Major New Features in Gurobi 7.0

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Dorothy Randall
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1 Advanced Models

2 Major New Features in Gurobi 7.0 Python modeling enhancements Much more direct mapping from mathematical notation to code General constraints Shorthand for modeling common logical constraints Multi-objective optimization Algorithms for trading off competing objectives Solution pool Returns the n best solutions instead of just the one best New default lazy update semantics Simplifies modeling Cloud Offering New Instant Cloud Solution New termination criteria BestObjStop, BestBdStop: stop when obj/bound reaches specified value 2

3 Python Modeling Enhancements 3

4 Python Modeling Enhancements Significant improvement in the expressiveness of our Python API New facilities Model.addVars: add a set of variables (indexed over given indices) Model.addConstrs: add a set of constraints (using a Python generator expression) tupledict: a collection of variables that makes it easy to build linear expressions on subsets Python models become more concise and easier to read Signatures: addvars(*indexes, lb=0.0, ub=grb.infinity, obj=0.0, vtype=grb.continuous, name="") addconstrs(constrs, name="") 4

5 Python Modeling Enhancements addvars Old: transport = {} for w in warehouses: for p in plants: transport[w,p] = model.addvar(obj=transportcosts[w,p]) New: transport = model.addvars(warehouses, plants, obj=transportcosts) First arguments provide indices Two dimensions in this example First iterates over members of list of warehouses, second over list of plants Arbitrary number of dimensions, each indexed over members of a list or an integer 5

6 Python Modeling Enhancements tupledict New tupledict class, returned by model.addvars() transport = model.addvars(warehouses, plants, obj=transportcosts) Makes it easier to build linear expressions on sets of variables transport.sum(): linear expression that captures the sum of the variables in the tupledict transport.sum(w, '*'): sum over a subset of the variables transport.prod(coeffs): weighted sum transport.prod(coeffs, '*', p): weighted sum Useful in many different situations 6

7 Python Modeling Enhancements addconstrs Old: New: for w in warehouses: model.addconstr(sum(transport[w,p] for p in plants) == demand[w]) model.addconstrs(transport.sum(w, '* ) == demand[w] for w in warehouses) 7

8 Putting It Together Old: transport = {} for w in warehouses: for p in plants: transport[w,p] = model.addvar(obj=transportcosts[w,p]) for w in warehouses: model.addconstr(sum(transport[w,p] for p in plants) == demand[w]) New: transport = model.addvars(warehouses, plants, obj=transportcosts) model.addconstrs(transport.sum(w, '* ) == demand[w] for w in warehouses) 8

9 The Power of Python Lives within a powerful and versatile programming language Thousands of modules available for downloading Example: Add 6 lines to our TSP example (using bokeh package) ptseq = [points[k] for k in tour+[tour[0]]] x, y = zip(*ptseq) p = figure(title="tsp tour", x_range=[0,100], y_range=[0,100]) p.circle(x,y, size=8) p.line(x, y) show(p) 9

10 General Constraints 10

11 General Constraints Constraint types: In 6.5: Linear constraints Quadratic constraints SOS constraints In 7.0: new general constraints Min, Max, Abs, And, Or, and Indicator Fully supported in all OO APIs and the C API and in the MPS (REW), LP (RLP) format General constraints easier to read, write, and maintain Example: r = max(x 1,x 2,x 3 ), in python model.addgenconstrmax(r, [x 1,x 2,x 3 ], name= max1") Transformed to: r = x 1 + s 1 ; r = x 2 + s 2 ; r = x 3 + s 3 (s j non-negative) z 1 + z 2 + z 3 = 1 (z j binary) SOS1(s 1,z 1 ), SOS1(s 2,z 2 ), SOS1(s 3,z 3 ) Which would you rather read/write/maintain? Mostly a modeling convenience feature, but Presolve can sometimes create a tighter formulation 11

