Use Multilevel Graph Partitioning Scheme to solve traveling salesman problem

The traveling salesman problem is although looking very simple problem but it is an important combinatorial problem. In this thesis I have tried to find the shortest distance tour in which each city is visited exactly one time and return to the starting city. I have tried to solve traveling salesman problem using multilevel graph partitioning approach.Although traveling salesman problem itself very difficult as this problem is belong to the NP-Complete problems but I have tried my best to solve this problem using multilevel graph partitioning it also belong to the NP-Complete problems. I have solved this thesis by using the k-mean partitioning algorithm which divides the problem into multiple partitions and solving each partition separately and its solution is used to improve the overall tour by applying Lin Kernighan algorithm on it. Through all this I got optimal solution which proofs that solving traveling salesman problem through graph partition scheme is good for this NP-Problem and through this we can solved this intractable problem within few minutes.Keywords: Graph Partitioning Scheme, Traveling Salesman Problem.

How does data quality in a network affect heuristic solutions?

To have good data quality with high complexity is often seen to be important. Intuition says that the higher accuracy and complexity the data have the better the analytic solutions becomes if it is possible to handle the increasing computing time. However, for most of the practical computational problems, high complexity data means that computational times become too long or that heuristics used to solve the problem have difficulties to reach good solutions. This is even further stressed when the size of the combinatorial problem increases. Consequently, we often need a simplified data to deal with complex combinatorial problems. In this study we stress the question of how the complexity and accuracy in a network affect the quality of the heuristic solutions for different sizes of the combinatorial problem. We evaluate this question by applying the commonly used p-median model, which is used to find optimal locations in a network of p supply points that serve n demand points. To evaluate this, we vary both the accuracy (the number of nodes) of the network and the size of the combinatorial problem (p). The investigation is conducted by the means of a case study in a region in Sweden with an asymmetrically distributed population (15,000 weighted demand points), Dalecarlia. To locate 5 to 50 supply points we use the national transport administrations official road network (NVDB). The road network consists of 1.5 million nodes. To find the optimal location we start with 500 candidate nodes in the network and increase the number of candidate nodes in steps up to 67,000 (which is aggregated from the 1.5 million nodes). To find the optimal solution we use a simulated annealing algorithm with adaptive tuning of the temperature. The results show that there is a limited improvement in the optimal solutions when the accuracy in the road network increase and the combinatorial problem (low p) is simple. When the combinatorial problem is complex (large p) the improvements of increasing the accuracy in the road network are much larger. The results also show that choice of the best accuracy of the network depends on the complexity of the combinatorial (varying p) problem.

GRASP and statistical bounds for heuristic solutions to combinatorial problems

The quality of a heuristic solution to a NP-hard combinatorial problem is hard to assess. A few studies have advocated and tested statistical bounds as a method for assessment. These studies indicate that statistical bounds are superior to the more widely known and used deterministic bounds. However, the previous studies have been limited to a few metaheuristics and combinatorial problems and, hence, the general performance of statistical bounds in combinatorial optimization remains an open question. This work complements the existing literature on statistical bounds by testing them on the metaheuristic Greedy Randomized Adaptive Search Procedures (GRASP) and four combinatorial problems. Our findings confirm previous results that statistical bounds are reliable for the p-median problem, while we note that they also seem reliable for the set covering problem. For the quadratic assignment problem, the statistical bounds has previously been found reliable when obtained from the Genetic algorithm whereas in this work they found less reliable. Finally, we provide statistical bounds to four 2-path network design problem instances for which the optimum is currently unknown.

Optimal Path Searching through Specified Routes using different Algorithms

To connect different electrical, network and data devices with the minimum cost and shortest path, is a complex job. In huge buildings, where the devices are placed at different locations on different floors and only some specific routes are available to pass the cables and buses, the shortest path search becomes more complex. The aim of this thesis project is, to develop an application which indentifies the best path to connect all objects or devices by following the specific routes.To address the above issue we adopted three algorithms Greedy Algorithm, Simulated Annealing and Exhaustive search and analyzed their results. The given problem is similar to Travelling Salesman Problem. Exhaustive search is a best algorithm to solve this problem as it checks each and every possibility and give the accurate result but it is an impractical solution because of huge time consumption. If no. of objects increased from 12 it takes hours to search the shortest path. Simulated annealing is emerged with some promising results with lower time cost. As of probabilistic nature, Simulated annealing could be non optimal but it gives a near optimal solution in a reasonable duration. Greedy algorithm is not a good choice for this problem. So, simulated annealing is proved best algorithm for this problem. The project has been implemented in C-language which takes input and store output in an Excel Workbook

Corruption, governance and collective sanctions: : can a wicked problem be tamed?

Tackling a problem requires mostly, an ability to read it, conceptualize it, represent it, define it, and then applying the necessary mechanisms to solve it. This may sound self-evident except when the problem to be tackled happens to be “complex, “ “ill-structured,” and/or “wicked.” Corruption is one of those kinds of problems. Both in its global and national manifestations it is ill-structured. Where it is structural in nature, endemic and pervasive, it is perhaps even wicked. Qualities of the kind impose modest expectations regarding possibilities of any definitive solution to this insidious phenomenon. If so, it may not suffice to address the problem of corruption using existing categories of law and/or good governance, which overlook the “long-term memory” of the collective and cultural specific dimensions of the subject. Such socio-historical conditions require focusing on the interactive and self-reproducing networks of corruption and attempting to ‘subvert’ that phenomenon’s entire matrix. Concepts such as collective responsibility, collective punishment and sanctions are introduced as relevant categories in the structural, as well as behavioral, subversion of some of the most prevalent aspects of corruption. These concepts may help in the evolving of a new perspective on corruption fighting strategies.