Observations in using Grid-enabled technologies for solving multi-objective optimization problems

https://doi.org/10.1016/j.parco.2006.06.004Get rights and content

Abstract

In this paper, we analyze some technical issues concerning the use of Grid-enabled technologies based on the Globus Toolkit to solve multi-objective optimization problems. We develop two distributed algorithms: an enumerative search and an evolutionary algorithm. The former is a simple technique, whose high time complexity is mastered down to acceptable execution times to some extent by the use of a Grid-enabled computing system such Globus. The second algorithm is an extension of PAES, a sequential evolutionary algorithm. The parallel results indicate that using Globus is a promising research line to solve multi-objective problems in Grid computing environments.

Introduction

A multi-objective optimization problem (MOP) can be defined as the problem of finding a vector of decision variables which satisfies constraints and optimizes a vector function whose elements represent a set of objective functions. These functions form a mathematical description of performance criteria which are usually in conflict with each other. Hence, the term “optimize” means finding a solution that hopefully contains values for all the objective functions that are acceptable to the designer [1]. More formally:

Definition MOP

Find a vector x=[x1,x2,,xn] which satisfies the m inequality constraints gi(x)0,i=1,2,,m, the p equality constraints hi(x)=0, i = 1, 2,  , p, and optimizes the vector function f¯(x)=[f1(x),f2(x),,fk(x)]T, where x¯=[x1,x2,,xn]T is the vector of decision variables.

In other words, one wishes to determine the particular set {x1,x2,,xn} yielding optimum values for all simultaneously considered k objective functions from among the set of all values satisfying the constraints.

Generally, multi-objective optimization does not restrict to finding a unique single solution, but a set of solutions called non-dominated solutions. Each solution in this set is said to be a Pareto optimum, and when they are plotted in the objective space they are collectively known as the Pareto front.

Obtaining the Pareto front of a given problem is the main goal of multi-objective optimization. The techniques that can be used to compute a Pareto front can be classified into exact and heuristic ones. In recent years, heuristic methods have been widely studied. In particular, evolutionary algorithms have been investigated by many authors [2], [3]. These methods do not guarantee to obtain the optimal solution, but they do provide near optimal solutions to a wide range of optimization problems for which exact methods are impractical.

In contrast to heuristic methods, enumerative search is a conceptually simple search strategy based on evaluating each possible solution in a finite search space, and thus it is able to find optimal solutions. The drawback of this technique resides in its inability to scale as the search space becomes larger. Despite this inconvenience, the results that can be obtained by using enumeration are of great interest to the multi-objective optimization research community, because the resulting Pareto fronts can be used to be compared against those obtained by using heuristic algorithms. In consequence, the quality of the solutions produced by these heuristic algorithms can be measured in a non-subjective way by researchers. In fact, enumeration is the only way of computing the exact Pareto front for an arbitrary multi-objective problem.

In this context, the increasing impact of Grid computing in last years [4], [5] makes this kind of systems to appear as a powerful solution for complex tasks demanding high computational resources that cannot be addressed in normal clusters. By using some Grid-enabled technology, enumerative methods can be viable to obtain optimal solutions for scenarios in which this is mandatory. Obviously, this does not mean that Grids are to replace heuristic techniques by enumerative search; when optimization problems exhibit a combinatorial behavior, the computational requirements grow exponentially, so even using a large Grid computing system is impractical. On the other hand, heuristic techniques can take advantage of Grid computing systems to solve complex problems of practical interest.

Much of the Grid technology relies on the Globus Toolkit [6]. Globus has emerged as the de facto standard for Grid computing. Globus allows researchers to set up a Grid of computers through different Internet administrative domains, solving the problems of resource management and security. Some examples of its wide are EU DataGrid (http://eu-datagrid.web.cern.ch/eu-datagrid/), TeraGrid (http://www.teragrid.org), and the NASA’s Information Power Grid (http://www.ipg.nasa.gov).

In this paper, we first analyze the utilization of the Globus Toolkit in order to parallelize an enumerative search algorithm for solving multi-objective optimization problems. We have built our test Grid in the context of a cluster of computers with the goal of obtaining experiences with this Grid technology, which will guide us to consider the development of more complex algorithms in the future in larger computational Grids. Second, we use Globus to develop a Grid-based evolutionary algorithm; in concrete, we have developed gPAES, a Grid extension of the well-known PAES algorithm [7].

The paper is organized as follows. In Section 2, we discuss related work concerning multi-objective optimization and parallel computing. Section 3 reviews the major components of the Globus Toolkit. It is followed by the description of the enumerative search algorithm for computing exact Pareto fronts in Section 4. Section 5 details the application of Globus to run the new gPAES algorithm. Finally, we outline the conclusions and future research lines in Section 6.