12 General Constraints MIN and MAX Model.addGenConstrMax(x 0, [x 1, x 2, x 3 ], 100, GC0 ) Sets variable x 0 = MAX(x 1, x 2, x 3, 100) Transformed to: r = x 1 + s 1 ; r = x 2 + s 2 ; r = x 3 + s 3 ; x (s j non-negative) z 1 + z 2 + z 3 1 (z j binary) SOS1(s 1,z 1 ), SOS1(s 2,z 2 ), SOS1(s 3,z 3 ) Depending on the PRESOS1BIGM parameter the SOS are linearized by using Big-M LP format (in the new General Constraint section): GC0: x0 = MAX (x1, x2, x3, 100) Model.addGenConstrMin(x 0, [x 1, x 2, x 3 ], 30, GC1 ) Sets variable x 0 = MIN(x 1, x 2, x 3, 30) Transformed to: -x 0 = MAX(-x 1, -x 2, -x 3, -30) 12

13 General Constraints AND and OR Model.addGenConstrAnd(x 0, [x 1, x 2, x 3, x 4 ], And1 ) Sets binary variable x 0 = x 1 x 2 x 3 x 4 (logical AND) Transformed to: x 1 + x 2 + x 3 + x 4 x 0 3 x 0 x i, for all i in {1,, 4} LP format (in the new General Constraint section): GC0: x0 = And (x1, x2, x3, x4) Model.addGenConstrOr(x 0, [x 1, x 2, x 3, x 4 ], Or1 ) Sets binary variable x 0 = x 1 x 2 x 3 x 4 (logical OR) Equivalent to ~x 0 = ~ x 1 ~ x 2 ~ x 3 ~ x 4 (logical AND) With ~x being the negation of x, i.e., ~x = 1 x 13

14 General Constraints ABS and Indicator Model.addGenConstrAbs(x 0, x 1, AbsCons1 ) Transformed to x 0 = MAX(x 1, -x 1 ) LP format (in the new General Constraint section): AbsCons1: x0 = ABS ( x1 ) Model.addGenConstrIndicator(x 0, 1, 2x 1 + 3x 2 + x 3 + 2x 4 1, C0 ) If binary x 0 = 1, then 2x 1 + 3x 2 + x 3 + 2x 4 1 must be satisfied LP format (in the Subject To section): C0: x0 = 1 -> 2 x1 + 3 x2 + x3 + 2 x4 <= 1 No support for equivalence (<->) indicators 14

15 Multi-Objective Optimization 15

16 Multi-Objective Optimization User can specify multiple objective functions Each objective has a priority, weight, an absolute and a relative tolerance Fully supported in all APIs and in the MPS (REW), LP (RLP) format Two options to use multiple objectives: Hierarchical Blended Can combine the two Two parameters to control the optimization MultiObjPre: presolve level on the whole multi-objective model MultiObjMethod: select barrier, dual and primal to optimize for subsequent objectives, only for continuous models 16

17 Multi-Objective Optimization - Options Hierarchical User provides priorities Optimize highest priority objective first Then optimize next highest, but without degrading highest priority objective (too much) Repeat for each objective, in order of decreasing priority Blended User provides weights Weights used to combine objectives Can combine the two 17

18 Multi-Objective Optimization # Set number of objectives model.numobj = 2 # Set and configure objective 0 model.setparam(grb.param.objnumber, 0) model.objnpriority = 2 model.objnweight = 1.0 model.objnname = 'TotalSlack' model.objnreltol = 0.1 model.objnabstol = 2.0 totslack.objn = # set and configure objective 1 model.setparam(grb.param.objnumber, 1) model.objnpriority = 1 model.objnweight = 1.0 model.objnname = 'Fairness maxshift.objn = 1.0 minshift.objn = -1.0

19 Multi-Objective Optimization LP format example Minimize multi-objectives OBJ0: Priority=0 Weight=1 AbsTol=0 RelTol=0 - x - y - 2 z OBJ1: Priority=1 Weight=0.3 AbsTol=0 RelTol=0-2 x - 3 y - z v Subject To 19

