OR-Tools Open-source from CO@Work 2020, Pawel Lichocki, 25.09.2020 - - PowerPoint PPT Presentation

▶
or tools open source from
SMART_READER_LITE
LIVE PREVIEW

OR-Tools Open-source from CO@Work 2020, Pawel Lichocki, 25.09.2020 - - PowerPoint PPT Presentation

Jan 13, 2024 151 likes •498 views

OR-Tools Open-source from CO@Work 2020, Pawel Lichocki, 25.09.2020 htups://developers.google.com/optimization Combinatorial optimization 3 2 8 4 6 5 3 1 6 3 5 4 1 6 4 8 7 9 9 5 8 7 9 6 2 8 Solvers 3 2 8 4 6 5 3 1

slide-1
SLIDE 1

OR-Tools

Open-source from

CO@Work 2020, Pawel Lichocki, 25.09.2020 htups://developers.google.com/optimization

slide-2
SLIDE 2

Combinatorial optimization

3 2 9 8 6 1 6 4 1 5 2 8 9 7 5 3 4 8 3 6 4 9 5 8 7 6

slide-3
SLIDE 3

Solvers

MIP LP SAT CP Graph VRP

3 2 9 8 6 1 6 4 1 5 2 8 9 7 5 3 4 8 3 6 4 9 5 8 7 6

slide-4
SLIDE 4

OR-tools

MIP LP SAT CP Graph VRP

3 2 9 8 6 1 6 4 1 5 2 8 9 7 5 3 4 8 3 6 4 9 5 8 7 6

slide-5
SLIDE 5

3 2 9 8 6 1 6 4 1 5 2 8 9 7 5 3 4 8 3 6 4 9 5 8 7 6

slide-6
SLIDE 6

enum SolverType GLOP_LINEAR_PROGRAMMING CLP_LINEAR_PROGRAMMING GLPK_LINEAR_PROGRAMMING GUROBI_LINEAR_PROGRAMMING XPRESS_LINEAR_PROGRAMMING CPLEX_LINEAR_PROGRAMMING SCIP_MIXED_INTEGER_PROGRAMMING GLPK_MIXED_INTEGER_PROGRAMMING CBC_MIXED_INTEGER_PROGRAMMING GUROBI_MIXED_INTEGER_PROGRAMMING XPRESS_MIXED_INTEGER_PROGRAMMING CPLEX_MIXED_INTEGER_PROGRAMMING BOP_INTEGER_PROGRAMMING SAT_INTEGER_PROGRAMMING KNAPSACK_MIXED_INTEGER_PROGRAMMING

LP / MIP solver wrapper

slide-7
SLIDE 7

enum SolverType GLOP_LINEAR_PROGRAMMING CLP_LINEAR_PROGRAMMING GLPK_LINEAR_PROGRAMMING GUROBI_LINEAR_PROGRAMMING XPRESS_LINEAR_PROGRAMMING CPLEX_LINEAR_PROGRAMMING SCIP_MIXED_INTEGER_PROGRAMMING GLPK_MIXED_INTEGER_PROGRAMMING CBC_MIXED_INTEGER_PROGRAMMING GUROBI_MIXED_INTEGER_PROGRAMMING XPRESS_MIXED_INTEGER_PROGRAMMING CPLEX_MIXED_INTEGER_PROGRAMMING BOP_INTEGER_PROGRAMMING SAT_INTEGER_PROGRAMMING KNAPSACK_MIXED_INTEGER_PROGRAMMING

LP / MIP solver wrapper

slide-8
SLIDE 8

MPVariableProto { double lower_bound double upper_bound double objective_coefficient bool is_integer } MPModelProto { bool maximize double objective_offset repeated MPVariableProto variable repeated MPConstraintProto constraint } MPConstraintProto { double lower_bound double upper_bound repeated int32 var_index repeated double coefficient }

min/max c0 + cTx lbct ≤ Ax ≤ ubct lbvar ≤ x ≤ ubvar xj ∈ Z, j∈J

  • rtools/linear_solver/linear_solver.proto
slide-9
SLIDE 9

max 2x0 + x1 x0 + x1 = 1 x0 ∈ {0, 1} x1 ∈ {0, 1}

maximize: true variable { lower_bound: 0.0 upper_bound: 1.0

  • bjective_coefficient: 2.0

is_integer: true } variable { lower_bound: 0.0 upper_bound: 1.0

  • bjective_coefficient: 1.0

is_integer: true } constraint { lower_bound: 1.0 upper_bound: 1.0 var_index: 0 coefficient: 1.0 var_index: 1 coefficient: 1.0 }

