www.localsolver.com

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Welcome

This is the first coming of the LocalSolver team in Japan

We are so pleased to come here in TokyoWarm welcome to all of you for joining this meeting

Special thanks to our Japanese partner MSI for the organization

Frédéric GardiCo-Founder & Managing Partner

fgardi@localsolver.com

Tiphaine RougerieOptimization Engineer

trougerie@localsolver.com

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Agenda

LocalSolver companyQuick tour of LocalSolverBenchmarksBusiness casesLicensing and pricingMore business cases

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LocalSolverCompany

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LocalSolver

Optimization Solver & Services

• Supply chain optimization

• Vehicle routing

• Production scheduling

• Workforce planning

• Network optimization

• Revenue management

• Asset management

• etc.

SOFTWARE EDITOR

SERVICE PROVIDER

15 experts in mathematics, computer science, information technology€2M in revenues, +50% grow in 2018, 5x grow since incorporation in 2012

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Passionate people

Thierry BenoistCo-Founder & Managing Partner, in charge of Services

• Ecole Polytechnique (X95), PhD and Habilitation in Computer Science

• 20 years of experience in Operations Research

• Sole author of a software optimizing an investment of €1 billion (Bouygues Telecom)

• Prize ASTI of the best applied PhD thesis (2005), 3rd Prize Robert Faure ROADEF (2006)

• Finalist of the EURO Excellence in Practice Award (2012)

Frédéric GardiCo-Founder & Managing Partner, in charge of LocalSolver

• PhD and Habilitation in Computer Science (UPMC, Paris 6)

• 20 years of experience in Operations Research

• Sole author of a software used by 10,000 users in the retail banking industry (Société Générale)

• 1st Prize Junior & Senior Challenge ROADEF 2005, 2nd Prix Senior Challenge ROADEF 2007

• 1st Prize Industrial Applications ROADEF (2011), 1st Prize Robert Faure ROADEF (2012)

• President of ROADEF, the French Operations Research Society (2014-2015)

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100 clients in 20 countries

100 clients50% with revenues > €1bn

from 20 countriesAustralia, Austria, Belgium, Brazil,

Canada, China, Denmark,Finland, France, Germany, Italy, India, Japan, Norway, Portugal,

Slovakia, Spain, Sweden, United Kingdom, USA

2,000 academic usersfrom 90 countries

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LocalSolver

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Swiss Army Knife for math optimization

All-Terrain & All-In-One

Discrete, Numerical, Black-Box

Fast & Scalable

Innovative Resolution Technology

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Differentiators

New-generation optimization technology• All-in-one: combines different optimization techniques

• Innovative: integrates unique heuristic search techniques

Easier to use than any other solver• Model & Run optimization solver

• Natural mathematical modeling formalism

• One-click resolution: no need of complex tuning

• LSP: innovative scripting & modeling language for fast prototyping

• Lightweight object-oriented Python, C++, Java, C# APIs for tight integration

• Available for all platforms: Windows, Linux, macOS, Solaris, 32-bit, 64-bit

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LocalSolver 9.0 coming soon

Major features• Better and faster solutions for list-based models, especially routing and scheduling problems

• Better and faster solutions for nonlinear continuous problems (NLP)

• Better and faster solutions for multiobjective models

• Better and faster lower bounds

Problems

LocalSolver 9.0

LP & MIP solvers

NLP solvers

DiscreteNumerical

CP & SAT solvers

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LocalSolverQuick tour

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Nonlinear optimization

Maximize the volume of a bucket with a given surface of metal

𝑟

𝑅

ℎ

𝑉 =𝜋ℎ

3(𝑅2 + 𝑅𝑟 + 𝑟2)

S = 𝜋𝑟2 + 𝜋(𝑅 + 𝑟) 𝑅 − 𝑟 2 + ℎ2

function model() {

R <- float(0,1);r <- float(0,1);h <- float(0,1);

V <- PI * h / 3.0 * (R*R + R*r + r*r);S <- PI * r * r + PI*(R+r) * sqrt(pow(R-r,2) + h*h);

constraint S <= PI;maximize V;

}

https://www.localsolver.com/docs/last/exampletour/optimalbucket.html

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Facility location

Select a subset H among N points minimizing the sum of distances from each point in N to the nearest point in H

function model() {

x[1..N] <- bool() ; // decisions: point i belongs to H if x[i] = 1

constraint sum[i in 1..N]( x[i] ) == H ; // constraint: H points selected among N

minDist[i in 1..N] <- min[j in 1..N]( x[j] ? Dist[i][j] : InfiniteDist ) ; // expressions: distance to the nearest point in H

minimize sum[i in 1..N]( minDist[i] ) ; // objective: minimize the sum of distances

}

https://www.localsolver.com/docs/last/exampletour/pmedian.html

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Mathematical operators

+ operator call : to call an external native functionwhich can be used to implement your own (black-box) operator

