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# Training

Artelys offers its training programs in mathematical optimization, analytics and statistical methods, energy system optimization and computer science for decision support to improve and develop your knowledge. A good understanding of the underlying mathematical methods and the results they can achieve, leads to a better comprehension of these tools. We emphasize techniques and their usage within our optimization tools and use real life financial and industrial applications to illustrate the methods.

Training program

## Optimization and Data Science

### Introduction to linear optimization

• ##### Paris - 2 days - English

Linear programming is an extremely powerful tool in increasingly complex economic systems in which the use of resources needs to be rationalized. Recent advances in linear programming solvers allow scientists and economists to quickly implement these techniques in a large number of operational and strategic problems. The success of such approaches depends, above all, on the choices made when modeling of the problem to be treated. This course will allow you to understand the principles behind linear optimization algorithms and to adopt the most efficient modeling approach.

Informations

• ### Course objectives

Ability to model decision problems through linear programming and interpreting results.

• ### Target Audience

Engineers, economists, scientists and developers interested in modeling decision problems and implementing optimization algorithms.

### Instructors

Artelys consultants specialized in modeling and solving large size optimization models applied to the domains of energy, transport and logistics.

### Program

#### Introduction to Linear Programming

Introduction: history, set-up.
Linear programming terminology: definitions, linear program formulation and graphical illustrations, classical reformulations.
Notion of convexity.

#### Simplex algorithm

Simplex method: principle, dictionary form, tabular form, non-degeneration and cycling, initial base. Implementation through simple examples.
Applying linear programming to scheduling problems. Illustrating the impact of modeling on solver results.

#### Duality

Duality: building a dual program, fundamental results (equality constraints and Lagrange multipliers, inequality constraints and Farkas’ lemma, KKT conditions, weak duality).
Economic interpretation of dual variables. Using dual variables to handle transportation and stock management problems.
Post-optimality and sensitivity analysis.
Variants of the simplex method: revised form, dual simplex.

#### Interior-point methods

Interior-point methods: quality of nonlinear approaches, Karmarkar’ algorithm, primal-dual interior algorithm, affine algorithm, complexity and polynomial convergence.

#### Using a solver

Taking advantage of a linear programming solver: tips and tricks, and good practices (illustrations with FICO Xpress).

### Information

 Training cost per person is 1400€ excluding taxes. Lunches, coffee breaks and documentation are supplied.
 You wish to join this training? Please complete the form on the left side.
 Artelys is a training institution, registered under n°11754066975.
 Location for the training Artelys FRANCE 81 rue Saint Lazare75009 Paris - France+33 (0)1 44 77 89 00 Métro Saint Lazare(lignes 3, 12, 13, 14) ou Trinité d'Estienne D'Orves (ligne 12)

### Information

Training cost per person is 1400€ excluding taxes. Lunches, coffee breaks and documentation are supplied.

You wish to join this training? Please complete the form below.

Artelys is a training institution, registered under n°11754066975.

Location for the training

Artelys FRANCE
81 rue Saint Lazare, 75009 Paris - France
+33 (0)1 44 77 89 00

Métro Saint Lazare(lignes 3, 12, 13, 14) ou Trinité d'Estienne D'Orves (ligne 12)

### Combinatorial Optimization I: Integer Programming

• ##### Paris - 2 days - English

The discrete nature of many decision problems can lead to a so-called combinatorial explosion. Whenever avoiding such phenomena (e.g. by relaxing integrity constraints) proves to be impossible, Integer Programming (IP) allows to tackle a great number of Combinatorial Optimization problems such as those found in the domain of logistics, production management or scheduling.

Informations

• ### Course objectives

Handle the discrete aspects of a decision problem with the help of Integer Programming (IP).

• ### Target Audience

Engineers, economists, scientists and developers interested in modeling decision problems and implementing optimization algorithms.

### Instructors

Artelys consultants specialized in modeling and solving large size optimization models applied to the domains of energy, transport and logistics.

### Program

#### Integer Linear Programming (ILP)

A brief reminder of Linear Programming.
Formulations: What is an Integer Program? Formulation of an Integer Linear Program. Combinatorial explosion. IP Formulations. Alternatives Formulations.
Optimality, relaxation and bounds: optimality and relaxation, linear relaxations, combinatorial relaxations, lagrangian relaxation, duality, primal bounds.
Modeling techniques and illustrations.
Solving Integer Linear Programs with Branch-and-Bound.
Principles of cutting methods and Branch- and-Cut. Numerical examples.

