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Xpress Optimizer Deliverable Version: A Last Revised: 3 June 2017 Contents 1 Introduction 1 1.1 Outline..............................................1 1.2 Installing the Python Xpress module.............................1 1.2.1 Installation from the Xpress Optimizer distribution................1 1.2.2 Installation from Conda................................2 2 Modeling an optimization problem3 2.1 Getting started.........................................3 2.2 Creating a problem.......................................3 2.3 Variables.............................................3 2.4 Constraints............................................4 2.5 Objective function........................................5 2.6 Special Ordered Sets (SOSs)..................................6 2.7 Indicator constraints......................................6 2.8 Modeling and solving nonlinear problems..........................6 2.9 Solving a problem........................................8 2.10 Querying a problem.......................................8 2.11 Reading and writing a problem................................ 10 2.12 Hints for building models efficiently............................. 10 3 Using Python numerical libraries 12 3.1 Using NumPy in the Xpress Python interface......................... 12 3.2 Products of NumPy arrays.................................... 13 4 Controls and Attributes 14 4.1 Controls.............................................. 14 4.2 Examples............................................. 15 4.3 Attributes............................................. 15 4.4 Examples............................................. 16 4.5 Accessing controls and attributes as object members................... 16 5 Using Callbacks 19 5.1 Introduction........................................... 19 6 Examples of use 21 6.1 Creating simple problems................................... 21 6.1.1 Generating a small Linear Programming problem................. 21 6.1.2 A Mixed Integer Linear Programming problem................... 22 6.2 Modeling examples....................................... 23 6.2.1 A simple model..................................... 23 6.2.2 Using IIS to investigate an infeasible problem................... 23 6.2.3 Modeling a problem using Python lists and vectors................ 24 6.2.4 A knapsack problem.................................. 24 6.2.5 A Min-cost-flow problem using NumPy....................... 25 6.2.6 A nonlinear model................................... 26 6.2.7 Finding the maximum-area n-gon.......................... 26 Fair Isaac Corporation Confidential and Proprietary Informationi Contents 6.2.8 Solving the n-queens problem............................. 27 6.2.9 Solving Sudoku problems............................... 27 6.3 Examples using NumPy..................................... 28 6.3.1 Using NumPy multidimensional arrays to create variables............. 28 6.3.2 Using the dot product to create arrays of expressions............... 29 6.3.3 Using the Dot product to create constraints and quadratic functions...... 29 6.3.4 Using NumPy to create quadratic optimization problems............. 30 6.4 Advanced examples: callbacks and problem querying/modifying............ 30 6.4.1 Visualize the branch-and-bound tree of a problem................ 30 6.4.2 Query and modify a simple problem......................... 32 6.4.3 Change a problem after solution........................... 32 6.4.4 Combining modeling and API functions....................... 34 6.4.5 A simple Traveling Salesman Problem (TSP) solver................. 34 7 Reference Manual 38 7.1 Using this chapter........................................ 38 Format of the reference.................................... 39 7.2 Global methods of the Xpress module............................ 39 7.3 Methods of the problem class................................. 40 7.4 Methods for branching objects................................ 42 7.5 Methods for adding/removing callbacks of a problem object............... 42 7.6 Methods to be used within a callback of a problem object................ 42 xpress.free............................................... 44 xpress.getbanner........................................... 45 xpress.getcheckedmode....................................... 46 xpress.getdaysleft........................................... 47 xpress.getlasterror.......................................... 48 xpress.getlicerrmsg.......................................... 49 xpress.getversion........................................... 50 xpress.init................................................ 51 xpress.setcheckedmode........................................ 52 xpress.setdefaults........................................... 53 xpress.setdefaultcontrol....................................... 54 xpress.Sum............................................... 55 xpress.Dot............................................... 56 xpress.Prod............................................... 58 xpress.exp............................................... 59 xpress.log................................................ 60 xpress.log10.............................................. 61 xpress.sin................................................ 62 xpress.cos................................................ 63 xpress.tan................................................ 64 xpress.asin............................................... 65 xpress.acos............................................... 66 xpress.atan............................................... 67 xpress.max............................................... 68 xpress.min............................................... 69 xpress.abs................................................ 70 xpress.sign............................................... 71 xpress.erf................................................ 72 xpress.erfc............................................... 73 xpress.sqrt............................................... 74 xpress.user............................................... 75 xpress.addcbmsghandler....................................... 76 xpress.removecbmsghandler..................................... 77 Fair Isaac Corporation Confidential and Proprietary Information ii Contents problem.addcbbariteration..................................... 78 problem.addcbbarlog......................................... 80 problem.addcbchgbranchobject................................... 81 problem.addcbcutlog......................................... 82 problem.addcbdestroymt...................................... 83 problem.addcbgapnotify....................................... 84 problem.addcbgloballog....................................... 86 problem.addcbinfnode........................................ 87 problem.addcbintsol......................................... 88 problem.addcblplog......................................... 89 problem.addcbmessage....................................... 90 problem.addcbmipthread.....................................