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- Integrated optimization methods - Papers (26)
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Articles 1 - 30 of 59
Full-Text Articles in Industrial Organization
A Partial Instantiation Based First Order Theorem Prover, Vijay Chandru, John N. Hooker, Anjul Shrivastava, Gabriela Rago
A Partial Instantiation Based First Order Theorem Prover, Vijay Chandru, John N. Hooker, Anjul Shrivastava, Gabriela Rago
John Hooker
Satisfiability algorithms for propositional logic have improved enormously in recent years. This increases the attractiveness of satisfiability methods for first order logic that reduce the problem to a series of ground-level satisfiability problems. Partial Instantiation for first order satisfiability differs radically from standard resolution based methods. Two approaches to partial instantiation based first order theorem provers have been studied by R. Jeroslow and by Plaisted and Zhu. Hooker and Rago have described improvements of Jeroslow's approach by a) extending it to logic with functions b) accelerating it through use of satisfiers as introduced by Gallo and Rago, and c) simplifying …
Predicting Cause-Effect Relationships From Incomplete Discrete Observations, E Boros, P. L. Hammer, John N. Hooker
Predicting Cause-Effect Relationships From Incomplete Discrete Observations, E Boros, P. L. Hammer, John N. Hooker
John Hooker
This paper addresses a prediction problem occurring frequently in practice. The problem consists in predicting the value of a function on the basis of discrete observational data that are incomplete in two senses. Only certain arguments of the function are observed, and the function value is observed only for certain combinations of values of these arguments. The problem is considered under a monotonicity condition that is natural in many applications. Applications to tax auditing, medicine, and real estate valuation are discussed. In particular, a special class of problems is identified for which the best monotone prediction can be found in …
Partial Instantiation Methods For Inference In First-Order Logic, John N. Hooker, G. Rago, V. Chandru, A. Shrivastava
Partial Instantiation Methods For Inference In First-Order Logic, John N. Hooker, G. Rago, V. Chandru, A. Shrivastava
John Hooker
Satisfiability algorithms for propositional logic have improved enormously in recently years. This improvement increases the attractiveness of satisfiability methods for first-order logic that reduce the problem to a series of ground-level satisfiability problems. R. Jeroslow introduced a partial instantiation method of this kind that differs radically from the standard resolution-based methods. This paper lays the theoretical groundwork for an extension of his method that is general enough and efficient enough for general logic programming with indefinite clauses. In particular we improve Jeroslow's approach by (1) extending it to logic with functions, (2) accelerating it through the use of satisfiers, as …
Boolean Regression, E. Boros, P. L. Hammer, John N. Hooker
Boolean Regression, E. Boros, P. L. Hammer, John N. Hooker
John Hooker
We take a regression-based approach to the problem of induction, which is the problem of inferring general rules from specific instances. Whereas traditional regression analysis fits a numerical formula to data, we fit a logical formula to boolean data. We can, for instance, construct an expert system for fitting rules to an expert's observed behavior. A regression-based approach has the advantage of providing tests of statistical significance as well as other tools of regression analysis. Our approach can be extended to nonboolean discrete data, and we argue that it is better suited to rule construction than logit and other types …
A Relaxation Of The Cumulative Constraint, John N. Hooker, Hong Yan
A Relaxation Of The Cumulative Constraint, John N. Hooker, Hong Yan
John Hooker
Hybrid methods that combine constraint programming with mathematical programming make essential use of continuous relaxations for global constraints. We state a relaxation for the cumulative constraint. In particular we identify facet-defining inequalities for problems in which some jobs have the same duration, release time, and resource consumption rate. We also identify a much larger class of valid inequalities that exist in all problems.
A Hybrid Method For Planning And Scheduling, John N. Hooker
A Hybrid Method For Planning And Scheduling, John N. Hooker
John Hooker
We combine mixed integer linear programming (MILP) and constraint programming (CP) to solve 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 (cumulative scheduling). We solve minimum cost problems, as well as minimum makespan problems in which all tasks have the same release date and deadline. We obtain computational speedups of several orders of magnitude relative to the state of the art in both MILP and CP.
