from other generalized duals that have been proposed. The approach is illustrated by working out the details for propositional satisfiability and 0-1 programming problems. Computational tests are carried out for the latter, but …
Mixed Global Constraints And Inference In Hybrid Clp-Ip Solvers, Greger Ottosson, Erlendur Thorsteinsson, John Hooker
Mixed Global Constraints And Inference In Hybrid Clp-Ip Solvers, Greger Ottosson, Erlendur Thorsteinsson, John Hooker
John Hooker
The complementing strengths of Constraint (Logic) Programming (CLP) and Mixed Integer Programming (IP) have recently received significant attention. Although various optimization and constraint programming packages at a first glance seem to support mixed models, the modeling and solution techniques encapsulated are still rudimentary. Apart from exchanging bounds for variables and objective, little is known of what constitutes a good hybrid model and how a hybrid solver can utilize the complementary strengths of inference and relaxations. This paper adds to the field by identifying constraints as the essential link between CLP and IP and introduces an algorithm for bidirectional inference through …