?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.relation=https%3A%2F%2Fmpra.ub.uni-muenchen.de%2F543%2F&rft.title=The+Barter+Method%3A+A+New+Heuristic+for+Global+Optimization+and+its+Comparison+with+the+Particle+Swarm+and+the+Differential+Evolution+Methods&rft.creator=Mishra%2C+SK&rft.subject=C6+-+Mathematical+Methods+%3B+Programming+Models+%3B+Mathematical+and+Simulation+Modeling&rft.subject=C63+-+Computational+Techniques+%3B+Simulation+Modeling&rft.subject=C61+-+Optimization+Techniques+%3B+Programming+Models+%3B+Dynamic+Analysis&rft.description=The+objective+of+this+paper+is+to+introduce+a+new+population-based+(stochastic)+heuristic+to+search+the+global+optimum+of+a+(continuous)+multi-modal+function+and+to+assess+its+performance+(on+a+fairly+large+number+of+benchmark+functions)+vis-%C3%A0-vis+that+of+two+other+well-established+and+very+powerful+methods%2C+namely%2C+the+Particle+Swarm+(PS)+and+the+Differential+Evolution+(DE)+methods+of+global+optimization.+We+will+call+this+new+method+the+Barter+Method+of+global+optimization.%0A%0AThis+method+is+based+on+the+well-known+proposition+in+welfare+economics+that+competitive+equilibria%2C+under+fairly+general+conditions%2C+tend+to+be+Pareto+optimal+In+its+simplest+version%2C+implementation+of+this+proposition+may+be+outlined+as+follows%3A%0A%0ALet+there+be+a+fairly+large+number+of+individuals+in+a+population+and+let+each+individual+own+(or+draw+from+the+environment)+an+m-element+real+vector+of+resources%2C+xi+%3D+(xi1%2C+xi2%2C+%E2%80%A6%2C+xim).+For+every+xi+there+is+a+(single-valued)+function+f(x)+that+may+be+used+as+a+measure+of+the+worth+of+xi+that+the+individual+would+like+to+optimize.+The+optimand+function+f(.)+is+unique+and+common+to+all+the+individuals.+Now%2C+let+the+individuals+in+the+(given)+population+enter+into+a+barter+of+their+resources+with+the+condition+that+(i)+a+transaction+is+feasible+across+different+persons+and+different+resources+only%2C+and+(ii)+the+resources+will+change+hands+(materialize)+only+if+such+a+transaction+is+beneficial+to+(more+desired+by)+both+the+parties+(in+the+barter).++The+choice+of+the+individuals%2C+(i+%2Ck)+and+the+resources%2C+(j%2C+l)+in+every+transaction+and+the+quantum+of+transaction+would+be+stochastic+in+nature.+If+such+transactions+are+allowed+for+a+large+number+of+times%2C+then+at+the+end+of+the+session%3A+(a)+every+individual+would+be+better+off+than+what+he+was+at+the+initial+position%2C+and+(b)+at+least+one+individual+would+reach+the+global+optimum.%0A%0AWe+have+uses+75+test+functions.+The+DE+succeeds+in+70+cases%2C+the+RPS+succeeds+in+60+cases%2C+while+the+Barter+method+succeeds+for+a+modest+number+of+51+cases.+The+DE+as+well+as+Barter+methods+are+unstable+for+stochastic+functions+(Yao-Liu%237+and+Fletcher-Powell+functions).+In+eight+cases%2C+the+Barter+method+could+not+converge+in+10000+iterations+(due+to+slow+convergence+rate)%2C+while+in+4+cases+the+MRPS+could+not+converge.+Seen+as+such%2C+the+barter+method+is+inferior+to+the+other+two+methods.+Additionally%2C+the+convergence+rate+of+the+Barter+method+is+slower+than+the+DE+as+well+as+the+MRPS.+However%2C+the+DE+and+the+RPS+have+a+history+of+a+full+decade+behind+them+and+they+have+been+improved+many+times.+In+the+present+exercise%2C+the+RPS+is+a+modified+version+(MRPS)+that+has+an+extra+ability+for+local+search.+The+DE+version+used+here+uses+the+latest+(available)+schemes+of+crossover%2C+mutation+and+recombination.++In+comparison+to+this%2C+the+Barter+method+is+a+nascent+one.++We+need+a+thorough+investigation+into+the+nature+and+performance+of+the+Barter+method.&rft.date=2006-10-21&rft.type=MPRA+Paper&rft.type=NonPeerReviewed&rft.format=application%2Fpdf&rft.language=en&rft.identifier=https%3A%2F%2Fmpra.ub.uni-muenchen.de%2F543%2F1%2FMPRA_paper_543.pdf&rft.identifier=++Mishra%2C+SK++(2006)%3A+The+Barter+Method%3A+A+New+Heuristic+for+Global+Optimization+and+its+Comparison+with+the+Particle+Swarm+and+the+Differential+Evolution+Methods.++++&rft.language=en