Optimization Methods In Logic, John N. Hooker
Optimization Methods In Logic, John N. Hooker
John Hooker
Optimization can make at least two contributions to boolean logic. Its solution methods can address inference and satisfiability problems, and its style of analysis can reveal tractable classes of boolean problems that might otherwise have gone unnoticed.
Tight Representation Of Logical Constraints As Cardinality Rules, John Hooker, Hong Yan
Tight Representation Of Logical Constraints As Cardinality Rules, John Hooker, Hong Yan
John Hooker
We address the problem of finding a "tight" representation of complex logical constraints in a mixed integer programming model by describing a convex hull representation of cardinality rules.
Optimality Conditions For Distributive Justice, John N. Hooker
Optimality Conditions For Distributive Justice, John N. Hooker
John Hooker
This paper uses optimization theory to address a fundamental question of ethics: how to divide resources justly among individuals, groups, or organizations. It formulates utilitarian and Rawlsian criteria for distributive justice as optimization problems. The formulations recognize that some recipients are more productive than others, so that an inequitable distribution may create greater overall utility. Conditions are derived under which a distribution of resources is utility maximizing, and under which it achieves a lexicographic maximum, which we take as formulating the difference principle of John Rawls. It is found that utility maximization requires at least as much inequality as results …
Inference-Based Sensitivity Analysis For Mixed Integer/Linear Programming, M. W. Dawande, John N. Hooker
Inference-Based Sensitivity Analysis For Mixed Integer/Linear Programming, M. W. Dawande, John N. Hooker
John Hooker
A new method of sensitivity analysis for mixed integer/linear programming (MILP) is derived from the idea of inference duality. The inference dual of an optimization problem asks how the optimal value can be deduced from the constraints. In MILP, a deduction based on the resolution method oftheorem proving can be obtained from the branch-and-cut tree that solves the primal problem. One can then investigate which perturbations ofthe problem leave this proof intact. On this basis it is shown that, in a minimization problem, any perturbation that satisfies a certain system of linear inequalities will reduce the optimal value no more …
Mathematical Programming Methods For Reasoning Under Uncertainty, John N. Hooker
Mathematical Programming Methods For Reasoning Under Uncertainty, John N. Hooker
John Hooker
We survey three applications of mathematical programming to reasoning under uncertainty: a) an application of linear programming to probabilistic logic, b) an application of nonlinear programming to Bayesian logic, a combination of Bayesian inference with probabilistic logic and c) an application of integer programming to Dempster-Shafer theory, which is a method of combining evidence from diffierent sources
A Cross-Cultural View Of Corruption, John N. Hooker
A Cross-Cultural View Of Corruption, John N. Hooker
John Hooker
The world is shrinking, but its cultures remain worlds apart, as do its ethical norms. The West views bribery, kickbacks, cronyism and nepotism as unethical, but they are standard practice in many parts of the world. This poses a familiar dilemma for business firms that operate globally: should they engage in what they see as corrupt behavior in order to do business? The position defended here is that firms should always resist corruption, but at the same time understand it from a broader perspective: as behavior that undermines a cultural system. Behavior that is acceptable in one country may be …
A Generalized Dilworth's Theorem, With Application To Routing And Scheduling, John N. Hooker, N R. Natraj
A Generalized Dilworth's Theorem, With Application To Routing And Scheduling, John N. Hooker, N R. Natraj
John Hooker
Dilworth's theorem states a duality relation between minimum chain decompositions of a directed, acyclic graph and maximum antichains. We generalize the theorem to apply when the chains of the decomposition are required to contain the chains of an initial decomposition. We show that duality obtains precisely when an associated undirected graph is perfect. We apply this result to a vehicle routing and scheduling problem with time windows. Here each chain of the initial decomposition contains nodes that correspond to the pickup, delivery and possibly intermediate stops associated with a piece of cargo.