  • rtools/linear_solver/linear_solver.proto
slide-10
SLIDE 10
  • rtools/linear_solver/linear_solver.proto

Constraints Objective indicator quadratic SOS quadratic abs and, or min, max

slide-11
SLIDE 11

3 2 9 8 6 1 6 4 1 5 2 8 9 7 5 3 4 8 3 6 4 9 5 8 7 6

slide-12
SLIDE 12

CP-SAT solver

OR-tools CP-SAT solver at MiniZinc Challenge 2016: 1 gold 2017: 1 gold + 1 silver 2018: 4 golds 2019: 4 golds Closed open MIPLIB 2017 problems amaze22012-07-04i (31s) neos-3209462-rhin (87s) l2p2i (16s) neos-3214367-sovi (341s, vs. solved in 21 days with ParaXpress) stoch-vrpvrp-s5v2c8vrp-v2c8i (30s)

slide-13
SLIDE 13

CP-SAT solver

OR-tools CP-SAT solver at MiniZinc Challenge 2016: 1 gold 2017: 1 gold + 1 silver 2018: 4 golds 2019: 4 golds Closed open MIPLIB 2017 problems amaze22012-07-04i (31s) neos-3209462-rhin (87s) l2p2i (16s) neos-3214367-sovi (341s, vs. solved in 21 days with ParaXpress) stoch-vrpvrp-s5v2c8vrp-v2c8i (30s)

slide-14
SLIDE 14
  • rtools/sat/cp_model.proto

Constraints NoOverlapConstraint CumulativeConstraint NoOverlap2D Boolean constraints LinearConstraint (with enforcement) ElementConstraint CircuitConstraint TableConstraint

Intervals cannot overlap

slide-15
SLIDE 15
  • rtools/sat/cp_model.proto

Constraints NoOverlapConstraint CumulativeConstraint NoOverlap2D Boolean constraints LinearConstraint (with enforcement) ElementConstraint CircuitConstraint TableConstraint

Intervals have heights, resource has capacity. Interval can overlap without

  • verloading capacity
slide-16
SLIDE 16
  • rtools/sat/cp_model.proto

Constraints NoOverlapConstraint CumulativeConstraint NoOverlap2D Boolean constraints LinearConstraint (with enforcement) ElementConstraint CircuitConstraint TableConstraint

2D boxes cannot overlap

slide-17
SLIDE 17
  • rtools/sat/cp_model.proto

Constraints NoOverlapConstraint CumulativeConstraint NoOverlap2D Boolean constraints LinearConstraint (with enforcement) ElementConstraint CircuitConstraint TableConstraint

A \/ B \/ -C A => B A ⇔ -B A /\ -B => C

slide-18
SLIDE 18
  • rtools/sat/cp_model.proto

Constraints NoOverlapConstraint CumulativeConstraint NoOverlap2D Boolean constraints LinearConstraint ElementConstraint CircuitConstraint TableConstraint

3 <= x + 2y + z <= 19

slide-19
SLIDE 19
  • rtools/sat/cp_model.proto

Constraints NoOverlapConstraint CumulativeConstraint NoOverlap2D Boolean constraints LinearConstraint (with enforcement) ElementConstraint CircuitConstraint TableConstraint

3 <= x + 2y + z <= 19 B => (x <= 2)

slide-20
SLIDE 20
  • rtools/sat/cp_model.proto

Constraints NoOverlapConstraint CumulativeConstraint NoOverlap2D Boolean constraints LinearConstraint (with enforcement) ElementConstraint CircuitConstraint TableConstraint

target = variables[index]

slide-21
SLIDE 21
  • rtools/sat/cp_model.proto

Constraints NoOverlapConstraint CumulativeConstraint NoOverlap2D Boolean constraints LinearConstraint (with enforcement) ElementConstraint CircuitConstraint TableConstraint

Graph + boolean variables for arcs Boolean variables must form a (sub) circuit

slide-22
SLIDE 22
  • rtools/sat/cp_model.proto

Constraints NoOverlapConstraint CumulativeConstraint NoOverlap2D Boolean constraints LinearConstraint (with enforcement) ElementConstraint CircuitConstraint TableConstraint

