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.

Experiences of Public-Private Collaboration for Stimulating

For over a decade now, work has been ongoing on the professional organization and management of town centre retail spaces in Spain under what is known as the Open Shopping Centre model. Introducing this model has involved a process of public-private collaboration in several different phases, conditioned to a large extent by the specific context of each initiative. With a view to furthering the process of benchmarking developed out of the experiences of recent years, we shall use case analysis to explain trends in initiatives for retail regeneration and stimulation undertaken in the Basque Country (an autonomous community in the north of Spain) since 2000. We analyze the factors that have prompted these initiatives, assessing and comparing the landmarks and conditions that have marked, or are determining, progress in the dynamic of collaboration between municipal authorities and retailers for a competitive improvement both in the retail sector and in the environment in which it operates: the city. Finally we list witch are these key factors.

New climate scenario framework implementation in the GCAM integrated assessment model

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