Approximate Compilation Of Constraints Into Multivalued Decision Diagrams, Tarik Hadzic, John Hooker, Barry O'Sullivan, Peter Tiedemann
Approximate Compilation Of Constraints Into Multivalued Decision Diagrams, Tarik Hadzic, John Hooker, Barry O'Sullivan, Peter Tiedemann
John Hooker
We present an incremental refinement algorithm for approximate compilation of constraint satisfaction models into multivalued decision diagrams (MDDs). The algorithm uses a vertex splitting operation that relies on detection of equivalent paths in the MDD. Although the algorithm is quite general, it can be adapted to exploit constraint structure by specializing the path equivalence test to particular constraints.We show how to modify the algorithm in a principled way to obtain an approximate MDD when the exact MDD is too large for practical purposes. This is done by replacing the equivalence test with a constraint-specific measure of distance. We demonstrate the …
Testing Heuristics: We Have It All Wrong, John Hooker
Testing Heuristics: We Have It All Wrong, John Hooker
John Hooker
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 that could be better spent doing more experiments. This article argues that a more scientific approach of controlled experimentation, similar to that used in other empirical sciences, avoids or alleviates these problems. We have confused research and development; competitive testing is suited only …
Solving The Capacitated Local Access Network Design Problem, F. Sibel Salman, R. Ravi, John N. Hooker
Solving The Capacitated Local Access Network Design Problem, F. Sibel Salman, R. Ravi, John N. Hooker
John Hooker
We propose an exact solution method for a routing and capacity installation problem in networks. Given an input graph, the problem is to route traffic from a set of source nodes to a sink node and to install transmission facilities on the edges of the graph to accommodate the flow at minimum cost. We give a branch-and-bound algorithm that solves relaxations obtained by approximating the noncontinuous cost function by its lower convex envelope. The approximations are refined by branching on the flow ranges on selected edges. Our computational experiments indicate that this method is effective in solving moderate-size problems and …
Logical Inference And Polyhedral Projection, John N. Hooker
Logical Inference And Polyhedral Projection, John N. Hooker
John Hooker
We explore connections between polyhedral projection and inference in propositional logic. We formulate the problem of drawing all inferences that contain a restricted set of atoms (i.e., all inferences that pertain to a given question) as a logical projection problem. We show that polyhedral projection partially solves this problem and in particular derives precisely those inferences that can be obtained by a certain form of unit resolution. We prove that this unit resolution algorithm is exponential in the number of atoms in the restricted set but is polynomial in the problem size when this number of fixed. We also survey …
A Search-Infer-And-Relax Framework For Integrating Solution Methods, John N. Hooker
A Search-Infer-And-Relax Framework For Integrating Solution Methods, John N. Hooker
John Hooker
We present an algorithmic framework for integrating solution methods that is based on search, inference, and relaxation and their interactions. We show that the following are special cases: branch and cut, CP domain splitting with propagation, popular global optimization methods, DPL methods for SAT with conflict clauses, Benders decomposition and other nogood-based methods, partial-order dynamic backtracking, various local search metaheuristics, and GRASPs (greedy randomized adaptive search procedures). The framework allows elements of different solution methods to be combined at will, resulting in a variety of integrated methods. These include continuous relaxations for global constraints, the linking of integer and constraint …
Planning And Scheduling To Minimize Tardiness, John N. Hooker
Planning And Scheduling To Minimize Tardiness, John N. Hooker
John Hooker
We combine mixed integer linear programming (MILP) and constraint programming (CP) to minimize tardiness in planning and scheduling. Tasks are allocated to facilities using MILP and scheduled using CP, and the two are linked via logic-based Benders decomposition. We consider two objectives: minimizing the number of late tasks, and minimizing total tardiness. Our main theoretical contribution is a relaxation of the cumulative scheduling subproblem, which is critical to performance. We obtain substantial computational speedups relative to the state of the art in both MILP and CP. We also obtain much better solutions for problems that cannot be solved to optimality.
