MPI parallel programming of mixed integer optimization problems using CPLEX with COIN-OR

The aim of this technical report is to present some detailed explanations in order to help to understand and use the Message Passing Interface (MPI) parallel programming for solving several mixed integer optimization problems. We have developed a C++ experimental code that uses the IBM ILOG CPLEX optimizer within the COmputational INfrastructure for Operations Research (COIN-OR) and MPI parallel computing for solving the optimization models under UNIX-like systems. The computational experience illustrates how can we solve 44 optimization problems which are asymmetric with respect to the number of integer and continuous variables and the number of constraints. We also report a comparative with the speedup and efficiency of several strategies implemented for some available number of threads.

Scenario Cluster Lagrangian Decomposition in two stage stochastic mixed 0-1 optimization

In this paper we introduce four scenario Cluster based Lagrangian Decomposition (CLD) procedures for obtaining strong lower bounds to the (optimal) solution value of two-stage stochastic mixed 0-1 problems. At each iteration of the Lagrangian based procedures, the traditional aim consists of obtaining the solution value of the corresponding Lagrangian dual via solving scenario submodels once the nonanticipativity constraints have been dualized. Instead of considering a splitting variable representation over the set of scenarios, we propose to decompose the model into a set of scenario clusters. We compare the computational performance of the four Lagrange multiplier updating procedures, namely the Subgradient Method, the Volume Algorithm, the Progressive Hedging Algorithm and the Dynamic Constrained Cutting Plane scheme for different numbers of scenario clusters and different dimensions of the original problem. Our computational experience shows that the CLD bound and its computational effort depend on the number of scenario clusters to consider. In any case, our results show that the CLD procedures outperform the traditional LD scheme for single scenarios both in the quality of the bounds and computational effort. All the procedures have been implemented in a C++ experimental code. A broad computational experience is reported on a test of randomly generated instances by using the MIP solvers COIN-OR and CPLEX for the auxiliary mixed 0-1 cluster submodels, this last solver within the open source engine COIN-OR. We also give computational evidence of the model tightening effect that the preprocessing techniques, cut generation and appending and parallel computing tools have in stochastic integer optimization. Finally, we have observed that the plain use of both solvers does not provide the optimal solution of the instances included in the testbed with which we have experimented but for two toy instances in affordable elapsed time. On the other hand the proposed procedures provide strong lower bounds (or the same solution value) in a considerably shorter elapsed time for the quasi-optimal solution obtained by other means for the original stochastic problem.

Contribution of Resource-Based View and Entrepreneurial Orientation on Small Firm Growth

[EN] This research provides a useful framework for identifying a small firms’ propensity to engage in entrepreneurial orientation. We examine the impact of the Entrepreneurial Orientation (EO) as a main resource and capability on small firm’ growth. The growth seems to come out as an important demonstration of the entrepreneurial orientation of small firms (Davidsson, 1989; Green and Brown, 1997; Janney and Gregory, 2006). Thus, this research builds on prior conceptual research that suggests a positive integration between entrepreneurial orientation and resource-based view. In the first instance, the research will focus on reviewing literature in the emerging area of entrepreneurial orientation as it applies to growth oriented small firms and resource-based view of the firm. Secondly, an empirical study was developed based on a stratified sample of small firms of manufacturing industry. Data were submitted to a multivariate statistical analysis and a linear regression model was performed in order to predict the influence of the resources and capabilities on small firms’ growth. In this sense, we consider the construct growth as a dependent variable and the ones relates with resources and capabilities (entrepreneur resources, firm resources, networks and EO) as independent variables. The research results suggest a set of resources and capabilities that promote the growth of the small firms. Also, the EO seems to have a predictive value on growth. Explaining variables related with resources and capabilities and EO were identified as essential in growth oriented small firms. It was still possible to conclude that the entrepreneurial firms which grew seem to have resources and develop more capabilities and take advantage in the search for those competences. This attitude reflects on the EO of the firm. This study has important implication for both researchers and practitioners. It highlights the necessity of firms to develop superior EO of all their members and also to invest on better resources and consequently superior capabilities as a way of reaching higher levels of growth. While previous authors have attempted to analyse certain aspects of this process (linkage between entrepreneurial orientation and growth), this research developed a framework that combines these and others factors (resource-based view) pertinent to growth oriented small firms. The results support the necessity to identify explicative variables of multiple levels to explain the growth of small firms. The adoption of an entrepreneurial orientation as an indispensable variable to the growth oriented small firms seems pertinent.

Reference Points Based on Dynamic Optimisation: A Versatil Algorithm for Mixed Fishery Management with Bio-economic Agestructured Models

Single-species management objectives may not be consistent within mixed fisheries. They may lead species to unsafe situations, promote discarding of over-quota and/or misreporting of catches. We provide an algorithm for characterising bio-economic reference points for a mixed fishery as the steady-state solution of a dynamic optimal management problem. The optimisation problem takes into account: i) that species are fishing simultaneously in unselective fishing operations and ii)intertemporal discounting and fleet costs to relate reference points to discounted economic profits along optimal trajectories. We illustrate how the algorithm can be implemented by applying it to the European Northern Stock of Hake (Merluccius merluccius), where fleets also capture Northern megrim (Lepidorhombus whiffiagonis) and Northern anglerfish (Lophius piscatorius and Lophius budegassa). We find that optimal mixed management leads to a target reference point that is quite similar to the 2/3 of the Fmsy single-species (hake) target. Mixed management is superior to singlespecies management because it leads the fishery to higher discounted profits with higher long-term SSB for all species. We calculate that the losses due to the use of the Fmsy single-species (hake) target in this mixed fishery account for 11.4% of total discounted profits.

Generating cluster submodels from a multistage stochastic mixed integer optimization model using break stage

We present a scheme to generate clusters submodels with stage ordering from a (symmetric or a nonsymmetric one) multistage stochastic mixed integer optimization model using break stage. We consider a stochastic model in compact representation and MPS format with a known scenario tree. The cluster submodels are built by storing first the 0-1 the variables, stage by stage, and then the continuous ones, also stage by stage. A C++ experimental code has been implemented for reordering the stochastic model as well as the cluster decomposition after the relaxation of the non-anticipativiy constraints until the so-called breakstage. The computational experience shows better performance of the stage ordering in terms of elapsed time in a randomly generated testbed of multistage stochastic mixed integer problems.

Orientation-Dependent Adhesion Strength Of A Rigid Cylinder In Non-Slipping Contact With A Transversely Isotropic Half-Space

Recently, Chen and Gao [Chen, S., Gao, H., 2007. Bio-inspired mechanics of reversible adhesion: orientation-dependent adhesion strength for non-slipping adhesive contact with transversely isotropic elastic materials. J. Mech. Phys. solids 55, 1001-1015] studied the problem of a rigid cylinder in non-slipping adhesive contact with a transversely isotropic solid subjected to an inclined pulling force. An implicit assumption made in their study was that the contact region remains symmetric with respect to the center of the cylinder. This assumption is, however, not self-consistent because the resulting energy release rates at two contact edges, which are supposed to be identical, actually differ from each other. Here we revisit the original problem of Chen and Gao and derive the correct solution by removing this problematic assumption. The corrected solution provides a proper insight into the concept of orientation-dependent adhesion strength in anisotropic elastic solids. (c) 2008 Elsevier Ltd. All rights reserved.