**TB-06: Global Optimization**

Stream: Global Optimization

Room: Moreau

Chair(s): Leocadio G. Casado

Exact and heuristic algorithms for solving a MINLP sigle facility location and design problem for firm expansion

Jose Fernandez, Boglárka G.-Tóth, Laura Anton-Sanchez

A firm has a given budget available to invest in a given geographical area where it already runs some other facilities. Competing facilities already exist in the market. In order to increase its profit, the firm can (1) locate a new facility, (2) change the quality of the existing facilities up or down or even close some of them (3) do both things. An MINLP formulation for this problem is introduced, and both an interval B&B algorithm and a heuristic procedure are proposed to cope with it. According to the results, small variations in the available budget may produce very different results.

Nested branch-and-bound algorithm for minmax problem and constraints with quantifiers

Jordan Ninin, Dominique Monnet, Benoit Clement

We consider global optimization problems of a minmax function subject to constraints with quantifiers. The goal is to minimize over x the maximum over y of f(x,y), and constraints with quantifiers must be satisfied for a set of value (for all y in S). We present an algorithm to address this non-smooth objective function and the constraints with quantifiers in the same way. Our approach is a set-valued method based on two nested branch-and-bound algorithm, using interval analysis. This problem arises in structured robust control, semi-infinite optimization or minmax optimization.

Towards accelerating global parameter estimation with reduced data sets

Susanne Sass, Angelos Tsoukalas, Ian H. Bell, Dominik Bongartz, Jaromil Najman, Alexander Mitsos

Many large parameter estimation problems are intractable for deterministic global optimization solvers. With a Branch and Bound algorithm in mind, we therefore investigate whether valid lower bounds can be constructed based on reduced data sets. To that end, we take the equation of state for propane as a case study. Our results indicate that reduced models can successfully identify regions where the model based on the full data set yields high and low objective values. However, whether and to what extent there is a time gain due to data reduction depends on the actual data sample chosen.

On simplex minds and monotonicity

Eligius M.T. Hendrix, Leocadio G. Casado, Frederic Messine, Boglárka G.-Tóth

Simplicial branch and bound type of methods could make use of gradient bounds in order to create novel bounds over a simplicial partition set. Our question is how to use ideas of Interval Arithmetic to generate novel bounds. Our second question is dealing with the concept of monotonicity and exploitation in a simplicial branch and bound framework. We will report on our findings thus far. This investigation has been supported by The Spanish Ministry (RTI2018-437 095993-B-100), in part financed by the European Regional Development Fund (ERDF).