Constraint programming (CP) is an advanced technique to solve complex optimization problems. It lies at the crossroads of many branches: artificial intelligence, operational research, ...

Efficiency of constraint programming is that it allows to separate the representation of the problem (definition of constraints and objectives) of solving. The designer of a program using an engine resolution constraints avoid described algorithm or sequence to get the solution but models space of solutions and what he does not want in this space. Then, the engine iterates through this space to find one or more solutions to the optimal solution. This system called "solver" has the ability to browse the entire solutions optimally through different techniques: reduction of space research, spread of constraints, "match", use of timers......

Daumas Autheman et Associés uses constraint programming for fields where find quickly an approiate solution is strategic stake.

PC advantages :

• Several answers possible: a solution, all the solutions, the optimal solution
• Combination of constraints of different natures in a homogeneous environment, for example set constraints, numerical constraints, Boolean constraints, disjunctives
• Flexibility: it is possible to add news constraints only programming theses new constraints.
• Inheritance of artificial intelligence techniques: symbolic processing, logic programming, problem solving techniques
• Very effective when there is a large number of constraints difficult to satisfy simultaneously.
• Search algorithms that can adapt to exact methods or heuristics.

Fields where CP is making a great performance :

• Combinatorial and logical allocation problems (very efficient especially when it must take into account the interactions between the different actors).
• Too irregular problems for mathematical optimization.

The objective of linear programming is find the optimal value of a linear function under linear constraints. The function to optimize is called cost function . When we can model a problem in the form of an economic function to maximize according to certain constraints, then it is exactly in linear programming domain

Linear programming is a tool of operational research. Once a problem in linear equations, methods ensure the exact resolution of the problem. One of the methods known for solving linear programs in real numbers is the simplex method. The simplex method has led to several algorithms to solve problems of big sizes.

Daumas Autheman et Associés uses linear programming when the resolution of the problem is mathematical and there is no interaction with human factors.

Fields wher Linear programming is dealing a great perfrmance:

• Transportation problems
• Operational research problems
• Time-table problems

Conception and realization of an optimization system requires the implementation of methods and techniques dedicated.

Daumas Autheman et Associés has the experts and know-how needed to realize such systems.

« La pensée demeure incommensurable avec le langage » (Bergson).

Your business is not incomprehensible for our experts, thanks to a unique know-how, we arrive to extract knowledge and shell mechanisms. After a thorough study, our business experts conceptually formalize the problem. This analytical structuring of business leads ultimately to a document in a clear and comprehensible text by experts in the field the entire expertise. After validation by the experts of the client, expertise is modelled according to the principles of the technique for solving the optimization problem posed.

We use ILOG tools:

• Ilog CP for constraint programming problems.
• Ilog CPlex for mathematical problems.

Daumas Autheman et Associés used to be an historical ILOG partner, after acquizition of ILOG by IBM, Daumas Autheman et Associés became an IBM partner.