(x, y, z) must be in 1 1 2 1 3 1 1 3 4 2 1 3 2 4 5

slide-23
SLIDE 23
  • rtools/sat/cp_model.proto

Constraints NoOverlapConstraint CumulativeConstraint NoOverlap2D Boolean constraints LinearConstraint (with enforcement) ElementConstraint CircuitConstraint TableConstraint ...

slide-24
SLIDE 24

3 2 9 8 6 1 6 4 1 5 2 8 9 7 5 3 4 8 3 6 4 9 5 8 7 6

slide-25
SLIDE 25

from ortools.constraint_solver import pywrapcp def distance(from_index, to_index): return from_index + to_index indexes = pywrapcp.RoutingIndexManager(num_nodes=10, num_vehicles=1, num_depots=0) routing = pywrapcp.RoutingModel(indexes) transit = routing.RegisterTransitCallback(distance) routing.SetArcCostEvaluatorOfAllVehicles(transit) solution = routing.Solve()

  • rtools/constraint_solver/routing.h
slide-26
SLIDE 26

3 2 9 8 6 1 6 4 1 5 2 8 9 7 5 3 4 8 3 6 4 9 5 8 7 6

slide-27
SLIDE 27

from ortools.graph import pywrapgraph ... # Initialize input data. min_cost_flow = pywrapgraph.SimpleMinCostFlow() for arc in num_arcs: min_cost_flow.AddArcWithCapacityAndUnitCost(from_node[arc], to_node[arc], capacities[arc], unit_costs[arc]) for node in num_nodes: min_cost_flow.SetNodeSupply(node, supplies[node]) if min_cost_flow.Solve() == min_cost_flow.OPTIMAL: print('Minimum cost:', min_cost_flow.OptimalCost())

  • rtools/graph/min_cost_flow.h
slide-28
SLIDE 28

MIP LP SAT CP Graph VRP

LP solver = primal/dual simplex (GLOP) CP solver = propagation VRP solver = CP + heuristics SAT solver = conflict-driven clause learning BP solver = heuristics + SAT (BOP) CP-SAT solver = propagation + (lazy) SAT + LP IP solver = CP-SAT + cuts Graph = linear assignment max flow min cost flow matching components cliques ...

slide-29
SLIDE 29

MIP LP SAT CP Graph VRP

LP solver = primal/dual simplex (GLOP) CP solver = propagation VRP solver = CP + heuristics SAT solver = conflict-driven clause learning BP solver = heuristics + SAT (BOP) CP-SAT solver = propagation + (lazy) SAT + LP IP solver = CP-SAT + cuts Graph = linear assignment max flow min cost flow matching components cliques ...

slide-30
SLIDE 30

MIP LP SAT CP Graph VRP

LP solver = primal/dual simplex (GLOP) CP solver = propagation VRP solver = CP + heuristics SAT solver = conflict-driven clause learning BP solver = heuristics + SAT (BOP) CP-SAT solver = propagation + (lazy) SAT + LP IP solver = CP-SAT + cuts Graph = linear assignment max flow min cost flow matching components cliques ...

slide-31
SLIDE 31

MIP LP SAT CP Graph VRP

LP solver = primal/dual simplex (GLOP) CP solver = propagation VRP solver = CP + heuristics SAT solver = conflict-driven clause learning BP solver = heuristics + SAT (BOP) CP-SAT solver = propagation + (lazy) SAT + LP IP solver = CP-SAT + cuts (CP-SAT-MIP) Graph = linear assignment max flow min cost flow matching components cliques ...

slide-32
SLIDE 32

MIP LP SAT CP Graph VRP

LP solver = primal/dual simplex (GLOP) CP solver = propagation VRP solver = CP + heuristics SAT solver = conflict-driven clause learning BP solver = heuristics + SAT (BOP) CP-SAT solver = propagation + (lazy) SAT + LP IP solver = CP-SAT + cuts (CP-SAT-MIP) Graph = linear assignment max flow min cost flow matching components cliques ...

slide-33
SLIDE 33

MIP LP SAT CP Graph VRP

LP solver = primal/dual simplex (GLOP) CP solver = propagation VRP solver = CP + heuristics SAT solver = conflict-driven clause learning BP solver = heuristics + SAT (BOP) CP-SAT solver = propagation + (lazy) SAT + LP IP solver = CP-SAT + cuts (CP-SAT-MIP) Graph = linear assignment max flow min cost flow matching components cliques ...

slide-34
SLIDE 34

Thank you!

htups://developers.google.com/optimization

CO@Work 2020, Pawel Lichocki, 25.09.2020