20 Solution Pool 20

21 Solution Pool In 6.5, we find an optimal solution In 7.0, you can ask for: The k best solutions k solutions within a specified gap from optimal New parameters PoolSolutions: number of solutions to keep Default is now 10 Previously kept as many as we found PoolSearchMode: strategy for finding solutions 0: default (one optimal solution) 1: more solutions (but not systematic) 2: k best solutions (systematic) PoolGap: maximum gap between best and worst solution Useful for limiting search time Why search for solutions with 50% gap if you don't want them anyway? 21

22 Solution Pool Runtime penalty usually small, but can be substantial Disables dual reductions in presolve Dual reduction: can discard a solution when you can prove that an equivalent or better solution always exists Dual reductions sometimes quite powerful 22

23 Solution Pool # Limit how many solutions to collect model.setparam(grb.param.poolsolutions, 10) # Limit the search space by setting a gap for the worst possible solution that will be accepted model.setparam(grb.param.poolgap, 0.10) # do a systematic search for the k-best solutions model.setparam(grb.param.poolsearchmode, 2) model.optimize() # Print number of solutions stored nsolutions = model.solcount # Print objective values of solutions for e in range(nsolutions): model.setparam(grb.param.solutionnumber, e) print( Sol%d: %g ' % (e, model.poolobjval)) for i in range(nvars): print( x%d = %g ' % vars[i].xn, end='') print( ) 23

24 Lazy Updates 24

25 New Default Lazy Update Semantics In Gurobi 6.5 default settings, model changes are put in a queue Must call update() to apply queued changes Plusses and minuses: Update is expensive good to have control over when it happens Adding appropriate update calls can be tedious Parameter UpdateMode set to 1 by default in Gurobi 7.0 Model changes are still put in a queue, but Can refer to newly created variables and constraints without first calling update() 25

26 New Default Lazy Update Semantics Typical usage pattern in Gurobi 6.5: Add new variables to model Call update() to clear queue and actually add variables Add constraints on those variables New update semantics avoid one update() call Less common usage pattern in Gurobi 6.5: Repeat: Add a few variables to model Call update() Add a few constraints on those variables Frequent update() calls can be expensive No longer needed 26

27 New Default Lazy Update Semantics Gurobi examples have been modified for new update semantics Every single update() call went away Uncommon usage pattern: "Here are a bunch of variables and constraints" "Can you remind me of what I just added?" This still requires an update() call with new semantics 27

28 Gurobi Instant Cloud 28

29 Gurobi Cloud Offering Gurobi has had a Cloud offering for over 6 years Important features: Many licensing options Install perpetual licenses on cloud machines or pay by the hour Available on Amazon EC2 EC2 has ~85% cloud market share Use any of our API's (C, C++, Java,.NET, Python, MATLAB, R) Full API support No code changes required to use cloud Security All communication encrypted with 256-bit AES encryption 29

30 New Instant Cloud Completely revamped Gurobi Instant Cloud New website New client launching facilities Launch cloud machine from user program Using gurobi.lic file: CLOUDACCESSID=79344c54-48af-4d cb8e9b2a1743 CLOUDKEY=p3XNjBlP5piz5huuzisS6w Using programming language APIs: env = Env.CloudEnv("79344c54-48af-4d cb8e9b2a1743", "p3xnjblp5piz5huuziss6w") Launch through REST API New pool facility Allow multiple client programs to share Configuration information A pool of servers 30

31 New Instant Cloud New Website 31

32 New Instant Cloud Pools 32

33 Thank You Questions?

What's New in Gurobi 7.0

What's New in Gurobi 7.0 What's New? New employees New features in 7.0 Major and minor Performance improvements New Gurobi Instant Cloud 2 The newest members of the Gurobi team Daniel Espinoza Senior Developer