Data correcting approaches in combinatorial optimization [electronic resource] /
Goldengorin, Boris I.author.
Pardalos, Panos M.author.(orcid)0000-0003-2824-101Xhttps://orcid.org/0000-0003-2824-101Xaut
Data Correcting Approaches in Combinatorial Optimization focuses on algorithmic applications of the well known polynomially solvable special cases of computationally intractable problems. The purpose of this text is to design practically efficient algorithms for solving wide classes of combinatorial optimization problems.  Researches, students and engineers will benefit from new bounds and branching rules in development efficient branch-and-bound type computational algorithms. This book examines applications for solving the Traveling Salesman Problem and its variations, Maximum Weight Independent Set Problem, Different Classes of Allocation and Cluster Analysis  as well as some classes of Scheduling Problems. Data Correcting Algorithms in Combinatorial Optimization  introduces the data correcting approach to algorithms which provide an answer to the following questions: how to construct a bound to the original intractable problem and find which element of the corrected instance  one should branch such that the total size of search tree will be minimized. The PC time needed for solving intractable problems will be adjusted with the requirements for solving real world problems.
Description based upon print version of record.
Data Correcting Approaches in Combinatorial Optimization; Preface; Acknowledgements; Contents; Chapter 1: Introduction; 1.1 Data Correcting Approach for Real-Valued Functions; 1.2 DC for NP-Hard Combinatorial Optimization Problems; 1.3 The DC Approach in Action; 1.4 Preliminary Computational Experience with ATSP Instances; 1.5 Concluding Remarks; Chapter 2: Maximization of Submodular Functions: Theory and Algorithms; 2.1 Introduction; 2.2 The Structure of Local and Global Maxima of Submodular Set Functions; 2.3 Excluding Rules: An Old Proof
2.4 Preservation Rules: Generalization and a Simple Justification2.5 The PPA; 2.6 Nonbinary Branching Rules; 2.7 Concluding Remarks; Chapter 3: Data Correcting Approach for the Maximization of Submodular Functions; 3.1 The Main Idea of the Data Correcting Algorithm: An Extension of the PPA; 3.2 The DC Algorithm (See golden99); 3.2.1 The Data Correcting Algorithm; 3.3 The SPLP: An Illustration of the DC Algorithm; 3.4 Computational Experiments with the QCP Problem and Quadratic Zero-One Optimization Problem: A Brief Review; 3.5 The QCP: Computational Experiments
3.6 Remarks for the DC Algorithm3.7 A Generalization of the DC Algorithm: A Multilevel Search in the Hasse Diagram; 3.7.1 PPA of Order r; 3.7.2 The Data Correcting Algorithm Based on the PPAr; 3.7.3 Branching Rule; 3.7.4 Computational Experiments for the QCP with the DCA(PPAr); 3.8 Concluding Remarks; Chapter 4: Data Correcting Approach for the Simple Plant Location Problem; 4.1 Introduction; 4.2 A Pseudo-Boolean Approach to SPLP; 4.3 Cherenin's Preprocessing Rules; 4.4 Ingredients of Data Correcting for the SPLP; 4.4.1 The Reduction Procedure; 4.4.2 The Data Correcting Procedure
4.5 Computational Experiments4.5.1 Bilde and Krarup-Type Instances; 4.5.2 Galvão and Raggi-Type Instances; 4.5.3 Instances from the OR-Library; 4.5.4 Körkel-Type Instances with 65 Sites; 4.5.5 Körkel-Type Instances with 100 Sites; 4.6 Concluding Remarks; Chapter 5: Summary; References
Includes bibliographical references.
Data Correcting Approaches in Combinatorial Optimization focuses on algorithmic applications of the well known polynomially solvable special cases of computationally intractable problems. The purpose of this text is to design practically efficient algorithms for solving wide classes of combinatorial optimization problems.  Researches, students and engineers will benefit from new bounds and branching rules in development efficient branch-and-bound type computational algorithms. This book examines applications for solving the Traveling Salesman Problem and its variations, Maximum Weight Independent Set Problem, Different Classes of Allocation and Cluster Analysis  as well as some classes of Scheduling Problems. Data Correcting Algorithms in Combinatorial Optimization  introduces the data correcting approach to algorithms which provide an answer to the following questions: how to construct a bound to the original intractable problem and find which element of the corrected instance  one should branch such that the total size of search tree will be minimized. The PC time needed for solving intractable problems will be adjusted with the requirements for solving real world problems.
Graph theory.
Mathematical optimization.
Data structures (Computer science).
Algorithms.
Graph Theory.
Optimization.
Data Structures.
Algorithm Analysis and Problem Complexity.
Algorithms.