This paper considers simultaneous gate and wire sizing for general VLSI circuits under the Elmore delay model. We present a fast and exact algorithm which can minimize total area subject to maximum delay bound. The algorithm can be easily modified to give exact algorithms for optimizing several other objectives (e.g. minimizing maximum delay or minimizing total area subject to arrival time specifications at all inputs and outputs). No previous algorithm for simultaneous gate and wire sizing can guarantee exact solutions for general circuits. Our algorithm is an iterative one with a guarantee on convergence to global optimal solutions. It is based on Lagrangian relaxation and "one-gate/wire-at-a-time" local optimizations, and is extremely economical and fast. For example, we can optimize a circuit with 13824 gates and wires in about 13 minutes using under 12 MB memory on an IBM RS/6000 workstation. 1 Introduction Since the invention of integrated circuits almost 40 years ago, gate si...

We consider the choice of an optimal sample size for multiple comparison problems. The motivating application is the choice of the number of microarray experiments to be carried out when learning about dierential gene expression. However, the approach is valid in any application that involves multiple comparison in a large number of hypothesis tests.

We examine scheduling problems where we control not only the assignment of jobs to machines, but also the time used by the job on the machine. For instance, many tooling machines allow control of the speed at which a job is run. Increasing the speed incurs costs due to machine wear but also increases throughput. We discuss some fundamental scheduling problems in this environment and give algorithms for some interesting cases. Some cases are inherently difficult so for these we give heuristics. Our approach illustrates the exploitation of underlying network structure in combinatorial optimization problems. We create heuristics that optimally schedule a large portion of the jobs and then attempt to fit in the remainder. This also gives a method for quickly finding valid inequalities violated by the linear relaxation solution. For the problem of minimizing the sum of makespan and production costs, a rounding heuristic is within a constant factor of optimal. Our heuristics ar...

Most existing methods for scheduling are based on centralized or hierarchical decision making using monolithic models. In this study, we investigate a new method based on a distributed and locally autonomous decision structure using the notion of combinatorial auction. In combinatorial auction the bidders demand a combination of dependent objects with a single bid. We show that not only can we use this auction mechanism to handle complex resource scheduling problems, but there exist strong links between combinatorial auction and Lagrangean-based decomposition. Exploring some of these properties, we characterize combinatorial auction using auction protocols and payment functions. This study is a #rst step toward developing a distributed scheduling framework that maintains system-wide performance while accommodating local preferences and objectives. We provide some insights to this framework by demonstrating four di#erent versions of the auction mechanism using job shop scheduling proble...

We consider non-uniform wire-sizing for general routing trees under the Elmore delay model. Three minimization objectives are studied: 1) total weighted sink-delays; 2) total area subject to sink-delay bounds; and 3) maximum sinkdelay. We first present an algorithm NWSA-wd for minimizing total weighted sink-delays based on iteratively applying the wire-sizing formula in [1]. We show that NWSA-wd always converges to an optimal wire-sizing solution. Based on NWSA-wd and the Lagrangian relaxation technique, we obtained two algorithms NWSA-db and NWSA-md which can optimally solve the other two minimization objectives. Experimental results show that our algorithms are efficient both in terms of runtime and storage. For example, NWSAwd, with linear runtime and storage, can solve a 6201-wiresegment routing-tree problem using about 1.5-second runtime and 1.3-MB memory on an IBM RS/6000 workstation. 1 Introduction As VLSI technology continues to scale down, interconnect delay has become the d...

TOMLAB is a general purpose, open and integrated MATLAB environment for solving optimization problems on UNIX and PC systems. TOMLAB has meny systems and driver routines for the most common optimization problems and more than 50 algorithms implemented in the toolbox NLPLIB and the toolbox OPERA. NLPLIB TB 1.0 is a MATLAB toolbox for nonlinear programming and parameter estimation and OPERA TB 1.0 is a MATLAB toolbox for operational research, with emphasis on linear and discrete optimization. Of special interest in NLPLIB TB 1.0 are the algorithms for general and separable nonlinear least squares parameter estimation. TOMLAB is using MEX-file interfaces to call solvers written in C/C++ and FORTRAN. Currently MEXfile interfaces have been developed for the commercial solvers MINOS, NPSOL, NPOPT, NLSSOL, LPOPT, QPOPT and LSSOL. From TOMLAB it is also possible to call routines in the MathWorks Optimization Toolbox. Interfaces are available for the model language AMPL and the CUTE (Cons...

Classical facility location models like the P-median problem (PMP) and the uncapacitated fixed-charge location problem (UFLP) implicitly assume that once constructed, the facilities chosen will always operate as planned. In reality, however, facilities "fail" from time to time due to poor weather, labor actions, changes of ownership, or other factors. Such failures may lead to excessive transportation costs as customers must be served from facilities much farther than their regularly assigned facilities. In this paper, we present models for choosing facility locations to minimize cost while also taking into account the expected transportation cost after failures of facilities. The goal is to choose facility locations that are both inexpensive under traditional objective functions and also reliable. This reliability approach is new in the facility location literature. We formulate reliability models based on both the PMP and the UFLP and present an optimal Lagrangian relaxation algorithm to solve them. We discuss how to use these models to generate a tradeo# curve between the day-to-day operating cost and the expected cost taking failures into account, and use these tradeo# curves to demonstrate empirically that substantial improvements in reliability are often possible with minimal increases in operating cost.

TOMLAB is a general purpose, open and integrated MATLAB environment for research and teaching in optimization on UNIX and PC systems. The motivation for TOMLAB is to simplify research on practical optimization problems, giving easy access to all types of solvers; at the same time having full access to the power of MATLAB. By using a simple, but general input format, combined with the ability in MATLAB to evaluate string expressions, it is possible to run internal TOMLAB solvers, MATLAB Optimization Toolbox and commercial solvers written in FORTRAN or C/C++ using MEX-file interfaces. Currently MEX-file interfaces have been developed for MINOS, NPSOL, NPOPT, NLSSOL, LPOPT, QPOPT and LSSOL. TOMLAB may either be used totally parameter driven or menu driven. The basic principles will be discussed. The menu system makes it suitable for teaching. Many standard test problems are included. More test problems are easily added. There are many example and demonstration files. Iterati...

We generalize the subgradient optimization method for nondifferentiable convex programming to utilize conditional subgradients. Firstly, we derive the new method and establish its convergence by generalizing convergence results for traditional subgradient optimization. Secondly, we consider a particular choice of conditional subgradients, obtained by projections, which leads to an easily implementable modification of traditional subgradient optimization schemes. To evaluate the subgradient projection method we consider its use in three applications: uncapacitated facility location, two-person zero-sum matrix games, and multicommodity network flows. Computational experiments show that the subgradient projection method performs better than traditional subgradient optimization; in some cases the difference is considerable. These results suggest that our simple modification may improve subgradient optimization schemes significantly. This finding is important as such schemes are very popula...

. The set covering problem is a paradigmatic NP-hard combinatorial optimization problem which is used as model in relevant applications, in particular crew scheduling in airline and mass-transit companies. This paper is concerned with the approximated solution of large scale set covering problems arising from crew scheduling in airline companies. We propose an adaptive heuristic-based evolutionary algorithm whose main ingredient is a mechanism for selecting a small core subproblem which is dynamically updated during the execution. This mechanism allows the algorithm to nd covers of good quality in rather short time. Experiments conducted on real-world benchmark instances from crew scheduling in airline companies yield results which are competitive with those obtained by other commercial/academic systems, indicating the eectiveness of our approach for dealing with large scale set covering problems. 1 Introduction The set covering problem (SCP) is one of the oldest and m...