Decisional Arithmetical Logical Relational Set & List

bool sum sub prod not == count

float min max abs and != contains

int div mod sqrt or at

set log exp pow xor indexOf

list cos sin tan iif > disjoint

floor ceil round array + at < partition

dist scalar piecewise

+ multiobjective capabilities

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Traveling salesman

function model() {

x <- list(N) ; // order the N cities {0, ..., N-1} to visit

constraint count(x) == N; // exactly N cities to visit

minimize sum[i in 1..N-1]( distance( x[i-1], x[i] ) ) + distance( x[N-1], x[0] ); // minimize traveled distance

}

Could you imagine a simpler model• Textbook-like, natural declarative model

• Compact, highly-scalable

Find the shortest tour that visits N cities exactly once

https://www.localsolver.com/docs/last/exampletour/tsp.html

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Vehicle routing

function model() {

routes[1..K] <- list(N) ; // for each vehicle, the list of visited clients

constraint partition[k in 1..K]( routes[k] ); // each client is visited once

for [k in 1..K] {route <- routes[k]; n <- count( route );

constraint sum( 0..n-1, i => demands[ route[i] ] ) <= capacity; // truck capacity constraint

distances[k] <- sum( 0..n-2, i => distance( route[i], route[i+1] ) ) // sum of distances between each pair+ distance( depot, route[0] ) + distance( route[n-1], depot ); // of clients along the route

}

minimize sum[k in 1..K]( count(routes[k] > 0 ); // minimize the number of trucks usedminimize sum[k in 1..K]( distances[k] ); // minimize sum of traveled distances

}

Find the shortest routes of a fleet of K vehicles with a given capacity to deliver N customers

https://www.localsolver.com/docs/last/exampletour/vrp.html

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LocalSolver modeling practices

1. Choose the right type and set of decisions

2. Do not limit yourself to linear operators

3. Model business constraints as primary objectives

4. Think of using external functions

5. Experiment reformulations

Lost in modeling? contact@localsolver.com

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LocalSolverBenchmarks

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Quadratic assignment

Assign facilities to locations with quadratic costs• Instances coming from QAPLIB

• Resolution time: 1 minute

• Main difficulty: quadratic expressions to manage in the objective

1 minute

x = no solution found

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Bin packing

Pack items into bins• Instances coming from BPP library (Falkenauer et al.)

• Resolution time: 1 minute

• Main difficulty: standard formulations induced a lot of symmetries

1 minute

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Traveling salesman

Find the shortest tour that visits all cities once• Instances coming from TSP library

• Resolution time: 1 minute

• Main difficulty: specific branch-and-cut required to get decent results

1 minute

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Traveling salesman

Find the shortest tour that visits all cities once• Instances coming from TSP library

• Resolution time: 1 hour

• Main difficulty: specific branch-and-cut required to get decent results

•

1 hour

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Vehicle routing

Find the shortest routes of a fleet of vehicles • Instances coming from CVRPLIB

• Resolution time: 1 minute

• Main difficulty: no general-purpose solver available to get decent results

• Many declinations to manage in real life: CVRPTW, PDP, DARP, LRP, …

1 minute

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Car sequencing • Smoothing car production loads along the assembly line

• 2005 ROADEF Challenge http://challenge.roadef.org/2005/en

• Up to 1,300 vehicles to sequence → 400,000 binary decisions

Instance with 540 vehicles• Small instance: 80,000 variables including 44,000 binaries

• State of the art: 3,109 (found by winner of the Challenge)

• Lower bound: 3,103

Benchmarks• MIP solver 3,027,000 in 10 min 194,161 in 1 hour

• LocalSolver 3,476 in 10 sec 3,114 in 10 min

Industrial benchmark

Minimization Lower is better

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LocalSolverBusiness cases

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100 clients in 20 countries

100 clients

Especially major industrial corporations in Europe

Airbus, Air Liquide, Beiersdorf, Bosch, CEZ, Dassault Aviation,

Deutsche Post, EDF, ENGIE, Norsk Hydro, Primagaz, PSA,

Renault, SNCF, Siemens, SITA, Tetra Pak, Thales, Veolia

Production schedulingWarehouse optimization

Vehicle routingWorkforce planning

Maintenance planning

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Pasco Japan supply chain optimization

Problems involving tens of millions of variables

Solved in minutes thanks to LocalSolver

Daily used since 2015

Testimonial by Mr. Shinichi Kuroda, Pasco Shikishima

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Optimization of Starbucks’ supply chain network

= Location Routing Problem (LRP)

Easily solved using LocalSolver• Huge problem: 200 depots, 20,000 stores

• Easy use of Python API

• List variables make the model much simpler than using a traditional MIP boolean modeling approach

Please have a look at the testimonial by Dr. Renaud Lecoeuche, Principal Data Scientist from Starbucks, USA, in the brochure

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LNG supply chain optimizationLong-term planning of delivery routes and storagesStakes in €bn

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Assigning trains to platforms

while respecting crossing constraints

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Optimizing rotations of locomotives & drivers for the freight division of the French Railways

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Optimization of the routing & scheduling of field service technicians at JCDecaux France

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Building several networks simultaneously

Considering Points Of Interest

User can modify the solution manually

Selection optimizes• Number of contacts• Number of panels• Geographical dispatch• Mandatory or forbidden panels• Language balancing • And so on…