#### Application

Introducing, modeling and solving a Travelling Salesman Problem with the FICO Xpress solver.
Introducing, modeling and solving an industrial problem with FICO Xpress.
Comparison between a naive formulation of the problem and a formulation including cuts.

#### Introduction to decomposition techniques

Introduction to decomposition techniques: illustration of the interest of column generation.
Principles and practical interest of column generation techniques.
Presentation of an industrial application.

### Information

 Training cost per person is 1400€ excluding taxes. Lunches, coffee breaks and documentation are supplied.
 You wish to join this training? Please complete the form on the left side.
 Artelys is a training institution, registered under n°11754066975.
 Location for the training Artelys FRANCE 81 rue Saint Lazare75009 Paris - France+33 (0)1 44 77 89 00 Métro Saint Lazare(lignes 3, 12, 13, 14) ou Trinité d'Estienne D'Orves (ligne 12)

### Information

Training cost per person is 1400€ excluding taxes. Lunches, coffee breaks and documentation are supplied.

You wish to join this training? Please complete the form below.

Artelys is a training institution, registered under n°11754066975.

Location for the training

Artelys FRANCE
81 rue Saint Lazare, 75009 Paris - France
+33 (0)1 44 77 89 00

Métro Saint Lazare(lignes 3, 12, 13, 14) ou Trinité d'Estienne D'Orves (ligne 12)

### Combinatorial Optimization II: Constraint Programming & Local Search

• ##### Paris - 2 days - English

Whenever Integer Programming (IP) turns out to be unfit for treating a combinatorial optimization problem, it might be necessary to use the problem’s attributes in order to overcome it. Based on this concept, constraint programming and local search provide a formal framework for solving difficult combinatorial problems.

Informations

• ### Course objectives

Treating difficult combinatorial optimization problems with the help of constraint programming and local search techniques.

• ### Target Audience

Engineers, economists, scientists and developers interested in modeling decision problems and implementing optimization algorithms.

### Instructors

Artelys consultants specialized in modeling and solving large size optimization models applied to the domains of energy, transport and logistics.

### Program

#### Constraint Programming

Constraint Programming: principles and applications.
Presentation of a constraint programming solver: Xpress-Kalis.

#### Practical applications of constraint programming

A simple staff scheduling example.
Solving a movie scenes allocation problem.
Solving a frequency assignment problem.
Enumeration configuration – Branching strategies – Definition of search strategies for an advanced user.

#### Local Search

Intuition (n-queens) - Neighborhood (car-sequencing, magic square) - Optimization (warehouse location) - 2-opt, k-opt
Optimality vs. Feasibility (graph coloring) – Complex neighborhood (sport scheduling) – Escaping from local minima, connectivity.
Formalization, heuristics – Introduction to metaheuristics: Variable Neighborhood Search, Simulated annealing, Tabu search.

#### Scheduling problems and resource management

Introduction to scheduling problems.
Disjunctive scheduling – application to the construction of a sports stadium.
Multi-machines disjunctive scheduling – Job Shop problem.
Cumulative scheduling – non-renewable resources.

### Information

 Training cost per person is 1400€ excluding taxes. Lunches, coffee breaks and documentation are supplied.
 You wish to join this training? Please complete the form on the left side.
 Artelys is a training institution, registered under n°11754066975.
 Location for the training Artelys FRANCE 81 rue Saint Lazare75009 Paris - France+33 (0)1 44 77 89 00 Métro Saint Lazare(lignes 3, 12, 13, 14) ou Trinité d'Estienne D'Orves (ligne 12)

### Information

Training cost per person is 1400€ excluding taxes. Lunches, coffee breaks and documentation are supplied.

You wish to join this training? Please complete the form below.

Artelys is a training institution, registered under n°11754066975.

Location for the training

Artelys FRANCE
81 rue Saint Lazare, 75009 Paris - France
+33 (0)1 44 77 89 00

Métro Saint Lazare(lignes 3, 12, 13, 14) ou Trinité d'Estienne D'Orves (ligne 12)

### Combinatorial Optimization III: relaxation & hybridization

• ##### Paris - 2 days - English

Aside from the attributes, it is possible to get around a problem by using its structure. In such a case, rather than solving a large size problem subject to combinatorial explosion, it is possible to solve several small problems in a coordinated way: this is the principle of decomposition. In some cases, it may even be advantageous to combine Combinatorial Optimization techniques (IP, CP, local search) to overcome a problem particularly difficult to solve. This is the principle of hybridization.

