Linear Integer Programming: Theory, Applications, Recent Developments

Description

This book presents the state-of-the-art methods in Linear Integer Programming, including some new algorithms and heuristic methods developed by the authors in recent years. Topics as Characteristic equation (CE), application of CE to bi-objective and multi-objective problems, Binary integer problems, Mixed-integer models, Knapsack models, Complexity reduction, Feasible-space reduction, Random search, Connected graph are also treated. Without mathematics no science would survive. This especially applies to the engineering sciences which highly depend on the applications of mathematics and mathematical tools such as optimization techniques, finite element methods, differential equations, fluid dynamics, mathematical modelling, and simulation. Neither optimization in engineering, nor the performance of safety-critical system and system security; nor high assurance software architecture and design would be possible without the development of mathematical applications. De Gruyter Series on the Applications of Mathematics in Engineering and Information Sciences (AMEIS) focusses on the latest applications of engineering and information technology that are possible only with the use of mathematical methods. By identifying the gaps in knowledge of engineering applications the AMEIS series fosters the international interchange between the sciences and keeps the reader informed about the latest developments. Acknowledgements Preface Contents About the authors Chapter 1 Segment search approach for the general linear integer model Chapter 2 Improved solution method for the 0-1 GAP model Chapter 3 A search for an optimal integer solution over the integer polyhedron – Two iterative approaches Chapter 4 Use of variable sum limits to solve the knapsack problem Chapter 5 The characteristic equation for linear integer programs Chapter 6 Random search method for integer programming Chapter 7 Some special linear integer models and related problems Chapter 8 The travelling salesman problem: Sub-tour elimination approaches and algorithms Index