Welcome to the Webinar. Gurobi Enhancements to MATLAB and R

Transcription

1 Welcome to the Webinar Gurobi Enhancements to MATLAB and R

2 What s new in 8.0 for Matlab and R? General constraints: min, max, abs, etc. Handling of hierarchical and concurring multiple objectives Access to multiple solutions through the solution pool Integration with Compute Server and Instant Cloud Better coverage of variable attributes Copyright 2018, Gurobi Optimization, Inc. 2

3 Matlab API: Creating & Solving a Model Interface consists of only six functions Most important function: gurobi() Model components are given as a struct constraint matrix, objective function, variable bounds ( ) Most fields are arrays Output argument result is a struct, containing all solution information solution vector objective value solution time ( ) % maximize % x + 2 y + 3 z % subject to % x + y <= 1 % y + z <= 1 % model.a = sparse([1 1 0; 0 1 1]); model.obj = [1 2 3]; model.modelsense = 'Max'; model.rhs = [1 1]; model.sense = [ '<' '<']; result = gurobi(model); Copyright 2018, Gurobi Optimization, Inc. 3

4 R API: Creating & Solving a Model Interface consists of only six functions Most important function: gurobi() Model components are given as a list constraint matrix, objective function, variable bounds ( ) Most components are vectors or matrices Output argument result is a list, containing all solution information solution vector objective value solution time ( ) # maximize # x + 2 y + 3 z # subject to # x + y <= 1 # y + z <= 1 library(matrix) library(gurobi) model <- list() model$a <- matrix(c(1,1,0,0,1,1), nrow=2, byrow=t) model$obj <- c(1,2,3) model$modelsense <- 'max' model$rhs <- c(1,1) model$sense <- c('<', '<') result <- gurobi(model) Copyright 2018, Gurobi Optimization, Inc. 4

5 Matlab & R: Comparison # maximize # x + y + 2 z # subject to # x + 2 y + 3 z <= 4 # x + y >= 1 # x, y, z binary # Construct model model <- list() model$a <- matrix(c(1,2,3,1,1,0), nrow=2, ncol=3, byrow=t) model$obj <- c(1,1,2) model$modelsense <- 'max' model$rhs <- c(4,1) model$sense <- c('<', '>') model$vtype <- 'B' # Solve result <- gurobi(model) # Print solution vector print(result$x) % maximize % x + y + 2 z % subject to % x + 2 y + 3 z <= 4 % x + y >= 1 % x, y, z binary % Construct model model.a = sparse([1 2 3; 1 1 0]); model.obj = [1, 1, 2]; model.rhs = [4, 1]; model.sense = '<>'; model.vtype = 'B'; model.modelsense = 'max'; % Solve result = gurobi(model); % Print solution vector disp(result.x); Copyright 2018, Gurobi Optimization, Inc. 5

6 Setting Parameters Second input argument to gurobi function Signature: gurobi(model, params) Matlab: params is a struct (again!) R: params is a list (again!) Use params to control limits, tolerances and algorithmic behavior Exhaustive list of parameters: documentation No need to dive into that without reason; defaults work well for most problems % Set a log file params.logfile = 'mylog.txt'; % Use barrier algorithm params.method = 2; % 10% MIPGap tolerance params.mipgap = 0.1; % Solve result = gurobi(model, params); params <- list() # Set a log file params$logfile <- 'mylog.txt' # Use barrier algorithm params$method <- 2 # 10% MIPGap tolerance params$mipgap <- 0.1 # Solve result <- gurobi(model, params) Copyright 2018, Gurobi Optimization, Inc. 6

7 The Zoo of model Fields / Components A obj sense rhs lb ub vtype modelsense modelname objcon varnames constrnames Q quadcon sos multiobj genconmax genconmin genconabs genconand genconor genconind pwlobj varhintval varhintpri branchpriority pstart dstart lazy start partition vbasis cbasis Copyright 2018, Gurobi Optimization, Inc. 7

8 New Fields in 8.0: General Constraints A obj sense rhs lb ub vtype modelsense modelname objcon varnames constrnames Q quadcon sos multiobj genconmax genconmin genconabs genconand genconor genconind pwlobj varhintval varhintpri branchpriority pstart dstart lazy start partition vbasis cbasis Copyright 2018, Gurobi Optimization, Inc. 8