Informations

• ### Course objectives

Mastering the principles of hybridization and decomposition methods in order to solve difficult problems of large size.

• ### Target Audience

Engineers, economists, scientists and developers interested in modeling decision problems and implementing optimization algorithms.

### Instructors

Artelys consultants specialized in modeling and solving large size optimization models applied to the domains of energy, transport and logistics.

### Program

#### Hybridization techniques

Linear programming / Constraint programming hybridization. Mixed modeling, common search trees, dialogue among branching schemes. Using reduced cost.
Constraint programming / Local search hybridization. Description of neighborhoods as constrained neighborhoods. Under constraints’ neighborhood exploration.

#### Decomposition techniques

Principles of Price Decomposition and Resource Decomposition. Types of information exchanges. Elementary examples.
Lagrangian. Duality. Definition and economic interpretation of the dual function. Duality gap. Convex and Non-Convex cases.
Price Decomposition: coordination algorithms and Non-differentiable Optimization.
Benders decomposition: principles and implementation.

#### Applications

Joint gas and electricity assets optimization: introduction, Benders and price decomposition.
Example of constraint programming and local search hybridization: timetables scheduling, frequency assignment.
Decomposition and hybridization for maintenance scheduling.

### Information

 Training cost per person is 1400€ excluding taxes. Lunches, coffee breaks and documentation are supplied.
 You wish to join this training? Please complete the form on the left side.
 Artelys is a training institution, registered under n°11754066975.
 Location for the training Artelys FRANCE 81 rue Saint Lazare75009 Paris - France+33 (0)1 44 77 89 00 Métro Saint Lazare(lignes 3, 12, 13, 14) ou Trinité d'Estienne D'Orves (ligne 12)

### Information

Training cost per person is 1400€ excluding taxes. Lunches, coffee breaks and documentation are supplied.

You wish to join this training? Please complete the form below.

Artelys is a training institution, registered under n°11754066975.

Location for the training

Artelys FRANCE
81 rue Saint Lazare, 75009 Paris - France
+33 (0)1 44 77 89 00

Métro Saint Lazare(lignes 3, 12, 13, 14) ou Trinité d'Estienne D'Orves (ligne 12)

### Nonlinear optimization with Artelys Knitro: from theory to practice

• ##### Paris - 2 days - English

Nonlinear optimization arises in various domains such as energy, economy, finance, machine learning, model predictive control, etc.

Informations

• ### Course objectives

Whichever is your application domain, this training will provide you with an introduction to the field of nonlinear optimization and will teach you how to apply nonlinear modeling techniques to industrial applications using Artelys Knitro.

• ### Target Audience

Scientists and developers interested in modeling and solving nonlinear programs using Artelys Knitro.

### Instructors

Professional consultants and software developers from Artelys with years of experience in solving large-scale nonlinear problems using Artelys Knitro.

### Program

#### Nonlinear programming (NLP)

Introduction, presentation of the training.
Problem statement and optimality conditions.
Newton method for unconstrained optimization. Globalization techniques.
Interior-point and active-set methods for constrained optimization.

#### Solving nonlinear problems with programmatic interfaces

Presentation, modeling and solving a nonlinear model with Artelys Knitro in Python™.
Impact of exact versus approximate derivatives. Quasi-Newton method.
Using Artelys Knitro in R/MATLAB®: a nonlinear least square minimization application.

#### Solving nonlinear problems with modeling interfaces

Using Artelys Knitro in AMPL: modeling syntax, automatic differentiation, examples.
Good practices in nonlinear modeling. Tips and tricks.
Fine-tuning Artelys Knitro parameters.
Global optimization using parallel multi-start.

#### Solving nonlinear models with special features

Mixed-integer nonlinear programming (MINLP) methods. Practical example.
Mathematical Programming with Equilibrium Constraints (MPEC). Application to computational economics and game theory.
Convex non-smooth models.

