Economic Policy Commons^™

The Economic Context: Growing Disparities Of Income And Wealth, Chuck Collins

New England Journal of Public Policy

In the last few years, poverty rates have remained constant in the New England states. The effort to reduce poverty in New England and the United States has been thwarted by trends of growing income and wealth inequality. Since the late 1970s, the real incomes for the majority of U.S. households have remained stagnant or fallen. During the same time, asset ownership has become dramatically more unequal, and the concentration of wealth in the hands of a few has increased. The causes of this accelerated inequality are complex, but underlying the picture are a series of rule changes, both public …

Devolution: The Retreat Of Government, Judith Kurland

New England Journal of Public Policy

Devolution as practiced in much of the world is decentralization of program authority and responsibility to achieve greater administrative efficiency or program standards. Devolution as practiced by the Bush administration and the Republican Congress is not that, nor is it a diminution of federal power and the strengthening of states’ rights. Rather, it is a radical restructuring of government to prevent the expenditure of funds for traditional Democratic programs of the New Deal and the Great Society, and to prohibit states from being either more generous in social programs or more stringent in regulating industry than this administration desires.

This …

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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 …