Sverre Storøy

Tabu search within a pivot and complement framework

Abstract The Pivot and Complement heuriitic is a procedure that frequently finds feasible solutions for general 0–1 integer programs. We present a refinement of the heuristic based on Tabu Search techniques. Local search strategies for the search phase, as well as the improvement phase of the heuristic are presented.

Massively parallel augmenting path algorithms for the assignment problem

In this paper we describe how to apply fine grain parallelism to augmenting path algorithms for the dense linear assignment problem. We prove by doing that the technique we suggest, can be efficiently implemented on commercial available, massively parallel computers. Using n processors, our method reduces the computational complexity from the sequentialO(n3) to the parallel complexity ofO(n2). Exhaustive experiments are performed on a Maspar MP-2 in order to determine which of the algorithmic flavors that fits best onto this kind of architecture.

Gradient schemes in iterative aggregation procedures for variable-aggregated lp-problems

Large-scale linear programming problems can be solved approximately with less effort by iterative aggregation procedures. We present several iterative (variable) aggregation and disaggregation strategies based on gradient considerations. The strategies are tested with some numerical examples

Decomposed enumeration of extreme points in the linear programming problem

In this paper we consider the problem of enumeration of extreme points in the linear programming problem when the matrix is of block-angular type. It is shown how decomposition methods can be used. Finally application of decomposed enumeration to the problem of computing equilibrium prices in a capital market network is given as an example.

An algorithm for finding a vector in the intersection of open convex polyhedral cones

This paper establishes necessary and sufficient conditions for the intersection ofm open convex polyhedral cones to be nonempty. An algorithm is given which indicates if the intersection is empty or not, and eventually computes a vector in the intersection.

Convergence aspects of adaptive clustering in variable aggregation

Abstract A convergent iterative aggregation procedure is described. The procedure makes use of both weight updating and reclustering of variables during the iterative process. Scope and purpose During the last two decades, aggregation/disaggregation has become an important tool in operations research, both for modeling purposes and for providing approximate solutions of large-scale mathematical programs. Methods for iteratively improving an aggregate model (iterative aggregation) have recently got a lot of interest. The present paper is a contribution in that context. A convergent iterative aggregation procedure is developed, which in principle can be used not only to find an approximate solution of a large-scale linear program, but also to find the exact solution.

Optimal weights and degeneracy in variable aggregated linear programs

It is well known that for any partitioning of the variables of a linear program, optimal aggregation weights exist. In the present paper we show that if two or more of the optimal basic variables of the original problem are aggregated into the same variable using optimal weights, the optimal solution of the aggregated problem is degenerate.

Weights improvement in column aggregation

Abstract In the present paper we study how the weights used in column aggregation of linear programs may be changed in order to improve the objective value. A procedure similar to postoptimal change of the coefficients of a basic variable is developed.

Ranking of vertices in the linear fractional programming problem

In this paper the problem of ranking vertices in the linear fractional programming problem is considered. It is shown that a class of vertex ranking algorithms for the linear programming problem can be used with only minor modifications.

Error control in the simplex-technique

The present paper describes a simple method to find an indicator of the error in solutions found by a procedure using the simplex-technique, and also describes a method for improving these solutions to any desired accuracy provided certain conditions are met.