### Information

 Training cost per person is 1400€ excluding taxes. Lunches, coffee breaks and documentation are supplied.
 You wish to join this training? Please complete the form on the left side.
 Artelys is a training institution, registered under n°11754066975.
 Location for the training Artelys FRANCE 81 rue Saint Lazare75009 Paris - France+33 (0)1 44 77 89 00 Métro Saint Lazare(lignes 3, 12, 13, 14) ou Trinité d'Estienne D'Orves (ligne 12)

### Information

Training cost per person is 1400€ excluding taxes. Lunches, coffee breaks and documentation are supplied.

You wish to join this training? Please complete the form below.

Artelys is a training institution, registered under n°11754066975.

Location for the training

Artelys FRANCE
81 rue Saint Lazare, 75009 Paris - France
+33 (0)1 44 77 89 00

Métro Saint Lazare(lignes 3, 12, 13, 14) ou Trinité d'Estienne D'Orves (ligne 12)

## Numerical software and optimization tools

### Artelys Knitro

Artelys Knitro is a numerical software component that implements advanced nonlinear optimization techniques. Its four algorithms and its numerous options allow it to offer excellent performance and great robustness in the solution of a variety of optimization problems. We offer on-demand training session that will allow you to learn how to solve nonlinear optimization problems, such as portfolio optimization, optimal network power flow, nonlinear predictive control, or Nash equilibrium models. Trusting its efficiency and robustness, hundreds of institutions worldwide have chosen Artelys Knitro to solve highly complex problems.

### Artelys Kalis

Artelys Kalis is a software component for modeling and solving large size combinatorial problems through hybrid constraint programming and mathematical programming techniques. We offer on-demand training sessions that will present the principles of constraint programming and a rapid and efficient implementation of combinatorial problems of different types: tasks and timetable scheduling, resource allocation, equipment or network configuration.

### FICO® Xpress Optimization

FICO® Xpress Optimization offers a complete range of modeling and numerical optimization tools. These solutions can be quickly integrated into business problems in order to provide decision-support insights into complex problems. The following are some examples of on-demand courses that we can offer:

Logistics - Defining master plans in sectors such as transport, manufacturing, etc.
Personnel planning - Timetabling in sectors such as aeronautics, medical, public transportation and distribution.
Networks – Defining investment strategies in sectors such as telecommunications or electricity networks, and establishing a medium-term strategy.

### AMPL

AMPL is a complete and powerful algebraic modeling language for solving linear and non-linear problems with discrete or continuous variables. We offer on-demand training sessions that will teach you how to use generic notation and familiar concepts necessary to formulate optimization problems and to examine the possible solutions. The flexibility and the ease of use of AMPL allow for a very fast prototyping and development of models, whereas its speed and options control make it a very efficient tool for repeated use in production.

### Artelys Crystal City

Used today to work out the Energy Master Plans of cities such as Lyon, Grenoble, Poitiers and Pays de Gex. Artelys Crystal City provides full support to territorial authorities in evaluating, monitoring and communicating their local multi-energy development plans. At the time of the energy transition, local decision-makers are confronted with new territory planning issues where the energy dimension is a key factor in the decision-making process. We offer on-demand training sessions based on the tool Artelys Crystal City allowing to treat a variety of challenges related to topics such as energy consumption, CO2 emissions reduction, coordinating the development of distribution networks and valuating local renewable production potential.

### Artelys Crystal Super Grid

The energy sector of most countries is currently undergoing a rapid and deep mutation: the development of renewable energies, interconnections, energy storage and demand-side response represents at the same time a challenge and an opportunity to rethink the way energy systems are operated and how we plan their evolution. Whether they are energy regulators, network operators, assets owners, researchers, all the actors have to evaluate the impacts of strategic choices that integrate this new energy reality. We offer on-demand training sessions based on Artelys Crystal Super Grid, providing quantitative elements to assess the costs and benefits of adding interconnection capacity between two countries or to optimize a national energy strategy using the investment planning module of Artelys Crystal Super Grid.

### Artelys Crystal Forecast

In a world in constant and rapid evolution, forecasters are increasingly requested to bring to light the future and to reinforce the understanding of the business activities. Based on our expertise in data analysis and statistical modeling, our business expertise, as well as the innovative and adaptive technologies of the suite Artelys Crystal, we offer on-demand training sessions based on the tool Artelys Crystal Forecast, in order to develop skills that will allow you to generate valuable forecasts and scenarios on short-, medium- and long-term time horizons. This training will prove especially useful in the sector of operational management and as well as in strategic planning.

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