Colin E. Bell

A new heuristic solution method in resource-constrained project scheduling

A new heuristic method is presented for the resolution of multiresource constrained conflicts in project scheduling. In attempting to find a minimal makespan solution, the algorithm employs a simple procedure to generate a feasible solution with no backtracking. A postanalysis phase then applies a hill-climbing search. The solution method is different from existing heuristic methods in that it repairs resource conflicts rather than constructs detailed schedules by dispatching activities. Resource-violating sets of activities are identified which must be prevented from concurrent execution because this would violate resource constraints. Repairs are made by imposing an arc to sequence two activities in such a resource violating set. Computational results are compared with those of existing heuristics for the minimal makespan problem.

Mixed integer programming methods for computing nonmonotonic deductive databases

Though the declarative semantics of both explicit and nonmonotonic negation in logic programs has been studied extensively, relatively little work has been done on computation and implementation of these semantics. In this paper, we study three different approaches to computing stable models of logic programs based on mixed integer linear programming methods for automated deduction introduced by R. Jeroslow. We subsequently discuss the relative efficiency of these algorithms. The results of experiments with a prototype compiler implemented by us tend to confirm our theoretical discussion. In contrast to resolution, the mixed integer programming methodology is both fully declarative and handles reuse of old computations gracefully. We also introduce, compare, implement, and experiment with linear constraints corresponding to four semantics for “explicit” negation in logic programs: the four-valued annotated semantics [Blair and Subrahmanian 1989], the Gelfond-Lifschitz semantics [1990], the over-determined models [Grant and Subrahmanian 1989], the Gelfond-Lifschitz semantics [1990], the over-determined models [Grant and Subrahmanian 1990], and the classical logic semantics. Gelfond and Lifschitz[1990] argue for simultaneous use of two modes of negation in logic programs, “classical” and “nonmonotonic,” so we give algorithms for computing “answer sets” for such logic programs too.

Solving resource‐constrained project scheduling problems by a* search

A new exact method is presented for finding a minimum makespan schedule for a multiresource constrained project scheduling problem. This method employs the philosophical approach used earlier to develop a successful heuristic algorithm for the same class of problems. The approach repairs resource conflicts rather than constructing detailed schedules by dispatching activities. Resource-violating sets of activities are identified whose concurrent execution would violate resource constraints. Repairs are made by imposing a precedence constraint to sequence two activities in such a resource-violating set. Computational results are discussed for a standard set of test problems. An A* algorithm is employed. The most successful version of our algorithm involves some perhaps surprising design choices which might be relevant to the design of A*-like search algorithms in other contexts.

Implementing deductive databases by linear programming

Logic programs incorporate forms of SLD resolution as the basis for query processing. Existing and past generations of Prolog systems have left deduction to run-time, and this may account for the poor runtime performance of such systems. Our work tries to minimize run-time deduction by shifting the deductive process to compile-time, not run-time. This approach fits into the bottom-up computation paradigm that has been studied by many researchers like Bancilhon, Beeri, Ramakrishnan and Unman [1, 2, 3, 19]. At least two of these paradigms have been implemented: the LDL system at MCC, developed by Zaniolo and his group [l

Implementing deductive databases by mixed integer programming

], and the NAIL system [15] at Stanford.

Weighted matching with vertex weights: an application to scheduling training sessions in NASA space shuttle cockpit simulators

Existing and past generations of Prolog compilers have left deduction to run-time and this may account for the poor run-time performance of existing Prolog systems. Our work tries to minimize run-time deduction by shifting the deductive process to compile-time. In addition, we offer an alternative inferencing procedure based on translating logic to mixed integer programming. This makes available for research and implementation in deductive databases, all the theorems, algorithms, and software packages developed by the operations research community over the past 50 years. The method keeps the same query language as for disjunctive deductive databases, only the inferencing procedure changes. The language is purely declarative, independent of the order of rules in the program, and independent of the order in which literals occur in clause bodies. The technique avoids Prologs problem of infinite looping. It saves run-time by doing primary inferencing at compile-time. Furthermore, it is incremental in nature. The first half of this article translates disjunctive clauses, integrity constraints, and database facts into Boolean equations, and develops procedures to use mixed integer programming methods to compute equations, and develops procedures to use mixed integer programming methods to compute equations, and develops procedures to use mixed integer programming methods to compute equations, and develops procedures to use mixed integer programming methods to compute —least models of definite deductive databases, and —minimal models and the Generalized Closed World Assumption of disjunctive databases.

Default Reasoning Through Integer Linear Programming

Abstract Necessary and sufficient conditions are provided for optimality of a matching in a weighted matching problem for which the weight of edge (i, j) is the sum of non-negative values, wi and wj. The impact of adding one or more dummy vertices i with wi = 0 is investigated. Results are exploited in the design of a heuristic approach for weekly scheduling of NASA space shuttle training sessions in each of two cockpit simulators.

A least commitment approach to avoiding protection violations in nonlinear planning

Least Exception Logic (LEL) is a model for default reasoning that is based upon integer linear programming (ILP) and the first order predicate calculus. The basic LEL model was presented by Post in [1987b and 1988]. This paper summarizes the current research on LEL and presents a new example of using LEL for hardware diagnosis.

Finding improving directions in Lagrangian relaxation by fictitious play: A NASA scheduling application

We suggest one alternative approach to creating a valid plan in which all temporal constraints are mutually satisfiable and all preconditions for actions hold where required. While simultaneously maintaining information on the status of protection intervals for all required preconditions in the plan, our approach avoids premature imposition of temporal constraints to correct for protection violations. At the expense of additional bookkeeping, we adopt the least commitment strategy of attempting to correct those protection violations which can be corrected in only one way. By postponing choice as much as possible, we attempt to generate a search tree with fewer nodes. Since scheduling problems which arise in our planning context are inherently intractable, our approach does not rule out the possibility of extensive search. However, it might well be a preferable mechanism for a planner which adopts a general least commitment strategy.

Analysis of the behavior of logic-based computation for deductive databases and default reasoning

Abstract An improving direction for Lagrangian dual prices can be found by solving (or solving approximately) a two person zero-sum game. While this method is impractical in many situations, its practical use is illustrated in a scheduling application. In this implementation, the game is solved approximately by fictitious play.