VLSI cell placement problem is known to be NP complete. A wide repertoire of heuristic algorithms exists in the literature for efficiently arranging the logic cells on a VLSI chip. The objective of this paper is to present a comprehensive survey of the various cell placement techniques, with emphasis on standard ce11and macro

. We describe algorithms for two-stage stochastic linear programming with recourse and their implementation on a grid computing platform. In particular, we examine serial and asynchronous versions of the L-shaped method and a trust-region method. The parallel platform of choice is the dynamic, heterogeneous, opportunistic platform provided by the Condor system. The algorithms are of master-worker type (with the workers being used to solve second-stage problems), and the MW runtime support library (which supports masterworker computations) is key to the implementation. Computational results are presented on large sample average approximations of problems from the literature. 1.

Benders Decomposition is a form of hybridisation that allows linear programming to be combined with other kinds of algorithms. It extracts new constraints for one subproblem from the dual values of the other subproblem. This paper describes an implementation of Benders Decomposition, in the ECLiPSe language, that enables it to be used within a constraint programming framework. The programmer is spared from having to write down the dual form of any subproblem, because it is derived by the system. Examples are used to show how problem constraints can be modelled in an undecomposed form. The programmer need only specify which variables belong to which subproblems, and the Benders Decomposition is extracted automatically. A class of minimal perturbation problems is used to illustrate how dierent kinds of algorithms can be used for the dierent subproblems. The implementation is tested on a set of minimal perturbation benchmarks, and the results are analysed.

This paper addresses a general class of two-stage stochastic programs with integer recourse and discrete distributions. We exploit the structure of the value function of the second stage integer problem to develop a novel global optimization algorithm. The proposed scheme departs from those in the current literature in that it avoids explicit enumeration of the search space while guaranteeing finite termination. Our computational results indicate superior performance of the proposed algorithm in comparison to the existing literature. Keywords: stochastic integer programming, branch and bound, finite algorithms. 1 Introduction Under the twostage stochastic programming paradigm, the decision variables of an optimization problem under uncertainty are partitioned into two sets. The first stage variables are those that have to be decided before the actual realization of the uncertain parameters. Subsequently, once the random events have presented themselves, further design or operational ...

The network design problem with connectivity requirements (NDC) models a wide variety of celebrated combinatorial optimization problems including the minimum spanning tree, Steiner tree, and survivable network design problems. We develop strong formulations for two versions of the edge-connectivity NDC problem: unitary problems re-quiring connected network designs, and nonunitary problems permitting non-connected networks as solutions. We (i) present a new directed formulation for the unitary NDC problem that is stronger than a natural undirected formulation, (ii) project out several classes of valid inequalities-partition inequalities, odd-hole inequalities, and combinatorial design inequalities-that generalize known classes of valid inequalities for the Steiner tree problem to the unitary NDC problem, and (iii) show how to strengthen and direct nonunitary problems. Our results provide a unifying framework for strengthening formulations for NDC problems, and demonstrate the strength and power of flow-based formulations for net-work design problems with connectivity requirements.

We study strategic capacity planning in the semiconductor industry. Working with a major US semiconductor manufacturer on the strategic configuration of their worldwide production capacities, we identify two unique characteristics of this problem as follows: (1) wafer demands and manufacturing capacity are both main sources of uncertainty, and (2) capacity planning must consider two distinct viewpoints: a product perspective concerning marketing and strategic demand management, and a process standpoint involving manufacturing, yield, and technology configuration. These two unique characteristics change, in a fundamental way, how strategic capacity planning problem should be approached. To describe this complex problem, we first formulate a multi-stage stochastic program with recourses where demand and capacity uncertainties are incorporated via a scenario structure. To reconcile the marketing and manufacturing perspectives to the problem, we consider a decomposition of the planning pro...

This paper considers how to optimally set the basestock level for a single buffer when demand is uncertain, in a robust framework. We present a family of algorithms based on decomposition that scale well to problems with hundreds of time periods, and theoretical results on more general models. 1

We describe three data-parallel implementations of the simplex method for dense linear programming problems. The first implementation uses a full tableau and the most-negative reduced cost pivot rule, the second uses a tableau and the steepest-edge pivot rule, and the third is a revised method with explicit inverse. All are implemented on a Connection Machine CM--2 massively parallel computer system, using a variant of Fortran 90. Using special data structures called stripe arrays, we produce efficient implementations. We compare the implementations to one another, and to MINOS 5.4 on a Sun workstation. Test problems are from NETLIB, supplemented by a few additional, genuinely dense models from real applications. An appendix also gives recent results on the Connection Machine CM--5. 0 Introduction This paper describes the implementation of simplex algorithms for solving dense linear programming problems in a data-level massively parallel computing environment. Data-parallel programs...

Given a power grid modeled by a network together with equations describing the power flows, power generation and consumption, and the laws of physics, the so-called N − k problem asks whether there exists a set of k or fewer arcs whose removal will cause the system to fail. The case where k is small is of practical interest. We present theoretical and computational results involving a mixed-integer model and a continuous nonlinear model related to this question. 1

The solution of large-scale scheduling problems involving the production of hundreds different products using a variety of process unit operations are typical for chemical and pharmaceutical companies. These problems however are translated to mathematical models involving a computationally infeasible number of variables and constraints independent of the mathematical modeling approach one choose to follow. In this paper, the continuous-time formulation proposed by Ierapetritou and Floudas (Ind. Eng. Chem. Res. 37 (1998) 4341) is used as a basic scheduling model. A number of different heuristic-based decomposition approaches are presented including time-based decomposition, required production method and resource-based decomposition. Lagrangean relaxation (LR) and Lagrangean decomposition (LD) are then employed that give rise to an upper bound of the original scheduling problem. Finally, an iterative solution framework is proposed that exploits the lower bound obtained through the heuristic-based approaches and the upper bound based on the LR and LD to result in a refined schedule for large-scale scheduling problems. Two examples are used to illustrate the application of the approaches presented and compare their efficiencies.