
Solving Optimization Problems with GridEnabled Technologies
by Enrique Alba and Antonio J. Nebro
Research in the ‘Networking and Emerging Optimization Research Line’ at the University of Málaga aims at solving optimization problems through the utilization of grid–enabled technologies and large computer networks.
Grid computing is a recent discipline related to the utilization of largescale distributed systems for a given purpose by taking advantage of the rich infrastructure provided by the Internet. To understand the basic idea that motivates our research, consider a grid of computers as a huge virtual multicomputer ready for processing, storage and communication. Since a grid can be made up of a set of geographically separate networks, enormous computer power is available for solving complex problems that are limited in CPU and that require long delays if solved in modern computer LANs.
Complex problems that can only be solved in nonpolynomial time arise in most fields of research and are becoming common in many areas of our lives: telecommunications, economy, bioinformatics, industrial environments,and so on. For such a wide spectrum of problems, heuristics come to the rescue, since exact techniques are unable to locate any kind of solution. This area is known as Networking and Emerging Optimization (NEO), and the GISUM group at the University of Málaga (Spain) is working on just these techniques.
In short, using Grid technology, our aim is to solve optimization problems that are otherwise out of the scope of researchers dealing with parallel algorithms. Five types of applications are usually identified as related to Grid computing: distributed supercomputing, highthroughput computing, ondemand computing, dataintensive computing and collaborative computing. At this stage of our research we are primary involved with the two first topics, ie distributed and highthroughput computing. However, we plan to enter the other three domains by developing an open optimization service for the Internet, solving datamining problems and facing software agent applications respectively. Figure 1 is an example of the goal of the present work: computing an exact Pareto front.

Figure 1: A simple example of a multiobjective optimization problem with the constraints (left), and its Pareto front (right). 
Multicriterion optimization in which several (nondominated) optimum solutions must be found is a promising research field. At present, this field lacks algorithms that could ensure the computation of the exact Pareto front for a general problem. We avoid this inconvenience by using an enumerativelike search that computes all the nondominated solutions in a grid. Later, researchers can use these results to find efficient heuristics achieving similar (optimal) results. We are in the first stage of research, and have solved problems at Málaga using a modest grid of around 110 processors. As simple as it sounds, finding the optimum Pareto front is extremely hard, even for small problems, and with most algorithms it is not guaranteed that the optimum front will be located for arbitrary problems as we do with our grid exact algorithm.

Figure 2: Tracking and managing the optimization algorithms in the grid with Condor. 
We are evaluating the performance of several gridenabled technologies for our applications. Concretely, we have tested Globus, Condor, Legion, and Sun Grid Engine. Of these, the first two seem the most suitable for optimization in the grid. The simplicity and powerful process management of Condor were greatly appreciated in setting up a grid from scratch within a few weeks. Globus is in this sense more complex to use, because users must deal with certificates, installation details and production tools that require a timeconsuming learning curve. However, Globus actually eases the next step of our research in connecting to foreign grids. In addition, we have tested the network usage and execution times of heuristic algorithms and tools like MPI on Globus with very satisfactory results, and this suggests that we could achieve fruitful research with Globus in the future.
Most of this work has been undertaken within the ongoing TRACER project (http://tracer.lcc.uma.es), which is developing advanced algorithms in close connection with the Internet. Two successful case studies in TRACER relating to Grid computing can be cited. Firstly, a grid algorithm was developed to compute the exact Pareto front of several hard multiobjective problems by using Condor in a grid with more than 110 computers (http://neo.lcc.uma.es/Software/ESaM). At present, we are extending the grid to other sites in Spain and Europe. Secondly, gridaware multiobjective heuristics, initially run on Globus, were developed. We are currently testing new grid algorithms derived from wellknown standard techniques like PAES or NSGA II.
We invite everyone to look at our results and contact us with any comments or suggestions for collaboration.
Link:
http://neo.lcc.uma.es
Please contact:
Enrique Alba, University of Málaga/SpaRCIM, Spain
Tel: +34 952 132803
Email: eatlcc.uma.es
