Browsing by Subject "Combinatorial optimization."

Now showing 1 - 5 of 5

Open Access
Essays on some combinatorial optimization problems with interval data
(1999) Yaman, Hande
In this study, we investigate three well-known problems, the longest path problem on directed acyclic graphs, the minimum spanning tree problem and the single machine scheduling problem with total flow time criterion, where the input data for all problems are given as interval numbers. Since optimal solutions depend on the realization of the data, we define new optimality concepts to aid decision making. VVe present characterizations for these “optimal” solutions and suggest polynomial time algorithms to find them in some special cases.
Open Access
Polyhedral Approaches to Hypergraph Partitioning and Cell Formation
(1994) Kandiller, Levent
Hypergraphs are generalizations of graphs in the sense that each hyperedge can connect more than two vertices. Hypergraphs are used to describe manufacturing environments and electrical circuits. Hypergraph partitioning in manufacturing models cell formation in Cellular Manufacturing systems. Moreover, hypergraph partitioning in VTSI design case is necessary to simplify the layout problem. There are various heuristic techniques for obtaining non-optimal hypergraph partitionings reported in the literature. In this dissertation research, optimal seeking hypergraph partitioning approaches are attacked from polyhedral combinatorics viewpoint. There are two polytopes defined on r-uniform hypergraphs in which every hyperedge has exactly r end points, in order to analyze partitioning related problems. Their dimensions, valid inequality families, facet defining inequalities are investigated, and experimented via random test problems. Cell formation is the first stage in designing Cellular Manufacturing systems. There are two new cell formation techniques based on combinatorial optimization principles. One uses graph approximation, creation of a flow equivalent tree by successively solving maximum flow problems and a search routine. The other uses the polynomially solvable special case of the one of the previously discussed polytopes. These new techniques are compared to six well-known cell formation algorithms in terms of different efficiency measures according to randomly generated problems. The results are analyzed statistically.
Open Access
The robust shortest path problem with interval data uncertainties
(2001) Karaman, Abdullah Sıddık
In this study, we investigate the well-known shortest path problem on directed acyclic graphs under arc length uncertainties. We structure data uncertainty by taking the arc lengths as interval ranges. In order to handle uncertainty in the decision making process, we believe that a robustness approach is appropriate to use. The robustness criteria we used are the minimax (absolute robustness) criterion and the minimax regret (relative robustness) criterion. Under these criteria, we de ne and identify paths which perform satisfactorily under any likely input data and give mixed integer programming formulation to nd them. In order to simplify decision making, we classify arcs based on the realization of the input data. We show that knowing which arcs are always on shortest paths and which arcs are never on shortest paths we can preprocess a graph for robust path problems. Computational results support our claim that the preprocessing of graphs helps us signi cantly in solving the robust path problems.
Open Access
Shortest path problem with re-routing en-route
(2008) Karakaya, Banu
In this study, we examine the shortest path problem under the possibility of “re-routing” when an arc that is being traversed is blocked due to reasons such as road and weather conditions, congestion, accidents etc. If an incident occurs along the arc being traversed, the vehicle either waits until all effects of the incident are cleared and then follows the same path thereafter, or returns to the starting node of that arc and follows an escape route to the destination node, the latter course of action is called as “re-routing”. Also, we consider that this arc is not visited again throughout the travel along the network when an incident occurs and the alternative of not following this arc after the event is chosen. We propose a labeling algorithm to solve this specific problem. Then, a real case problem is analyzed by the proposed algorithm and several numerical studies are conducted in order to assess the sensitivity of the probability and travel time parameters.
Open Access
A successive algorithm for the Chinese Postman Problem
(1991) Narin, Noyan
The Chinese Postman Problem being one of the well known problems in combinatorial optimization has many applications in real life problems such as mail delivery, road maintenance and bus scheduling. In this thesis work, we present a successive algorithm for the solution of Chinese Postman Problem. Additionally, we present efficient data structures for the existing algorithms in literature and for the implementation of our successive algorithm.