A7121B7F9A15>I<EA7FFEA2EA7000A7EA73E0EA7FF013F8EA7E3CEA7C1E1278130F1200A6EA401E12C0EA603CEA3878EA1FF0EA0FC0101C7E9A15>I<12E0A31200AC12E0A303127C910C>58 D<131C133EA2132E1367A2EBE78013C713C300017F1383138100037FA248C67EA21206000E1378380FFFF8A2381C003CA2121800387FA248131F80A248EB0780191D7F9C1C>65 D<EAFFF813FF38F00F80EB03C0EB01E0EB00F0A5EB01E0EB07C0B51280EBFE00EBFF8038F03FC0EB03E0EB01F013001478A514F0EB01E0EB07C0B51280EBFC00151D7C9C1C>I<EB3FC0EBFFF0EA03C03807803048C7FC121E5AA25AA35AA91278A37EA27E6C1308380780183803C0783800FFF0EB3F80151F7D9D1B>I<EAFFFC13FF38F00F80EB03E0EB01F0130014781438143CA2141C141EA8143CA3147814F0A2EB03E0EB0FC0B5120013FC171D7C9C1E>I<B512C0A200F0C7FCABB51280A200F0C7FCACB512C0A2121D7C9C19>I<B51280A200F0C7FCABB5FCA200F0C7FCAE111D7C9C18>I<EB3F803801FFF03803C0F838078038380F0018001E13005AA25AA35AA6EB07F8A2EB00381278A37EA27E7EEA07803803C0F83801FFF038003F80151F7D9D1C>I<00F013F0ADB5FCA2EAF000AE141D7C9C1D>I<12F0B3AB041D7C9C0C>I<1378B3A712C0EAE0F012FFEA7FE0EA1F800D1E7E9C14>I<00F0133C147814F0EB01E0EB03C0EB0780EB0F00131E5B5B5B5BEAF1F012F3EAF778EAFE7CEAFC3C7FEAF81F487E14801307EB03C014E01301EB00F0A21478147C161D7C9C1D>I<12F0B3A9EAFFFEA20F1D7C9C16>I<00FCEB07E0A300EE130DA300E71319A3EB803900E31331EBC071A200E11361A2EBE0E1A200E013C113F1EB7181A3EB3B01A3131EA313001B1D7C9C24>I<00FC1370A27E12EE12EF12E7A2138012E313C0A2EAE1E0A212E013F013701378A2133CA2131C131E130EA2130F130714F01303A2141D7C9C1D>I<133F3801FFE0487F3807C0F8380F807C381E001E003E131F003C7F48EB0780A348EB03C0A86C130700781480A2007C130F003C1400003E5B6C133E6C6C5A6C6C5A6CB45A6C5BD8003FC7FC1A1F7E9D1F>I<EAFFFC13FF38F00F80EB03C0EB01E0EB00F0A6EB01E01303EB0FC0B51280EBFE0000F0C7FCAD141D7C9C1B>I<EAFFF813FF38F00F80EB03C0EB01E0EB00F0A5EB01E01303EB0FC0B51280140013F8EAF03C131C131E7FA2EB0780A2EB03C0A2EB01E0EB00F0A21478151D7C9C1B>82D<EA03F8EA0FFEEA1C0F487E487E0060C7FC12E0A47E1278127FEA3FE0EA1FFCEA07FEEA01FF38001F801307EB03C0A21301A400C01380EAE00338F00700EA7C0EEA1FFCEA07F0121F7E9D17>I<B61280A2D8001EC7FCB3A9191D7F9C1C>I<00F01370B3A5007813E0A2383C01C0381E0380EA0F073807FE00EA01F8141E7C9C1D>I<00F8EB01E0007C14C06CEB0380001E1307001F1400380F800E0007131EEBC01C3803E03C000113386D5A000013F0EB78E0EB7DC0133F6D5A91C7FC7FAC1B1D809C1C>89 D<EA0FC0EA3FF0EA7FF8EA7038EA401C1200A213FC120F123FEA781C12E0A3EAF07CEA7FFC13DCEA3F1C0E127E9114>97D<EA07E0EA0FF8EA1FFCEA3C1CEA700413005AA612701304EA3C1CEA1FFCEA0FF8EA07E00E127E9112>99 