9 General Constraints Model logical dependencies between binary variables:! = #$%( ' (, ' *, ' + )! = -.( ' (, ' *, ' + ) Model min, max and abs functions:! = min{3 (, 3 *, 3 + }! = max{3 (, 3 *, 3 + }! = abs{3 ( } Model logical implications ( indicator constraint ): If the binary variable ' is true, then the constraint 9 : 3 < must be satisfied Input through corresponding fields / components in model struct/list genconmax, genconmin, genconabs, genconand, genconor, genconind Copyright 2018, Gurobi Optimization, Inc. 9

10 Toy Examples % max r % s.t. r = AND(x,y,z,w) % r, x, y, z, w binary m.a = sparse(0,5); m.modelsense = 'max'; m.obj = [1,0,0,0,0]; m.varnames = {'r','x','y','z','w'}; m.genconand.resvar = 1; m.genconand.vars = [2,3,4,5]; res = gurobi(m); % min x + y + z + w % s.t. r1 = OR(x,y) % r2 = OR(z,w) % r1 + r2 >= 2 % r1, r2, x, y, z, w binary m.obj = [0,0,1,1,1,1]; m.a = sparse([1,1,0,0,0,0]); m.sense = '>'; m.rhs = 2; m.varnames = {'r1','r2','x','y','z','w'}; m.genconor(1).resvar = 1; m.genconor(1).vars = [3,4]; m.genconor(2).resvar = 2; m.genconor(2).vars = [5,6]; res = gurobi(m); Copyright 2018, Gurobi Optimization, Inc. 10

11 Anatomy of genconand R: model$genconand is a list of lists model$genconand[[1]] AND constr. #1 model$genconand[[2]] AND constr. #2 ( ) Matlab: model.genconand is a struct array model.genconand(1) AND constr. #1 model.genconand(2) AND constr. #2 ( ) Fields of genconand(i) / Components of genconand[[i]] resvar index of resultant binary variable vars indices of argument binary variables name constraint name Anatomy of other general constraints is similar Full documentation in the reference manual and constraints overview Examples in the distribution: workforce5.{m,r}, genconstr.{m,r} Copyright 2018, Gurobi Optimization, Inc. 11

12 New in 8.0: Multiple Objectives A obj sense rhs lb ub vtype modelsense modelname objcon varnames constrnames Q quadcon sos multiobj genconmax genconmin genconabs genconand genconor genconind pwlobj varhintval varhintpri branchpriority pstart dstart lazy start partition vbasis cbasis Copyright 2018, Gurobi Optimization, Inc. 12

13 Multiple Objectives Let s say that!(#) and %(#) are linear functions We want to solve min!(#) and %(#) s.t. &# = (, # 0 What does it mean? Blended optimization We want to minimize +,! # + +. %(#) for some weight factors +,, +. Hierarchical optimization We want to solve min!(#) s.t. %(#) minimal, &# = (, # 0 Combinations of the two types Any number of objective functions Copyright 2018, Gurobi Optimization, Inc. 13

14 A Toy Example % minimize % -1/2 * (x + y + 2 z) * (x) % subject to % x + 2 y + 3 z <= 4 % x + y >= 1 % Construct model m.a = sparse([1 2 3; 1 1 0]); m.rhs = [4, 1]; m.sense = '<>'; m.multiobj(1).objn = [1, 1, 2]; m.multiobj(1).weight = -0.5; m.multiobj(2).objn = [1, 0, 0]; m.multiobj(2).weight = 1.0; % Solve result = gurobi(m); % minimize % x % subject to % x + y + 2 z -> minimal % x + 2 y + 3 z <= 4 % x + y >= 1 % Construct model m.a = sparse([1 2 3; 1 1 0]); m.rhs = [4, 1]; m.sense = '<>'; m.multiobj(1).objn = [1, 1, 2]; m.multiobj(1).priority = 1; m.multiobj(2).objn = [1, 0, 0]; m.multiobj(2).priority = 0; % Solve result = gurobi(m); Copyright 2018, Gurobi Optimization, Inc. 14

