## Nested Partitions Method, Theory and ApplicationsThesubjectofthisbookisthenested partitions method(NP),arelativelynew optimization method that has been found to be very e?ective solving discrete optimization problems. Such discrete problems are common in many practical applications and the NP method is thus useful in diverse application areas. It can be applied to both operational and planning problems and has been demonstrated to e?ectively solve complex problems in both manufacturing and service industries. To illustrate its broad applicability and e?ectiveness, in this book we will show how the NP method has been successful in solving complex problems in planning and scheduling, logistics and transportation, supply chain design, data mining, and health care. All of these diverse app- cationshaveonecharacteristicincommon:theyallleadtocomplexlarge-scale discreteoptimizationproblemsthatareintractableusingtraditionaloptimi- tion methods. 1.1 Large-Scale Optimization IndevelopingtheNPmethodwewillconsideroptimization problemsthatcan be stated mathematically in the following generic form: minf(x), (1.1) x?X where the solution space or feasible region X is either a discrete or bounded ? set of feasible solutions. We denote a solution to this problem x and the ? ? objective function value f = f (x ). |

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### Contents

LXII | 131 |

LXIII | 136 |

LXV | 137 |

LXVI | 139 |

LXVII | 142 |

LXVIII | 147 |

LXIX | 149 |

LXX | 154 |

X | 19 |

XI | 23 |

XIII | 25 |

XIV | 26 |

XV | 29 |

XVI | 30 |

XVIII | 32 |

XX | 33 |

XXII | 35 |

XXIII | 37 |

XXV | 40 |

XXVI | 45 |

XXVII | 47 |

XXVIII | 48 |

XXX | 51 |

XXXI | 57 |

XXXIII | 59 |

XXXIV | 63 |

XXXV | 69 |

XXXVI | 70 |

XXXVIII | 72 |

XXXIX | 73 |

XLI | 74 |

XLII | 76 |

XLIII | 79 |

XLIV | 81 |

XLVI | 84 |

XLVII | 86 |

XLVIII | 91 |

XLIX | 92 |

L | 93 |

LI | 97 |

LII | 99 |

LIII | 102 |

LIV | 105 |

LV | 108 |

LVI | 110 |

LVII | 113 |

LIX | 125 |

LX | 126 |

LXI | 130 |

LXXI | 158 |

LXXII | 161 |

LXXIII | 162 |

LXXIV | 164 |

LXXV | 166 |

LXXVIII | 168 |

LXXIX | 170 |

LXXX | 172 |

LXXXI | 174 |

LXXXII | 175 |

LXXXIII | 176 |

LXXXIV | 177 |

LXXXV | 181 |

LXXXVI | 182 |

LXXXVIII | 193 |

LXXXIX | 210 |

XC | 212 |

XCI | 213 |

XCII | 215 |

XCIII | 216 |

XCIV | 217 |

XCV | 218 |

XCVI | 221 |

XCVII | 222 |

XCVIII | 223 |

XCIX | 224 |

C | 226 |

CI | 228 |

CII | 230 |

CIV | 231 |

CV | 234 |

CVI | 236 |

CVII | 238 |

CVIII | 242 |

CIX | 244 |

CX | 245 |

CXI | 246 |

247 | |

255 | |

### Other editions - View all

Nested Partitions Method, Theory and Applications Leyuan Shi,Sigurdur Ólafsson No preview available - 2008 |

Nested Partitions Method, Theory and Applications Leyuan Shi,Sigurdur Ólafsson No preview available - 2010 |

### Common terms and phrases

accuracy angle set applied approach backtracking beam angle selection biased sampling buﬀer cell chapter complimentary region consider constraints convergence correct move CPLEX data mining data sets decision variables deﬁned denote determine diﬀerent diﬃcult discrete optimization eﬀective eﬃcient equation estimate evaluated example feasible region feasible solutions feature selection feature subsets ﬁnd ﬁnite ﬁrst ﬁxed ﬂexible formulation global optimum heuristic high-quality hybrid algorithm improve incorporated instances integer programming intelligent partitioning job shop scheduling load lower bound LP relaxation machine makespan Markov chain maximum depth metaheuristics NP algorithm NP framework NP method NP wrapper NP-Filter objective function obtained OCBA operation optimal solution optimization problem ordinal optimization performance probability procedure promising index promising region random sampling randomly resource allocation sample rate scheduling problem Section sequence signiﬁcant simulation solution space solve Speciﬁcally Step subregions suﬃciently Table tabu search Theorem tion valid region voxels warehouse