Anthony Vannelli

Tight Mixed Integer Linear Programming Formulations for the Unit Commitment Problem

This paper examines the polytope of feasible power generation schedules in the unit commitment (UC) problem. We provide computational results comparing formulations for the UC problem commonly found in the literature. We introduce a new class of inequalities, giving a tighter description of feasible operating schedules for generators. Computational results show that these inequalities can significantly reduce overall solution times.

A tutorial description of an interior point method and its applications to security-constrained economic dispatch

The authors deal with the use of successive linear programming (SLP) for the solution of the security-constrained economic dispatch (SCED) problem. They tutorially describe an interior point method (IPM) for the solution of linear programming (LP) problems, discussing important implementation issues that really make this method far superior to the simplex method. A study of the convergence of the SLP technique and a practical criterion to avoid oscillatory behavior in the iteration process are also proposed. A comparison of the proposed method with an efficient simplex code (MINOS) is carried out by solving SCED problems on two standard IEEE systems. The results show that the interior point technique is reliable, accurate, and more than two times as fast as the simplex algorithm. >

A nonlinear optimization approach for solving facility layout problems

Abstract Facility layout research has many subproblems for which optimization models can be developed. Although modeling these problems is often simple, the resulting large size of these models can make solution by decision makers very difficult. This paper is concerned with the development of new heuristics to be used as aids in finding good solutions to the facility layout problem. In particular, nonlinear programming (NLP) techniques are developed that minimize the material handling cost. Descriptions of the problems to be solved are presented along with the formulations of the NLP models to be optimized and the methods used to solve them. Also presented are computational results and a comparison of these results to those of other layout algorithms. The heuristics developed are shown to produce solutions comparable to, and in many cases better than, those of other algorithms. The approach is particularly effective for problems with unequal-size departments. As well, the models are shown to be computationally practical for solving real-world problems.

A semidefinite optimization approach for the single-row layout problem with unequal dimensions

The facility layout problem is concerned with the arrangement of a given number of rectangular facilities so as to minimize the total cost associated with the (known or projected) interactions between them. We consider the one-dimensional space-allocation problem (ODSAP), also known as the single-row facility layout problem, which consists in finding an optimal linear placement of facilities with varying dimensions on a straight line. We construct a semidefinite programming (SDP) relaxation providing a lower bound on the optimal value of the ODSAP. To the best of our knowledge, this is the first non-trivial global lower bound for the ODSAP in the published literature. This SDP approach implicitly takes into account the natural symmetry of the problem and, unlike other algorithms in the literature, does not require the use of any explicit symmetry-breaking constraints. Furthermore, the structure of the SDP relaxation suggests a simple heuristic procedure which extracts a feasible solution to the ODSAP from the optimal matrix solution to the SDP relaxation. Computational results show that this heuristic yields a solution which is consistently within a few percentage points of the global optimal solution.

Computing Globally Optimal Solutions for Single-Row Layout Problems Using Semidefinite Programming and Cutting Planes

This paper is concerned with the single-row facility layout problem (SRFLP). A globally optimal solution to the SRFLP is a linear placement of rectangular facilities with varying lengths that achieves the minimum total cost associated with the (known or projected) interactions between them. We demonstrate that the combination of a semidefinite programming relaxation with cutting planes is able to compute globally optimal layouts for large SRFLPs with up to 30 facilities. In particular, we report the globally optimal solutions for two sets of SRFLPs previously studied in the literature, some of which have remained unsolved since 1988.

An efficient eigenvector approach for finding netlist partitions

A fast eigenvector technique for obtaining good initial node partitions of netlists for use in interchange heuristics is described. The method is based on approximating the netlist or hypergraph by a weighted graph G, such that the sum of the cut edges in G tightly underestimates the number of cut nets in any netlist partition. An eigenvector technique is used to partition the graph G into k blocks of fixed module size. Another feature of this graph underestimation model of the netlist is that it allows one to obtain lower bounds on the actual number of cut nets. A multiblock node interchange heuristic is tested on the one resulting netlist partition obtained by this eigenvector approach on a variety of small to large sized benchmark netlist partitioning problems (between 300 to 12000 modules and nets). Test results on the larger netlists show that in most cases this eigenvector-node interchange approach yields netlist partitions with comparable or fewer cut nets than the best netlist partitions obtained by using node interchange heuristics alone on many random initial netlist partitions. >

A fast algorithm for power system optimization problems using an interior point method

Variants of simplex-based methodologies are generally used to solve underlying linear programming (LP) problems. An implementation of the dual affine (DA) algorithm (a variant of N. Karmarkars (1984) interior point method) is described in detail and some computational results are presented. This algorithm is particularly suitable for problems with a large number of constraints, and is applicable to linear and nonlinear optimization problems. In contrast with the simplex method, the number of iterations required by the DA algorithm to solve large-scale problems is relatively small. The DA algorithm has been implemented considering the sparsity of the constraint matrix. The normal equation that is required to be solved in every iteration is solved using a preconditioned conjugate gradient method. An application of the technique to a hydro-scheduling is presented; the largest problem is solved over nine times faster than an efficient simplex (MINOS) code. A new heuristic basis recovery procedure is implemented to provide primal and dual optimal basic solutions which are not generally available if interior point methods are used. The tested examples indicate that this new approach requires less than 10% of the original iterations of the simplex method to find the optimal basis. >

Engineering details of a stable force-directed placer

Analytic placement methods that simultaneously minimize wire length and spread cells are receiving renewed attention from both academia and industry. We describe the implementation details of a force-directed placer, FDP. Specifically, we provide: (1) a description of efficient force computation for spreading cells; (2) an illustration of numerical instability in these methods and a means by which these instabilities are avoided; (3) spread metrics for measuring cell distribution throughout the placement region; and (4) a complementary technique which aids in directly minimizing HPWL. We present results comparing our analytic placer to other academic tools for both standard cell and mixed-size designs. Compared to Kraftwerk and Capo 8.7, our tool produces results with an average improvement of 9% and 3%, respectively.

An adaptation of the interior point method for solving the global routing problem

A linear-programming (LP) solution technique is applied to solve the global routing problem. Minimal spanning trees that were found in the subgrid by generating vertical and horizontal lines about the points of a given net and a modified interior point approach that reduces the number of arc constraints which were considered in the routing problem were used to reduce the problem site. An interior point algorithm approach is developed to solve the resulting LP problem. A FORTRAN code ROUTFAST is tested on several problems of varying arc capacities. ROUTFAST is compared with MINOS 5.0 which is a Simplex-based code on the same set of problems. ROUTFAST is at least 8-20 times faster than MINOS on the largest problems tested and seems to be getting faster as the problem size and arc capacity increases. Using a modification (ROUTLP) to solve four benchmark gate-array layout problems, ROUTFAST yielded competitive global routing results to TimberWolfSC Version 5.4 and in a fraction of TimberWolfSCs running time. >

A novel power quality monitoring allocation algorithm

Summary form only given. Distributed measurement architecture, due to its efficiency, is used to monitor the power quality in the electric systems. This paper introduces a novel algorithm to determine the optimum allocations of power quality monitors to reduce the cost of the distributed monitoring system taking into account the data redundancy. The optimization problem is formulated as a covering and packing one which can be manipulated by integer linear programming algorithms. The appropriate constraints are deduced by the electrical circuit topology independent of the load parameters. In addition, the problem is adopted to a general form which can be implemented by any optimization package. The proposed algorithm is applied to five different systems for validation. Then, the results are discussed in terms of the cost and data redundancy