346 research outputs found
Complete local search with memory
Neighborhood search heuristics like local search and its variants are some of the most popular approaches to solve discrete optimization problems of moderate to large size. Apart from tabu search, most of these heuristics are memoryless. In this paper we introduce a new neighborhood search heuristic that makes effctive use of memory structures in a way that is different from tabu search. We report computational experiments with this heuristic on the traveling salesperson problem and the subset sum problem.
Sensitivity analysis of the greedy heuristic for binary knapsack problems
Greedy heuristics are a popular choice of heuristics when we have to solve a large variety of NP -hard combinatorial problems. In particular for binary knapsack problems, these heuristics generate good results. If some uncertainty exists beforehand regarding the value of any one element in the problem data, sensitivity analysis procedures can be used to know the tolerance limits within which the value may vary will not cause changes in the output. In this paper we provide a polynomial time characterization of such limits for greedy heuristics on two classes of binary knapsack problems, namely the 0-1 knapsack problem and the subset sum problem. We also study the relation between algorithms to solve knapsack problems and algorithms to solve their sensitivity analysis problems, the conditions under which the sensitivity analysis of the heuristic generates bounds for the toler-ance limits for the optimal solutions, and the empirical behavior of the greedy output when there is a change in the problem data.
Convexities related to path properties on graphs; a unified approach
Path properties, such as 'geodesic', 'induced', 'all paths' define a convexity on a connected graph. The general notion of path property, introduced in this paper, gives rise to a comprehensive survey of results obtained by different authors for a variety of path properties, together with a number of new results. We pay special attention to convexities defined by path properties on graph products and the classical convexity invariants, such as the Caratheodory, Helly and Radon numbers in relation with graph invariants, such as clique numbers and other graph properties.
Decomposed versus integrated control of a one-stage production system
This paper considers the case of a one-stage production system with several products and operating under tight production capacity constraints. The production schedule is cyclical, and there are long and sequence dependent setup times. The production system is regarded to consist of two components, namely a production unit and an inventory unit. The performance, with respect to inventory costs, timing and production quantity determination, of two types of control of the production system are compared, namely so-called decomposed and integrated control. For the generation of production orders, decomposed control uses only information from the inventory unit, while integrated control combines the information from both units. The main conclusion, based on simulation experiments, is that the inventory costs are just slightly lower in case of integrated control. Integration outperforms decomposition with respect to timing and quantity determination. However, since the differences between both approaches are small, the less sophisticated approach of decomposition is preferable when choices between both types of control have to be made.
On the complexity of determining tolerances for ->e--optimal solutions to min-max combinatorial optimization problems
On the complexity of determining tolerances for ->e--optimal solutions to min-max combinatorial optimization problems
On the complexity of determining tolerances for ->e--optimal solutions to min-max combinatorial optimization problems
Convexities related to path properties on graphs
AbstractA feasible family of paths in a connected graph G is a family that contains at least one path between any pair of vertices in G. Any feasible path family defines a convexity on G. Well-known instances are: the geodesics, the induced paths, and all paths. We propose a more general approach for such ‘path properties’. We survey a number of results from this perspective, and present a number of new results. We focus on the behaviour of such convexities on the Cartesian product of graphs and on the classical convexity invariants, such as the Carathéodory, Helly and Radon numbers in relation with graph invariants, such as the clique number and other graph properties
On vertex adjacencies in the polytope of pyramidal tours with step-backs
We consider the traveling salesperson problem in a directed graph. The
pyramidal tours with step-backs are a special class of Hamiltonian cycles for
which the traveling salesperson problem is solved by dynamic programming in
polynomial time. The polytope of pyramidal tours with step-backs is
defined as the convex hull of the characteristic vectors of all possible
pyramidal tours with step-backs in a complete directed graph. The skeleton of
is the graph whose vertex set is the vertex set of and the
edge set is the set of geometric edges or one-dimensional faces of .
The main result of the paper is a necessary and sufficient condition for vertex
adjacencies in the skeleton of the polytope that can be verified in
polynomial time.Comment: in Englis
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