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Ant Stigmergy on the Grid: Optimizing the Cooling Process inContinuous Steel CastingPeter Koroˇsec1,JurijˇSilc1, Bogdan Filipiˇc2, and Erkki Laitinen31Joˇzef Stefan Institute2Joˇzef Stefan InstituteComputer Systems Department Department of Intelligent SystemsJamova 39, SI-1000 Ljubljana, Slovenia Jamova 39, SI-1000 Ljubljana, Slovenia{peter.korosec, jurij.silc}@ijs.si bogdan.fi[email protected] of OuluDepartment of Mathematical SciencesP.O. Box 3000, SF-90014 Oulu, Finlanderkki.laitinen@oulu.fiAbstractThe paper presents a new distributed metaheuristicalgorithm in an optimal control problem related to thecooling process in the continuous casting of steel. Theoptimization task is to tune 18 coolant flows in thecaster secondary cooling system to achieve the targetsurface temperatures along the slab. Sequential searchalgorithms are proved inefficient for this problem be-cause they take too much time to compute an appropri-ate solution. For this reason a new distributed searchalgorithm based on stigmergy perceived in ant colonywas developed. The algorithm was run on the Grid thatallows us to solve this optimization problem in muchshorter time. As a matter of fact, the computationtime can be decreased from half a day to a few hourswithout any decrease in the solution quality.1. IntroductionMost of the world steel production is nowadaysbased on continuous casting. This is a complex met-allurgical process in which liquid steel is cooled andshaped into semi-manufactures. To achieve properquality of cast steel, it is essential to control themetal flow and heat transfer during the casting pro-cess. They depend on numerous parameters, such asthe casting temperature, casting speed and coolantflows. Finding optimal values of process parametersis difficult since different, often conflicting criteria areinvolved, the number of possible parameter settings ishigh, and parameter tuning through real-world exper-imentation is not feasible because of costs and safetyrisk. Over the last years, however, several computa-tional techniques have been used to enhance the pro-cess performance and product characteristics, includ-ing knowledge-based heuristic search [3], genetic algo-rithms [1, 10], particle swarm optimization [18], andevolutionary multiobjective optimization [2].In this paper we report on numerical experiments inoptimizing secondary coolant flows for a casting ma-chine of the Ruukki steel plant in Finland using stig-mergic algorithm on the Grid. Here we meet withmulti-parameter optimization. Multi-parameter opti-mization is the process of finding a point in a multi-dimensional parameter space where a cost function isminimized and constraints satisfied. Most commonly,the cost function contains information about the prob-lem goal and the constraints the solution point has tomeet (constrained optimization).The paper describes the distributed optimization al-gorithm based on stigmergy and the problem that itsolves, provides the results of numerical experiments,and discusses their implications for future work.2. Ants on the GridThis section describes the basic concept and majorissues pertaining to distributed optimization algorithm1-4244-0054-6/06/$20.00 ©2006 IEEEbased on stigmergy that will be used on the Grid. Stig-mergy is a method of communication in decentralizedsystems where the individual parts of the system com-municate with one another by modifying their local en-vironment. For example, ants communicate by layingdown pheromone along their trails, so an ant colonyis a stigmergic system. The term stigmergy (from theGreek stigma = sting, and ergon = work) was orig-inally defined in 1959 by the French biologist Grass´e[12].Because of the nature of the ant-based algorithms wefirst have to discretize a continuous multi-parameterproblem and translate it into a graph representation(search graph). Then we use a selected optimizationtechnique to find the cheapest path in the constructedsearch graph; this path consists of the values of theoptimized parameters. For this purpose, we use an op-timization algorithm, the routes of which can be foundin the ant colony optimization (ACO) metaheuristic[5,6,7].We considered the multilevel approach and its po-tential to enhance the optimization procedure. Themultilevel approach in its most basic form involves re-cursive coarsening to create a hierarchy of approxima-tions to the original problem. An initial solution isfound (sometimes for the original problem, sometimesat the coarsest level) and then iteratively refined ateach level. As a general solution strategy the multi-level procedure has been in use for many years andhas been applied to various problem areas [22]. Wemerge stigmergy and the multilevel approach into onemethod, called the Multilevel Ant Stigmergy Algorithm(MASA) [14].Like many other metaheuristic approaches, theMASA admits direct parallelization schemes and par-allelism can be exploited on one or more scales [20].We applied it on the largest scale where entire searchprocedures can be performed concurrently. Such imple-mentation, called Distributed Multilevel Ant StigmergyAlgorithm (DMASA), is based on parallel interactingant colonies [16].2.1 Search graph constructionSearch graph construction consists of translation ofthe discrete parameter values of the problem into asearch graph G =(V,E) with a set of vertices V and setE of edges between the vertices. For each parameterpd, 1 ≤ d ≤ D, parameter value vd,i, 1 ≤ i ≤ nd,nd= |pd|, represents a vertex in a search graph, andeach vertex is connected to all the vertices that belongto the next parameter pd+1. The so-called start vertexis also added to the graph. This vertex is connected toall vertices of the parameter p1and used as a startingpoint for all ants.This way we transform the multi-parameter opti-mization problem into a problem of finding the cheap-est path. Once this is done, we can deploy the initialpheromone values on all the vertices.2.2 Multilevel approachCoarsening of the problem representation is done bymerging two or more neighboring vertices into one ver-tex; this is done in L iterations (we call them levels  =1, 2,...,L). Let us consider coarsening from level  tolevel +1 at distance d. Here Vd= {vd,1,...,vd,nd}is a set of vertices at level  and distance d of the searchgraph G,where1≤ d ≤ D.Ifn1dis the number ofvertices at the initial level of coarsening and distanced, then for every level  the


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