We consider the question of finding deep cuts from a model constructed with two rows of a simplex tableau. To do that, we show how to reduce the complexity of setting up the polar of such model from a quadratic number of integer hull computations to a linear number of integer hull computations. Furthermore we … Read more
This paper develops a new VNS approach to Permutational Flow shop Scheduling Problem with Total Flow time criterion. There are many hybrid approaches inthe problem’s literature, that make use of VNS internally, usually applying job insert neighbourhood followed by job interchange neighbourhood. In this study different ways to combine both neighbourhoods were examined. All tests … Read more
Recent developments have drawn focus towards the efficient calculation of flows in AC power grids, which are difficult to solve systems of nonlinear equations. The common linearization approach leads to the well known and often used DC formulation, which has some major drawbacks. To overcome these drawbacks we revisit an alternative linearization of the AC … Read more
Pochet and Wolsey [Y. Pochet, L.A. Wolsey, Integer knapsack and flow covers with divisible coefficients: polyhedra, optimization and separation. Discrete Applied Mathematics 59(1995) 57-74] introduced partition inequalities for three substructures arising in various mixed integer programs, namely the integer knapsack set with nonnegative divisible/arbitrary coefficients and two forms of single-node capacitated flow set with divisible … Read more
In this paper branching for attacking MILP is investigated. Under certain circumstances branches can be done concurrently. By introducing a new calculus it is shown there are restrictions for certain dual values and reduced costs. As a second unexpected result of this study a new class of cuts for MILP is found, which are defined … Read more
We investigate the multi-trip elementary shortest path problem (MESPPRC) with resource constraints in which the objective is to find a shortest path between a source node and a sink node such that nodes other than the specified replenishment node are visited at most once and resource constraints are not violated. After each visit to the … Read more
There exist efficient algorithms to project a point onto the intersection of a convex cone and an affine subspace. Those conic projections are in turn the work-horse of a range of algorithms in conic optimization, having a variety of applications in science, finance and engineering. This chapter reviews some of these algorithms, emphasizing the so-called … Read more
In this paper, we propose a new dwindling multidimensional filter second-order line search method for solving large-scale unconstrained optimization problems. Usually, the multidimensional filter is constructed with a fixed envelope, which is a strict condition for the gradient vectors. A dwindling multidimensional filter technique, which is a modification and improvement of the original multidimensional filter, … Read more
We give an explicit characterization of all extreme rays of the cone of 5×5 copositive matrices. The results are based on the work of Baumert [L. D. Baumert, “Extreme copositive quadratic forms”, PhD thesis, 1965], where an implicit characterization was given. We show that the class of extreme rays found by Baumert forms a 10-dimensional … Read more
A new nonlinear conjugate gradient method, based on Perry’s idea, is presented. And it is shown that its sufficient descent property is independent of any line search and the eigenvalues of $P_{k+1}^{\T}P_{k+1}$ are bounded above, where $P_{k+1}$ is the iteration matrix of the new method. Thus, the global convergence is proven by the spectral analysis … Read more