15 Anatomy of multiobj R: model$multiobj is a list of lists model$multiobj[[1]] objective #1 model$multiobj[[2]] objective #2 ( ) Matlab: model.multiobj is a struct array model.multiobj(1) objective #1 model.multiobj(2) objective #2 ( ) Fields of multiobj(i) / Components of multiobj[[i]] objn objective function vector ( n-th objective ) objcon objective constant priority priority for hierarchical objectives weight weight factor for blended objectives reltol relative degradation tolerance for hierarchical objectives abstol absolute degradation tolerance for hierarchical objectives name objective name Full documentation in the reference manual and the multiobjective overview Examples in the distribution: workforce5.{m,r}, multiobj.{m,r} Copyright 2018, Gurobi Optimization, Inc. 15

16 Querying Multiple Solutions m = gurobi_read('misc07'); res = gurobi(m); m <- gurobi_read('misc07') res <- gurobi(m) Optimize a model with 212 rows, 260 columns and 8619 nonzeros Variable types: 1 continuous, 259 integer (0 binary) [...] H % s H % s H % s H % s H % s Explored 3925 nodes (44769 simplex iterations) in 1.56 seconds Thread count was 4 (of 4 available processors) Solution count 7: Solution pool Optimal solution found (tolerance 1.00e-04) Best objective e+03, best bound e+03, gap % Copyright 2018, Gurobi Optimization, Inc. 16

17 New in 8.0: Access to the Solution Pool > m <- gurobi_read('misc07') > res <- gurobi(m) > str(res$pool) List of 7 $ :List of 2..$ objval: num $ xn : num [1:260] $ :List of 2..$ objval: num $ xn : num [1:260] $ :List of 2..$ objval: num $ xn : num [1:260] $ :List of 2..$ objval: num $ xn : num [1:260] $ :List of 2..$ objval: num $ xn : num [1:260] $ :List of 2..$ objval: num $ xn : num [1:260] $ :List of 2..$ objval: num $ xn : num [1:260] >> m = gurobi_read('misc07'); >> res = gurobi(m); >> disp(res.pool) 1x7 struct array with fields: objval xn >> res.pool(2).objval ans = 2875 Copyright 2018, Gurobi Optimization, Inc. 17

18 Anatomy of pool R: result$pool is a list of lists result$pool[[1]] solution #1 result$pool[[2]] solution #2 ( ) Matlab: result.pool is a struct array result.pool(1) solution #1 result.pool(2) solution #2 ( ) Fields of pool(i) / Components of pool[[i]] objval objective value of i-th solution xn variable values of the i-th solution ( n-th x ) Pool population is controlled by parameters params.poolsolutions sets the pool size params.poolsearchmode sets how the pool is populated Full documentation in the reference manual and in the solution pool overview Examples in the distribution: mip2.{m,r}, multiobj.{m,r}, poolsearch.{m,r} Copyright 2018, Gurobi Optimization, Inc. 18

19 New in 8.0: Integration with Remote Services Local setup: Build model and solve it on a local machine Gurobi Remote Services: Build model locally, but solve on a remote machine Capabilities greatly improved in Gurobi 8.0 Gurobi Instant Cloud Easy-to-use cloud solution provided by Gurobi Built on top of EC2 All communication with cloud instance via HTTPS Gurobi Compute Server Allows to setup a local compute host in your network Or a whole cluster of local compute nodes Automatic load balancing and queue management Copyright 2018, Gurobi Optimization, Inc. 19

20 It s That Easy We only need to pass cloud / compute server configuration data to the gurobi function: m <- gurobi_read('misc07') env <- list() env$accessid <- 'hgs2352v-5adf-3fc6h5zf--13ac26787a19' env$secretkey <- 'topsecret' res <- gurobi(m, env=env) Instant Cloud from R m = gurobi_read('misc07'); env.computeserver = 'localhost:33334'; env.password = 'password'; res = gurobi(m, [], env); Compute Server from Matlab Copyright 2018, Gurobi Optimization, Inc. 20

21 Anatomy of the env struct/list R: env is a list (just like model and params) Matlab: env is a struct (just like model and params) Fields/components for Instant Cloud: accessid access ID for cloud license secretkey key for cloud license pool destination pool for job priority job priority Fields/components for Compute Server: computeserver server name/port password access password router router for the cluster priority job priority tlsinsecure switch for insecure TLS mode Full documentation: Reference manual for env struct Remote Services reference manual Copyright 2018, Gurobi Optimization, Inc. 21