Vijay Chandru

Minimizing total completion time on batch processing machines

We study the problem of minimizing total completion time on single and parallel batch processing machines. A batch processing machine is one which can process up to B jobs simultaneously. The processing time of a batch is equal to the largest processing time among all jobs in the batch. This problem is motivated by burn-in operations in the final testing stage of semiconductor manufacturing and is expected to occur in other production environments. We provide an exact solution procedure for the single-machine problem and heuristic algorithms for both single and parallel machine problems. While the exact algorithms have limited applicability due to high computational requirements, extensive experiments show that the heuristics are capable of consistently obtaining near-optimal solutions in very reasonable CPU times.

Optimization Methods for Logical Inference

Propositional Logic: Special Cases. Propositional Logic: The General Case. Probabilistic and Related Logics. Predicate Logic. Nonclassical and Many--Valued Logics. Appendix. Bibliography. Index.

Voxel-based modeling for layered manufacturing

Layered manufacturing (LM) technologies have revolutionized the prototyping of complex geometric designs, but still employ traditional CAD tools. A voxel-based approach is under development in a modeling tool called G-WoRP (Geometric Workbench for Rapid Prototyping), which is tuned toward fabrication with LM equipment. The user interacts with the workbench through an input layer that provides two major primitives-the slice and the voxel-and the operations that support them. An import facility also permits designs from other CAD systems. Central to the internal layer is V-Rep, a new representation scheme that provides an efficient interface among the various G-WoRP modules. The output layer gives the part description in a form suitable to the actual LM technology employed. It also supports a process description for manufacturing the part using traditional processes. The design and manufacturing phases do not require an explicit process-planning step because the design description of the part closely resembles the input description needed by the LM equipment. >

Extended Horn sets in propositional logic

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 from a theorem of Chandresekaran that characterizes when an integer solution of a system of inequalities can be found by rounding a real solution in a certain way. A linear-time procedure is provided for identifying “hidden” extended Horn sets (extended Horn but for complementation of variables) that correspond to a specified arborescence. Finally, a way to interpret extended Horn sets in applications is suggested.

Modelling electricity demand with representative load curves

Models for electricity planning require inclusion of demand. Depending on the type of planning, the demand is usually represented as an annual demand for electricity (GWh), a peak demand (MW) or in the form of annual load–duration curves. The demand for electricity varies with the seasons, economic activities, etc. Existing schemes do not capture the dynamics of demand variations that are important for planning. For this purpose, we introduce the concept of representative load curves (RLCs). Advantages of RLCs are demonstrated in a case study for the state of Karnataka in India. Multiple discriminant analysis is used to cluster the 365 daily load curves for 1993–94 into nine RLCs. Further analyses of these RLCs help to identify important factors, namely, seasonal, industrial, agricultural, and residential (water heating and air-cooling) demand variations besides rationing by the utility.

Partial Instantiation Methods for Inference in First-Order Logic

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 Jeroslows approach by (1) extending it to logic with functions, (2) accelerating it through the use of satisfiers, as introduced by Gallo and Rago, and (3) simplifying it to obtain further speedup. We provide a similar development for a “dual” partial instantiation approach defined by Hooker and suggest a primal–dual strategy. We prove correctness of the primal and dual algorithms for full first-order logic with functions, as well as termination on unsatisfiable formulas. We also report some preliminary computational results.

Variable elimination in linear constraints

Gauss and Fourier have together provided us with the essential techniques for symbolic computation with linear arithmetic constraints over the reals and the rationals. These variable elimination techniques for linear constraints have particular significance in the context of constraint logic programming languages that have been developed in recent years. Variable elimination in linear equations (Guassian Elimination) is a fundamental technique in computational linear algebra and is therefore quite familiar to most of us. Elimination in linear inequalities (Fourier Elimination), on the other hand, is intimately related to polyhedral theory and aspects of linear programming that are not quite as familiar. In addition, the high complexity of elimination in inequalities has forces the consideration of intricate specializations of Fouriers original method. The intent of this survey article is to acquaint the reader with these connections and developments. The latter part of the article dwells on the thesis that variable elimination in linear constraints over the reals extends quite naturally to constraints in certain discrete domains.

The algorithmics of folding proteins on lattices

It should be possible to predict the fold of a protein into its native conformation, once we are given the sequence of the constituent amino acids. This is known as the protein structure prediction problem and is sometimes referred to as the problem of deciphering the second half of the genetic code. While large proteins fold in nature in seconds, computational chemists and biologists have found that folding proteins to their minimum energy conformations is a challenging unsolved optimization problem. Computational complexity theory has been useful in explaining, at least partially, this (Levinthals) paradox. The pedagogic cross-disciplinary survey by Ngo, Marks and Karplus (Computational Complexity, Protein Structure Prediction and the Levinthal Paradox, Birkhauser, Basel, 1994) provides an excellent starting point for nonbiologists to take a plunge into the problem of folding proteins. Since then, there has been remarkable progress in the algorithmics of folding proteins on discrete lattice models, an account of which is presented herein.

Supply demand matching in resource constrained electricity systems

This paper describes an integrated mathematical modeling approach to minimize the social cost of dynamically matching electricity supply with demand in the context of resource constrained electricity systems. We present a linear programming formulation of this optimization problem in which the temporal and structural variations in demand are captured through representative daily load curves. The utility focused alternatives, viz. supply, non-supply and new supply of electricity are considered for obtaining supply demand matching. Implementation of such an approach is demonstrated through a case study of the electricity system of Karnataka (a state in India). The analyses presented include a base case (1993–1994) and three scenarios.

Detecting embedded Horn structure in propositional logic

We show that the problem of finding a maximum renamable Horn problem within a propositional satisfiability problem is NP-hard but can be formulated as a set packing and therefore a maximum clique problem, for which numerous algorithms and heuristics have been developed.