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 …
Optimal Movement Of Factory Cranes, Ionuţ Aron, Latife Genç-Kaya, Iiro Harjunkoski, Samid Hoda, John Hooker
Optimal Movement Of Factory Cranes, Ionuţ Aron, Latife Genç-Kaya, Iiro Harjunkoski, Samid Hoda, John Hooker
John Hooker
We study the problem of finding optimal space-time trajectories for two factory cranes or hoists that move along a single overhead track. Each crane is a assigned a sequence of pickups and deliveries at specified locations that must be performed within given time windows. The cranes must be operated so as not to interfere with each other, although one crane may need to yield to another. The objective is generally to follow a production schedule as closely as possible. We show that only certain types of trajectories need be considered to obtain an optimal solution. This simplifies the operation of …
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.
Inference Duality As A Basis For Sensitivity Analysis, John N. Hooker
Inference Duality As A Basis For Sensitivity Analysis, John N. Hooker
John Hooker
The constraint programming community has recently begun to address certain types of optimization problems. These problems tend to be discrete or to have discrete elements. Although sensitivity analysis is well developed for continuous problems, progress in this area for discrete problems has been limited. This paper proposes a general approach to sensitivity analysis that applies to both continuous and discrete problems. In the continuous case, particularly in linear programming, sensitivity analysis can be obtained by solving a dual problem. One way to broaden this result is to generalize the classical idea of a dual to that of an ldquoinference dual,rdquo …
A Linear Programming Framework For Logics Of Uncertainty, K. Andersen, John Hooker
A Linear Programming Framework For Logics Of Uncertainty, K. Andersen, John Hooker
John Hooker
Several logics for reasoning under uncertainty distribute “probability mass” over sets in some sense. These include probabilistic logic, Dempster-Shafer theory, other logics based on belief functions, and second-order probabilistic logic. We show that these logics are instances of a certain type of linear programming model, typically with exponentially many variables. We also show how a single linear programming package can implement these logics computationally if one “plugs in” a different column generation subroutine for each logic, although the practicality of this approach has been demonstrated so far only for probabilistic logic.
Planning And Scheduling By Logic-Based Benders Decomposition, John N. Hooker
Planning And Scheduling By Logic-Based Benders Decomposition, John N. Hooker
John Hooker
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 (cumulative scheduling). We solve problems in which the objective is to minimize cost, makespan, or total tardiness. We obtain significant computational speedups, of several orders of magnitude for the first two objectives, relative to the state of the art in both MILP and CP. We also obtain …
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 …
On Integrating Constraint Propagation And Linear Programming For Combinatorial Optimization, John N. Hooker, Greger Ottosson, Erlendur S. Thorsteinsson, Hak-Jin Kim
On Integrating Constraint Propagation And Linear Programming For Combinatorial Optimization, John N. Hooker, Greger Ottosson, Erlendur S. Thorsteinsson, Hak-Jin Kim
John Hooker
Linear programming and constraint propagation are complementary techniques with the potential for integration to benefit the solution of combinatorial optimization problems.
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.
Corruption From A Cross-Cultural Perspective, John Hooker
Corruption From A Cross-Cultural Perspective, John Hooker
John Hooker
This paper views corruption as activity that tends to undermine a cultural system. Because cultures operate in very different ways, different activities are corrupting in different parts of the world. The paper analyzes real-life situations in Japan, Taiwan, India, China, North America, sub-Saharan Africa, the Middle East, and Korea to distinguish actions that structurally undermine a cultural system from those that are merely inefficient or are actually supportive. Activities such as nepotism or cronyism that are corrupting in the rule-based cultures of the West may be functional in relationship-based cultures. Behavior that is normal in the West, such as bringing …