D<130EABEA0F8EEA1FEEEA3FFEEA7C3EEA700EA212E0A612F0EA701EEA7C3EEA3FFEEA1FEEEA0F8E0F1D7E9C15>I<EA07C0EA1FE0EA3FF0EA7878EA7018EA601CEAFFFCA3EAE000A312701304EA3C1CEA3FFCEA1FF8EA07E00E127E9112>I<12E0ABEAE3E0EAEFF0EAFFF8EAF83CEAF01C12E0AD0E1D7D9C15>104 D<12F0A41200A71270B2041D7E9C0A>I<12E0AB133C137813F0EAE1E0EAE3C0EAE780EAEF00B4FC138012FBEAF9C0EAF1E012E013F013781338133C131E0F1D7D9C14>107 D<12E0B3AB031D7D9C0A>I<38E3F03F39EFF8FF80D8FFFD13C039F81F81E038F00F00EAE00EAD1B127D9122>I<EAE3E0EAEFF0EAFFF8EAF83CEAF01C12E0AD0E127D9115>I<EA03F0EA0FFC487EEA3C0F38780780EA700338E001C0A5EAF00300701380EA7807383C0F00EA1FFE6C5AEA03F012127F9115>I<EAE3E0EAEFF0EAFFF8EAF87CEAF01CEAE01E130EA6131CEAF03CEAF87CEAFFF8EAEFF0EAE3C0EAE000A80F1A7D9115>I<EAE38012E712EFEAFC005A5AA25AAB09127D910E>114D<EA1FC0EA3FF0127FEAF030EAE000A27E127FEA3FC0EA1FE0EA00F01338A21280EAF078EAFFF0EA7FE0EA1FC00D127F9110>I<121CA6EAFFE0A2EA1C00AC1320EA1FF0120FEA07C00C187F970F>I<EAE01CAE137CEAFFFCEA7FDCEA3F1C0E127D9115>I<EAE007A2EA7006130EA2EA381CA3EA1C38A3EA0E70A2EA0660120713E0EA03C0A210127F9113>I<EAE007A2EA700EA21278EA381CA2EA1C181338120CEA0E3013701206EA0760120313C01201A21380A2EA0300A25A12FE5A5A101A7F9113>121 D<EA7FFCA3EA007813F013E01201EA03C01380EA07005A121E121C123C5AEAFFFCA30E127F9112>I E /Fy24 123 df<12FCA61200B312FCA6061F7A9E13>58 D<147EA214FFA3903801EF80A3903803CFC014C7A290380787E01483010F7FA21403496C7EA2131E90383E00FCA2133C017C137EA2137801F87FA25B0001EC1F80A25B48B612C0A34815E09038C000075B000FEC03F0A248C713F81501A2003E15FC1500A24815FE167EA248157F163F28327EB12D>65D<B612F0A500FCC8FCB2B61280A400FCC8FCB3A51C327AB126>70D<EC3FE0903801FFFC010713FF011F14C04914E090387FC03F9038FF0007D801FCEB01C04848130048481440484814005B121F5B123F90C9FCA2127EA312FE5AA8913803FFF0A27E127EEC0001A27EA27F121F7F120F7F6C7E6C7E6C7E6CB4130390387FC01F6DB5FC6D14E0010714800101EBFC009038003FE024347CB22D>I<12FCB3B3AE06327AB113>73D<B46CEC07FCA36D140FA200FB150E6D141EA2D8F9F0143CA36D147C00F81578A26D14F8017C14F0A2017E1301A2013E14E0013F1303A26D14C0EC8007A2010F1480ECC00FA2010714006E5AA20103131EECF03E0101133CA2ECF87C01001378A3EC7CF0A3EC3CE0A2143F6E5AA36E5A91C8FC2E327AB13B>77 D<147F903803FFE0010F13F8013F13FE90387F80FF9039FE003F8048486D7ED803F0EB07E048486D7EA248486D7E48486D7EA290C8127C48157E003E153E007E153FA3007C8100FC1680AB6C153F007E1600A46C157EA26D14FE001F5D6D1301000F5D6C6C495A6D13076C6C495A6C6C495A6C6C495A90267F80FFC7FC6DB45A010F13F8010313E0D9007FC8FC29347CB232>79 D<13FE3807FF80001F13C04813E0EB03F0383800F812300020137CC7FCA5EB07FC13FF12075A383FC07C1300127C5AA414FCEAFC01EA7F0713FF6C137CEA1FFCEA0FE0161F7D9E20>97 