Publication

Integrating advanced discrete choice models in mixed integer linear optimization

Michel Bierlaire
2018
Talks

Abstract

The integration of choice models in mixed integer linear programming (MILP) is appealing to operators because it provides a better understanding of the preferences of customers while planning for their systems. However, the complexity of choice models leads to mathematical formulations that are highly nonlinear and non convex in the variables of interest, and therefore difficult to be included in MILP. In this research, we present a general framework that overcomes these limitations by relying on simulation to integrate advanced discrete choice models in MILP formulations.

Official source

https://infoscience.epfl.ch/entities/publication/d648b717-6bfa-4359-9cb8-9656f9bdbf21

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Michel Bierlaire
2018
Talks

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/d648b717-6bfa-4359-9cb8-9656f9bdbf21

About this result

Related concepts (25)

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.

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.

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.

Related publications (14)

Integrating advanced discrete choice models in mixed integer linear optimization

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