On the use of biased-randomized algorithms for solving non-smooth optimization problems

Soft constraints are quite common in real-life applications. For example, in freight transportation, the fleet size can be enlarged by outsourcing part of the distribution service and some deliveries to customers can be postponed as well; in inventory management, it is possible to consider stock-outs generated by unexpected demands; and in manufacturing processes and project management, it is frequent that some deadlines cannot be met due to delays in critical steps of the supply chain. However, capacity-, size-, and time-related limitations are included in many optimization problems as hard constraints, while it would be usually more realistic to consider them as soft ones, i.e., they can be violated to some extent by incurring a penalty cost. Most of the times, this penalty cost will be nonlinear and even noncontinuous, which might transform the objective function into a non-smooth one. Despite its many practical applications, non-smooth optimization problems are quite challenging, especially when the underlying optimization problem is NP-hard in nature. In this paper, we propose the use of biased-randomized algorithms as an effective methodology to cope with NP-hard and non-smooth optimization problems in many practical applications. Biased-randomized algorithms extend constructive heuristics by introducing a nonuniform randomization pattern into them. Hence, they can be used to explore promising areas of the solution space without the limitations of gradient-based approaches, which assume the existence of smooth objective functions. Moreover, biased-randomized algorithms can be easily parallelized, thus employing short computing times while exploring a large number of promising regions. This paper discusses these concepts in detail, reviews existing work in different application areas, and highlights current trends and open research lines

An alternative solution to the model structure selection problem

An alternative solution to the model structure selection problem is introduced by conducting a forward search through the many possible candidate model terms initially and then performing an exhaustive all subset model selection on the resulting model. An example is included to demonstrate that this approach leads to dynamically valid nonlinear model

An iterated greedy heuristic for a market segmentation problem with multiple attributes

[EN] A real-world customer segmentation problem from a beverage distribution firm is addressed. The firm wants to partition a set of customers, who share geographical and marketing attributes, into segments according to certain requirements: (a) customers allocated to the same segment must have very similar attributes: type of contract, type of store and the average difference of purchase volume; and (b) compact segments are desired. The main reason for creating a partition with these features is because the firm wants to try different product marketing strategies. In this paper, a detailed attribute formulation and an iterated greedy heuristic that iteratively destroys and reconstructs a given partition are proposed. The initial partition is obtained by using a modified k-means algorithm that involves a GRASP philosophy to get the initial configuration of centers. The heuristic includes an improvement method that employs two local search procedures. Computational results and statistical analyses show the effectiveness of the proposed approach and its individual components. The proposed metaheuristic is also observed very competitive, faster, and more robust when compared to existing methods. (C) 2017 Elsevier B.V. All rights reserved.This research has been supported by the Mexican National Council for Science and Technology (CONACYT) through grants CB2005-01-48499Y and CB2011-01-166397, and a scholarship for graduate studies, and by the Universidad Autonoma de Nuevo Leon through its Scientific and Technological Research Support Program (PAICYT), grants CA1478-07, CE012-09, IT511-10, and CE331-15. Ruben Ruiz is partially supported by the Spanish Ministry of Economy and Competitiveness, under the project "SCHEYARD - Optimization of Scheduling Problems in Container Yards" (No. DPI2015-65895-R) financed by FEDER funds. We would like to thank Rafael Frinhani, Richard Fuchshuber, and their corresponding research teams for providing us the source code of their algorithms to carry out the corresponding tests. Furthermore, we are grateful to the editor and the four anonymous reviewers for their careful reading of our manuscript and their constructive comments and suggestions which helped us improve its quality.Huerta-Muñoz, D.; Ríos-Mercado, RZ.; Ruiz García, R. (2017). An iterated greedy heuristic for a market segmentation problem with multiple attributes. European Journal of Operational Research. 261(1):75-87. https://doi.org/10.1016/j.ejor.2017.02.013S7587261

Protein Docking by the Underestimation of Free Energy Funnels in the Space of Encounter Complexes

Similarly to protein folding, the association of two proteins is driven by a free energy funnel, determined by favorable interactions in some neighborhood of the native state. We describe a docking method based on stochastic global minimization of funnel-shaped energy functions in the space of rigid body motions (SE(3)) while accounting for flexibility of the interface side chains. The method, called semi-definite programming-based underestimation (SDU), employs a general quadratic function to underestimate a set of local energy minima and uses the resulting underestimator to bias further sampling. While SDU effectively minimizes functions with funnel-shaped basins, its application to docking in the rotational and translational space SE(3) is not straightforward due to the geometry of that space. We introduce a strategy that uses separate independent variables for side-chain optimization, center-to-center distance of the two proteins, and five angular descriptors of the relative orientations of the molecules. The removal of the center-to-center distance turns out to vastly improve the efficiency of the search, because the five-dimensional space now exhibits a well-behaved energy surface suitable for underestimation. This algorithm explores the free energy surface spanned by encounter complexes that correspond to local free energy minima and shows similarity to the model of macromolecular association that proceeds through a series of collisions. Results for standard protein docking benchmarks establish that in this space the free energy landscape is a funnel in a reasonably broad neighborhood of the native state and that the SDU strategy can generate docking predictions with less than 5 � ligand interface Ca root-mean-square deviation while achieving an approximately 20-fold efficiency gain compared to Monte Carlo methods