This paper contains the description of a traveling salesman problem library (TSPLIB) which is meant to provide researchers with a broad set of test problems from various sources and with various properties. For every problem a short description is given along with known lower and upper bounds. Several references to computational tests on some of the problems are given. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.

We study the problem of finding ground states of spin glasses with exterior magnetic field, and the problem of minimizing the number of vias (holes on a printed circuit board, or contacts on a chip) subject to pin preassignments and layer preferences. The former problem comes up in solid-state physics, and the latter in very-large-scale-integrated (VLSI) circuit design and in printed circuit board design. Both problems can be reduced to the max-cut problem in graphs. Based on a partial characterization of the cut polytope, we design a cutting plane algorithm and report on computational experience with it. Our method has been used to solve max-cut problems on graphs with up to 1,600 nodes.

The linear ordering problem is an NP-hard combinatorial optimization problem with a large number of applications (including triangulation of input-output matrices, archaeological senation, minimizing total weighted completion time in one-machine scheduling, and aggregation of individual preferences). In a former paper, we have investigated the facet structure of the 0/1-polytope associated with the linear ordering problem. Here we report on a new algorithm that is based on these theoretical results. The main part of the algorithm is a cutting plane procedure using facet defining inequalities. This procedure is combined with various heuristics and branch and bound techniques. Our computational results compare favorably with the results of existing codes. In particular, we could triangulate all input-output matrices, of size up to 60 × 60, available to us within acceptable time bounds.

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In this paper we study 2-dimensional Ising spin glasses on a grid with nearest neighbor and periodic boundary interactions, based on a Gaussian bond distribution, and an exterior magnetic eld. We s h o w h o w using a technique called branch and cut, the exact ground states of grids of sizes up to 100 100 can be determined in a moderate amount of computation time, and we r e p o r t on extensive computational tests. With our method we produce results based on more than 20 000 experiments on the properties of spin glasses whose errors depend only on the assumptions on the model and not on the computational process. This feature is a clear advantage of the method over other more popular ways to compute the ground state, like M o n te Carlo simulation including simulated annealing, evolutionary, and genetic algorithms, that provide only approximate ground states with a degree of accuracy that cannot be determined a priori. Our ground state energy estimation at zero eld is ;1:317.

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