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Solving Non-standard Packing Problems by Global Optimization and Heuristics [Minkštas viršelis]

  • Formatas: Paperback / softback, 135 pages, aukštis x plotis: 235x155 mm, weight: 2685 g, 51 Illustrations, color; XIV, 135 p. 51 illus. in color., 1 Paperback / softback
  • Serija: SpringerBriefs in Optimization
  • Išleidimo metai: 07-May-2014
  • Leidėjas: Springer International Publishing AG
  • ISBN-10: 3319050044
  • ISBN-13: 9783319050041
Kitos knygos pagal šią temą:
Solving Non-standard Packing Problems by Global Optimization and HeuristicsDidesnis paveikslėlis
  • Formatas: Paperback / softback, 135 pages, aukštis x plotis: 235x155 mm, weight: 2685 g, 51 Illustrations, color; XIV, 135 p. 51 illus. in color., 1 Paperback / softback
  • Serija: SpringerBriefs in Optimization
  • Išleidimo metai: 07-May-2014
  • Leidėjas: Springer International Publishing AG
  • ISBN-10: 3319050044
  • ISBN-13: 9783319050041
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9783319050041.html
Raktažodžiai:
This book results from a long-term research effort aimed at tackling complex non-standard packing issues which arise in space engineering. The main research objective is to optimize cargo loading and arrangement, in compliance with a set of stringent rules. Complicated geometrical aspects are also taken into account, in addition to balancing conditions based on attitude control specifications.

Chapter 1 introduces the class of non-standard packing problems studied. Chapter 2 gives a detailed explanation of a general model for the orthogonal packing of tetris-like items in a convex domain. A number of additional conditions are looked at in depth, including the prefixed orientation of subsets of items, the presence of unusable holes, separation planes and structural elements, relative distance bounds as well as static and dynamic balancing requirements. The relative feasibility sub-problem which is a special case that does not have an optimization criterion is discussed in Chapter 3. This setting can be exploited by introducing an ad hoc objective function, aimed at facilitating the finding of integer-feasible solutions. The third chapter also discusses the issue of tightening the general MIP model by introducing valid inequalities. A MIP-based heuristic approach is developed in Chapter 4, where the basic concept of abstract configuration is presented. Chapter 5 is devoted to experimental results relevant to a real-world application framework. Chapter 6 adopts both extensions of the general MIP model and non-linear formulations to tackle two further non-standard packing issues. The final Chapter 7 presents conclusions and provides insights regarding prospective developments (including non-standard scheduling aspects).

Practitioners and researchers interested in advanced optimization model development and solution in the context of logistics, transportation systems, complex structures, manufacturing and electronics will find this book useful. The book can also be used in graduate courses on nonlinear - including global and mixed integer - optimization, as a valuable collection of practically meaningful object packing applications.
1 Non-standard Packing Problems: A Modelling-Based Approach
1(6)
2 Tetris-like Items
7(20)
2.1 General Problem Statement and Mathematical Model Formulation
7(7)
2.2 Excluding Non-realistic Solutions
14(2)
2.3 Additional Conditions
16(11)
2.3.1 Conditions on Item Position and Orientation
16(1)
2.3.2 Conditions on Pairwise Relative Distance
16(3)
2.3.3 Conditions on Domains
19(1)
2.3.4 Conditions on the Total Mass Loaded and Its Distribution
20(3)
2.3.5 Further Loading Restrictions
23(4)
3 Model Reformulations and Tightening
27(12)
3.1 Alternative Models
27(7)
3.1.1 General MIP Model First Linear Reformulation
28(2)
3.1.2 General MIP Model Second Linear Reformulation
30(1)
3.1.3 A Non-restrictive Reformulation of the General MIP Model
31(1)
3.1.4 General MIP Model Nonlinear Reformulation
32(2)
3.2 Implications and Valid Inequalities
34(5)
4 Heuristic Approaches for Solving the Tetris-like Item Problem in Practice
39(20)
4.1 Intrinsic Difficulties
39(2)
4.2 Abstract Configurations
41(4)
4.3 Solution Search
45(14)
4.3.1 Initialization
45(4)
4.3.2 Heuristic Process Based on Suggested Abstract Configurations
49(1)
4.3.3 Heuristic Process Based on Imposed Abstract Configurations
50(7)
4.3.4 Interaction with the Solution Process
57(2)
5 Computational Experience and Real-World Context
59(16)
5.1 Direct Solutions Obtained from the General MIP Model
59(2)
5.2 Direct Solutions Obtained by Reformulations of the General MIP Model
61(4)
5.3 Use of the Linear Reformulations to Obtain Approximate Solutions
65(1)
5.4 Nonlinear Reformulation Approach to Improve Approximate Solutions
66(3)
5.5 The Use of Heuristics
69(6)
5.5.1 Test Instances from the Literature
69(3)
5.5.2 Instance Adopted to Tune the Solution Strategy
72(1)
5.5.3 Close-to-Real-World Instances
73(2)
6 Extensions and Mixed-Integer Nonlinear Approaches for Further Applications
75(16)
6.1 Exploiting Empty Volumes by Adding Virtual Items
75(7)
6.1.1 Model Formulation
76(2)
6.1.2 Model Approximations
78(2)
6.1.3 Applications
80(2)
6.2 Non-orthogonal Packing of Non-rectangular Items
82(9)
6.2.1 Approximate MINLP Model N
83(4)
6.2.2 Applications
87(4)
7 Directions for Future Research
91(12)
7.1 Experimental Context
91(3)
7.2 Modeling Enhancements and New Applications
94(9)
7.2.1 Extension of the Packing Models
94(2)
7.2.2 Application to Scheduling Problems with Nonconstant Resource Availability and Nonconstant Operational Cycles
96(7)
Appendix 103(1)
Case Studies 1.1--1.20 103(4)
Case Studies 2.2--2.4 107(4)
Case Studies 3.2 and 3.3 111(4)
Case Study 6 115(2)
Virtual Items 117(4)
References 121(10)
Index 131