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Piecewise Regression through the Akaike Information Criterion using Mathematical programming⁎

IFAC-PapersOnLine 2018年第15期51卷 730-735页

作者： Gkioulekas, Ioannis Papageorgiou, Lazaros G. Torrington Place LondonWC1E 7JE United Kingdom

In machine learning, regression analysis is a tool for predicting the output variables from a set of known independent variables. Through regression analysis, a function that captures the relationship between the variables is fitted to the data. Many methods from literature tackle this problem with various degrees of difficulty. Some simple methods include linear regression and least squares, while some are more complicated such as support vector regression. Piecewise or segmented regression is a method of analysis that partitions the independent variables into intervals and a function is fitted to each interval. In this work, the Optimal Piecewise linear Regression Analysis (OPLRA) model is used from literature to tackle the problem of segmented analysis. This model is a mathematical programming approach that is formulated as a mixed integer linear programming problem that optimally partitions the data into multiple regions and calculates the regression coefficients, while minimising the Mean Absolute Error of the fitting. However, the number of regions is a known priori. For this work, an extension of the model is proposed that can optimally decide on the number of regions using information criteria. Specifically, the Akaike Information Criterion is used and the objective is to minimise its value. By using the criterion, the model no longer needs a heuristic approach to decide on the number of regions and it also deals with the problem of overfitting and model complexity. © 2018

关键词： Regression analysis Artificial intelligence Heuristic methods Information use integer programming Learning systems Least squares approximations Mathematical programming Piecewise linear techniques Akaike information criterion Independent variables Information criterion mixed integer linear programming problems Optimisations Piecewise linear regression Regression coefficient Support vector regression (SVR)

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Instance scale, numerical properties and design of metaheuristics: A study for the facility location problem

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IFAC-PapersOnLine 2019年第13期52卷 2219-2224页

作者： Chalupa, David Nielsen, Peter Operations Research Group Department of Materials and Production Aalborg University Fibigerstræde 16 Aalborg9220 Denmark

We present an in-depth computational study of two local search metaheuristics for the classical uncapacitated facility location problem. We investigate four problem instance models, studied for the same problem size, for which the two metaheuristics exhibit intriguing and contrasting behaviours. The metaheuristics explored include a local search (LS) algorithm that chooses the best moves in the current neighbourhood, while a randomised local search (RLS) algorithm chooses the first move that does not lead to a worsening. The experimental results indicate that the right choice between these two algorithms depends heavily on the distribution of coefficients within the problem instance. This is also put further into context by finding optimal or near-optimal solutions using a mixed-integer linear programming problem solver. © 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

关键词： integer programming Combinatorial optimization Heuristic algorithms Local search (optimization) Location Algorithm efficiency Facility location problem integer linear programming Local search Local search algorithm Local search metaheuristics mixed integer linear programming problems Uncapacitated facility locations

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An incremental model repair approach to timed discrete event systems

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IFAC-PapersOnLine 2017年第1期50卷 13636-13641页

作者： Basile, F. Chiacchio, P. Coppola, J. DIEM Università di Salerno Italy

New results on the model repair for timed discrete systems, modeled as Time Petri net systems, are presented in this paper. Unexpected and missed behavior in the nominal model, leading to observed but unexpected events and missed event observations, are formulated as logical conditions that can be directly transformed into linear mixed-integer inequalities. The repair model algorithm is incremental, also when multiple deviations from the nominal behavior are observed at a time. A set of logical conditions is preliminarily built from the observed behavior, then a mixed-integer linear programming problem is solved to repair the model. © 2017

关键词： Discrete event simulation Discrete time control systems Identification (control systems) integer programming Petri nets Repair Discrete systems Incremental modeling mixed integer linear programming problems Model repair Nominal models Time Petri nets Timed discrete event systems Unexpected events

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