Packing While Traveling: Mixed Integer Programming for a Class of Nonlinear Knapsack Problems

Packing and vehicle routing problems play an important role in the area of supply chain management. In this paper, we introduce a non-linear knapsack problem that occurs when packing items along a fixed route and taking into account travel time. We investigate constrained and unconstrained versions of the problem and show that both are NP-hard. In order to solve the problems, we provide a pre-processing scheme as well as exact and approximate mixed integer programming (MIP) solutions. Our experimental results show the effectiveness of the MIP solutions and in particular point out that the approximate MIP approach often leads to near optimal results within far less computation time than the exact approach

Physical Electronics

Contains reports on three research projects

Emergency preparedness to accidental chemical spills from tankers in Istanbul Strait

Istanbul Strait is one of the most important and dangerous maritime passage in the world. In this study, the hazards for possible accidents of the tankers carrying various chemicals through the Istanbul Strait were investigated and a significant risk was identified due to the intensive transportation of the chemicals. The purpose of this work is to define some risk control options in order to establish an efficient management system which can minimize the probability of accidents and hazardous effects of possible chemical spills to human life and environment. The risk is assessed by using the Formal Safety Assessment Methodology of the International Maritime Organization. Following this methodology hazards of accidents were identified through a questionnaire which is applied to a group of experts focussed on a passage of Istanbul Strait. In addition to this, a frequency analysis of the accidents was carried out on the defined sections along the strait using the accident database in order to determine the geographical distribution of the type and cause of the accidents. On the other hand, the maritime traffic of the Istanbul Strait was simulated using computer based software in order to investigate the effects of the local traffic on the passage. As a conclusion of the simulation the hot spots were defined as the potential locations for collisions. Also the consequences of such probable accidents were evaluated by using different dispersion modelling software for the spilled chemicals. As a result, a comprehensive management system for preparedness and response to chemical spills in the Istanbul Strait were proposed by taking into account the current management system and response equipment. Furthermore, a detailed economic analysis of the proposed system was also performed

Optimization by thermal cycling

Thermal cycling is an heuristic optimization algorithm which consists of cyclically heating and quenching by Metropolis and local search procedures, respectively, where the amplitude slowly decreases. In recent years, it has been successfully applied to two combinatorial optimization tasks, the traveling salesman problem and the search for low-energy states of the Coulomb glass. In these cases, the algorithm is far more efficient than usual simulated annealing. In its original form the algorithm was designed only for the case of discrete variables. Its basic ideas are applicable also to a problem with continuous variables, the search for low-energy states of Lennard-Jones clusters.Comment: Submitted to Proceedings of the Workshop "Complexity, Metastability and Nonextensivity", held in Erice 20-26 July 2004. Latex, 7 pages, 3 figure

Nonlinear Integer Programming

Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject to integrality requirements for the variables. This chapter is dedicated to this topic. The primary goal is a study of a simple version of general nonlinear integer problems, where all constraints are still linear. Our focus is on the computational complexity of the problem, which varies significantly with the type of nonlinear objective function in combination with the underlying combinatorial structure. Numerous boundary cases of complexity emerge, which sometimes surprisingly lead even to polynomial time algorithms. We also cover recent successful approaches for more general classes of problems. Though no positive theoretical efficiency results are available, nor are they likely to ever be available, these seem to be the currently most successful and interesting approaches for solving practical problems. It is our belief that the study of algorithms motivated by theoretical considerations and those motivated by our desire to solve practical instances should and do inform one another. So it is with this viewpoint that we present the subject, and it is in this direction that we hope to spark further research.Comment: 57 pages. To appear in: M. J\"unger, T. Liebling, D. Naddef, G. Nemhauser, W. Pulleyblank, G. Reinelt, G. Rinaldi, and L. Wolsey (eds.), 50 Years of Integer Programming 1958--2008: The Early Years and State-of-the-Art Surveys, Springer-Verlag, 2009, ISBN 354068274

Physical Electronics

Contains reports on three research projects

Physical Electronics

Contains reports on three research projects