Section snippets

Related work

Parallel computers have been widely used in the field of mono-objective optimization [8], [9]. In the case of exact techniques, a typical example is the solution of optimization problems by means of parallel branch and bound algorithms [10]. The idea is, in general, to solve the problems more rapidly or to solve more complex problems. In the context of heuristic methods, parallelism is not only a way for speeding up the computations, but for developing more efficient models of search: a

Globus

The Globus project seeks to enable the construction of computational Grids. In this context, a Grid is a hardware and software infrastructure that provides dependable, consistent, and pervasive access to high-end computational capabilities, despite the geographical distribution of both, resources and users. A central element of Globus is the Globus Toolkit, a community-based, open-architecture, open-source set of services and software libraries that supports Grids and Grid applications.

Enumerative search algorithm

In this section, we describe the sequential enumerative search algorithm we have developed as well as its parallelization using Globus.

Globus and heuristic techniques for multi-objective optimization

We now turn to apply Globus to run a distributed evolutionary algorithm. Furthermore, we will make use of the Pareto fronts obtained by the enumerative search algorithm to evaluate the quality of the solutions produced by this evolutionary algorithm. As commented in the introduction, this is the main use that justifies the interest in developing a Grid-enabled enumerative search algorithm, as we have already shown in [32].

Our Grid-enabled evolutionary algorithm, named gPAES, is based on the

Conclusions and future work

Grid-enabled technologies offer a strategic opportunity to develop new algorithms for solving optimization problems. In this context, we have used the Globus Toolkit, a de facto standard system for Grid computing, to implement a distributed enumerative search algorithm for solving multi-objective problems. Our goal has been to gain experience with Grid technologies to face more complex algorithms in the future, as we did with 110 machines and Condor in [32].

We have solved a benchmark composed

Acknowledgements

This work has been partially funded by the Ministry of Science and Technology and FEDER under contract TIN2005-08818-C04-01 (the OPLINK project).

References (38)

  • F. de Toro Negro et al.

    PSFGA: parallel processing and evolutionary computation for multiobjective optimisation

    Parallel Computing

    (2004)
  • A. Osyczka

    Multicriteria Optimization for Engineering Design

    (1985)
  • K. Deb

    Multi-Objective Optimization using Evolutionary Algorithms

    (2001)
  • C. Coello et al.

    Evolutionary Algorithms for Solving Multi-Objective Problems, Genetic Algorithms and Evolutionary Computation

    (2002)
  • M. Baker et al.

    Grids and grid technologies for wide area distributed computing

    Software: Practice and Experience

    (2002)
  • I. Foster et al.

    The Grid: Blueprint for a New Computing Infrastructure

    (1999)
  • I. Foster et al.

    Globus: a metacomputing infrastructure toolkit

    International Journal of Supercomputer Applications

    (1997)
  • J. Knowles et al.

    Approximating the nondominated front using the Pareto archived evolution strategy

    Evolutionary Computation

    (2000)
  • A. Grama et al.

    State of the art in parallel search techniques for discrete optimization

    IEEE Transactions on Knowledge and Data Engineering

    (1999)
  • A. Migdalas et al.

    Parallel Computing in Optimization

  • B. Gendron et al.

    Parallel branch and bound algorithms: survey and synthesis

    Operations Research

    (1994)
  • E. Alba et al.

    Parallelism and evolutionary algorithms

    IEEE Transactions on Evolutionary Computation

    (2002)
  • E. Alba et al.

    A survey of parallel distributed genetic algorithms

    Complexity

    (1999)
  • D. Van Veldhuizen et al.

    Considerations in engineering parallel multiobjective evolutionary algorithms

    IEEE Transactions on Evolutionary Computation

    (2003)
  • J. Lemesre, C. Dhaenens, E.-G. Talbi, A parallel exact method for a bicriteria permutation flow-shop problem, in:...
  • D. Van Veldhuizen, G. Lamont, Multiobjective evolutionary algorithm test suites, in: Proc. of the 1999 ACM Symp. on...
  • J. Kamiura, T. Hiroyasu, M. Miki, S. Watanabe, MOGADES: multi-objective genetic algorithm with distributed environment...
  • N. Keerativuttitumrong, C. Chaiyaratana, V. Varavithya, Multi-objective co-operative co-evolutionary genetic algorithm,...
  • M. Knarr, M. Goltz, G. Lamont, J. Huang, In situ bioremediation of perchlorate-contaminated groundwater using a...
  • Cited by (0)

    View full text