Programmatic advertising for out-of-home (OOH) media campaigns at JCDecaux Belgium

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High-quality support

All-inclusive maintenance & support• Included in the license price

• Provided by PhD-level optimization experts

• Dedicated: email, phone, web or physical meeting

• Reactive: we answer you during the day, generally within hours

• We help you to model & solve your problems using LocalSolver

• New versions for free (two per year)

• Corrective patches for any version

• Free migration of your license in case of replacement of your hardware

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Thanks

This is the first coming of the LocalSolver team in Japan

We are so pleased to come here in TokyoWarm welcome to all of you for joining this meeting

Special thanks to our Japanese partner MSI for the organization

Frédéric GardiCo-Founder & Managing Partner

fgardi@localsolver.com

Tiphaine RougerieOptimization Engineer

trougerie@localsolver.com

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LocalSolverMore business cases

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Network optimization

ADSL network expansion planning

Context• Choose remote concentrator units to unbundle

• Local and global constraints. Ex: forbid paths with too much clients to limit impacts of an incident

Prize collecting Steiner forest problem• Network: 14,000 nodes, 180,000 edges

• Resulting model: 1.4 million variables

• Required resolution time: minutes

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Energy management

Hydro power plant production optimization• Hydroelectric dams with pumps

• Forecasted energy prices over the horizon

• Management of thermal power plants

• From daily to yearly horizon

→Nonlinear large-scale dynamic system with mixed-variable (0/1 + continuous) decisions and tight coupling constraints

Outperform MILP approaches on the hardest instances

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Nuclear power plant maintenance

Quadratic assignment problem• Placement of nuclear fuel assemblies in pools

• Minimizing the completion time of the operations

• Inducing millions of variables

• Out of scope of MILP & MIQP solvers

Testimonial by EDF R&DLocalSolver follows the claims made by its designers. It was able to adaptand to provide good-quality solutions to the problem of placement ofnuclear fuel assemblies in pools in very short running times on a standardcomputer. It was able to outperform a simulated annealing algorithmwhich however considered the structure of the problem.

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Infrastructure maintenance planning

Street lighting maintenance planning

« Illuminate better with less energy » • Plan the replacement and maintenance

of street lighting fixtures over 25 years

• Considering costs, resources, energy consumptions, failure rates, etc.

Large-scale combinatorial optimization• Thousands of streets, tens of thousands of lighting fixtures

• Nonlinear discrete model with 1,000,000 variables

• Resolution time: minutes

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Oil refinery optimization

Software solutions based on LocalSolver• Refinery planning solution

• Refinery scheduling solution

• Product blending solution

• Crude blending solution

Why moving from MILP solvers? • Broader modeling scope + ability to

connect external simulation codes

→ simpler resolution approaches

• Faster & more scalable

• Better, expert & friendly, support

• Competitive pricing agreement

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Banking & finance optimization

How combining mortgages at best to satisfy a financial need?

Example of plan composed of two mortgages• Financial need €300,000, monthly payment €1,200

• Total cost €415,000 -> gain by composition €15,000

€200,000

240 months

2,20%

€100,000

331 months

2,58%

High-quality solutions required in seconds by bank branch sales

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Media planningSelling advertising spaces in Paris underground

60,000 ad faces to partition into products from 100 to 500 faces• Covering a maximum of stations

• Balanced according to the traffic

• + a dozen of quality criteria

Huge partitioning problemsolved in 1 minute

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Mechanical system design

Designing sailboat weathervanes

Context• Used to measure the wind, to drive sailboats

• High precision needed in racing competition

Heterogeneous variables• Continuous decisions

• Highly nonlinear physics

• Precision: 0.1 millimeter

• 2 criteria optimized

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Agronomic optimization

Optimal fertilization of agricultural parcels

How to best fertilize soils from mineral and organic fertilizers?

Highly-nonlinear dynamic system• Nonlinear dynamics of N, C, K over time

• Thousands of 0/1 and continuous decisions

• Analytical or simulation-based

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Engine calibration

Calibrate engine cartography• Nonlinear parametric models

• Large scale: 5,000 parameters

• Plugged to Matlab Simulink statistical models: 10 calls per sec

• 1st objective: fitting experimental measures

• 2nd objective: smoothing the cartography (avoiding large variations)

• LocalSolver allows to reduce computation time from weeks to hours

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Data science applications

Sparse Least Square Linear Regression

Find a sparse fitting model with only a few nonzero parameters

Applications in many fields• Data analysis in geomarketing

• Data analysis in email marketing

• Data analysis in biotechnologies

min𝛽

𝑌 − 𝑋𝛽 2

𝑠𝑡. 𝛽 0 ≤ 𝑘

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Data science applications

Map antennas in a hidden telco network

ContextHaving approximate distances between antennas from signals, find the positions of the antennas in the network

Unconstrained quadratic problem• 25 antennas, 10,000 point-to-point signals

• Resulting model: 100,000 float variables

• Resolution time: 1 minute

www.localsolver.com