Publication

Lagrangian relaxation for the integration of discrete choice models in mixed integer linear problems

Michel Bierlaire
2017
Talks

Abstract

The integration of discrete choice models in mixed integer linear problems provides a better understanding of the preferences of clients to policy makers while planning for their systems. In this research, we present a general framework that is able to combine both formulations by relying on simulation. The approach has been characterized for bene?t maximization and tested on a real case study. The complexity of the resulting model is currently being addressed with Lagrangian relaxation.

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Michel Bierlaire
2017
Talks

Abstract

Official source

Related concepts (20)

Cutting-plane method

In mathematical optimization, the cutting-plane method is any of a variety of optimization methods that iteratively refine a feasible set or objective function by means of linear inequalities, termed cuts. Such procedures are commonly used to find integer solutions to mixed integer linear programming (MILP) problems, as well as to solve general, not necessarily differentiable convex optimization problems. The use of cutting planes to solve MILP was introduced by Ralph E. Gomory.

Linear programming

Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. Linear programming is a special case of mathematical programming (also known as mathematical optimization). More formally, linear programming is a technique for the optimization of a linear objective function, subject to linear equality and linear inequality constraints.

Integer programming

An integer programming problem is a mathematical optimization or feasibility program in which some or all of the variables are restricted to be integers. In many settings the term refers to integer linear programming (ILP), in which the objective function and the constraints (other than the integer constraints) are linear. Integer programming is NP-complete. In particular, the special case of 0-1 integer linear programming, in which unknowns are binary, and only the restrictions must be satisfied, is one of Karp's 21 NP-complete problems.

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Lagrangian relaxation for the integration of discrete choice models in mixed integer linear problems

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