Extended Formulations in Mixed-integer Convex Programming

We present a unifying framework for generating extended formulations for the polyhedral outer approximations used in algorithms for mixed-integer convex programming (MICP). Extended formulations lead to fewer iterations of outer approximation algorithms and generally faster solution times. First, we observe that all MICP instances from the MINLPLIB2 benchmark library are conic representable with standard symmetric and nonsymmetric cones. Conic reformulations are shown to be effective extended formulations themselves because they encode separability structure. For mixed-integer conic-representable problems, we provide the first outer approximation algorithm with finite-time convergence guarantees, opening a path for the use of conic solvers for continuous relaxations. We then connect the popular modeling framework of disciplined convex programming (DCP) to the existence of extended formulations independent of conic representability. We present evidence that our approach can yield significant gains in practice, with the solution of a number of open instances from the MINLPLIB2 benchmark library.Comment: To be presented at IPCO 201

Decomposition techniques with mixed integer programming and heuristics for home healthcare planning

We tackle home healthcare planning scenarios in the UK using decomposition methods that incorporate mixed integer programming solvers and heuristics. Home healthcare planning is a difficult problem that integrates aspects from scheduling and routing. Solving real-world size instances of these problems still presents a significant challenge to modern exact optimization solvers. Nevertheless, we propose decomposition techniques to harness the power of such solvers while still offering a practical approach to produce high-quality solutions to real-world problem instances. We first decompose the problem into several smaller sub-problems. Next, mixed integer programming and/or heuristics are used to tackle the sub-problems. Finally, the sub-problem solutions are combined into a single valid solution for the whole problem. The different decomposition methods differ in the way in which subproblems are generated and the way in which conflicting assignments are tackled (i.e. avoided or repaired). We present the results obtained by the proposed decomposition methods and compare them to solutions obtained with other methods. In addition, we conduct a study that reveals how the different steps in the proposed method contribute to those results. The main contribution of this paper is a better understanding of effective ways to combine mixed integer programming within effective decomposition methods to solve real-world instances of home healthcare planning problems in practical computation time

Data for: Performance Analysis of Waste-to-Energy Technologies for Sustainable Energy Generation in Integrated Supply Chains

The Excel-file contains the cost coeffients and other data not given in the manuscript.THIS DATASET IS ARCHIVED AT DANS/EASY, BUT NOT ACCESSIBLE HERE. TO VIEW A LIST OF FILES AND ACCESS THE FILES IN THIS DATASET CLICK ON THE DOI-LINK ABOV

A simultaneous optimization approach for off-line blending and scheduling of oil-refinery operations

This paper presents a novel MILP-based method that addresses the simultaneous optimization of the off-line blending and the short-term scheduling problem in oil-refinery applications. Depending on the problem characteristics as well as the required flexibility in the solution, the model can be based on either a discrete or a continuous time domain representation. In order to preserve the model’s linearity, an iterative procedure is proposed to effectively deal with non-linear gasoline properties and variable recipes for different product grades. Thus, the solution of a very complex MINLP formulation is replaced by a sequential MILP approximation. Instead of predefining fixed component concentrations for products, preferred blend recipes can be forced to apply whenever it is possible. Also, different alternatives for coping with infeasible problems are presented. Sufficient conditions for convergence for the proposed approach are presented as well as a comparison with NLP and MINLP solvers to demonstrate that the method provides an effective integrated solution method for the blending and scheduling of large-scale problems. The new method is illustrated with several real world problems requiring very low computational requirements.Fil: Mendez, Carlos Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; ArgentinaFil: Grossmann, Ignacio E.. University Of Carnegie Mellon; Estados UnidosFil: Harjunkoski, I.. ABB Corporate Research Center; AlemaniaFil: Kaboré, P.. ABB Corporate Research Center; Alemani