D<12F8B3EB1F80EBFFE000F97FB57EEB83FCEAFE0048137E48133E80A3EC0F80A9EC1F00A25C143E6C137E6C5B38FF03F8EBFFF000FB5B00F85B013FC7FC19327AB123>I<EB3FC0EBFFF8000313FE4813FF380FE03F381F800FEB0002003E1300127E127CA25AA9127CA2127E003E13016C1303EB800F380FE07F6CB5FC6C13FEC613F8EB3FC0181F7D9E1E>I<EB3F80EBFFE0000313F8487FEA0FE0381F803E383F001E003E131F487FA2EC0780B6FCA400F8C8FCA5127CA27EA26C1480EBC003380FF01F6CB5FC000114006C13FCEB1FE0191F7E9E1E>101 D<EB07FC131F133F137FEBFC04EBF00012015B1203ABB512C0A43803E000B3A916327FB115>I<017F13F83901FFC7FC4813FF5A390FC1FC00EA1F80EB007CA2003E7FA66C5BA2EB80FC380FC1F8EBFFF0485B001D5BD81C7FC7FC003CC8FCA37E381FFFF814FF6C14804814C04814E0393E000FF048130300FCEB01F8481300A46C1301007EEB03F06CEB07E0EBE03F000FB512806C1400000113FC38003FE01E2E7E9E22>I<12F8B3EB3F80EBFFE000F913F000FB13F8EAFF8313004813FC48137CA35AB3A316327AB123>I<12FCA61200AB127CB3AD06307CAF10>I<12F8B3B3AE05327BB110>108 D<3AF81FC007F090397FF01FFC3AF9FFF87FFE00FB14FF3AFF81FDE07F9039007FC01F48028013804890383F000FA348133EB3A3291F7A9E36>I<38F83F80EBFFE000F913F000FB13F8EAFF8313004813FC48137CA35AB3A3161F7A9E23>I<EB1FC0EBFFF8487F000713FF390FE03F80391F800FC0EB0007003EEB03E0A248EB01F0A20078130000F814F8A76C1301007C14F0A26CEB03E0003F13076C14C0EBC01F390FF07F806CB51200000113FC6C5BEB1FC01D1F7E9E22>I<38F81F80EBFFE000F97FB57EEB83FCEAFE0048137E48133E143F80A2EC0F80A8141F1500A25C143E6C137E6C5B38FF03F8EBFFF000FB5B00F85B013FC7FC90C8FCAE192D7A9E23>I<EAF81E137E13FE12F912FBEAFFF0138013005AA25AA25AB30F1F7A9E17>114 D<EA03E0A9B512E0A43803E000B3A31420EBF0E03801FFF0A26C13C0EB7E0014287FA718>116 D<00F8137CB3A514FCA21301EAFC07EA7FFFEBFE7CEA3FFCEA0FE0161F7A9E23>I<007FB5FCA314FEC7127E14FC14F81301EB03F0EB07E014C0130FEB1F8014005B137E5B5B1201485A5B1207485A485A90C7FC5A127E007FB5FCB6FCA3181F7E9E1D>122 D E end%%EndProlog%%BeginSetup%%Feature: *Resolution 300dpiTeXDict begin%%EndSetup%%Page: 1 11 0 bop 225 193 a Fy(A)22 b(Genetic)h(Algo)n(rithm)e(fo)n(r)h(F)n(unction)g(Optimization:)29 b(A)225 276 y(Matlab)23 b(Implementation)225 392 y Fx(Christopher)15 b(R.)e(Houck)225 450 y(No)o(rth)h(Ca)o(rolina)g(State)g(Universit)o(y)225 509 y(and)225 567y(Je\013ery)h(A.)e(Joines)225 625 y(No)o(rth)h(Ca)o(rolina)g(State)g(Universit)o(y)225 683 y(and)225 741 y(Michael)h(G.)e(Ka)o(y)225799 y(No)o(rth)h(Ca)o(rolina)g(State)g(Universit)o(y)p225 861 1495 1 v 225 938 a Fw(A)c(genetic)e(algorithm)e(implemen)o(ted)g(in)j(Matlab)f(is)i(presen)o(ted.)i(Matlab)c(is)i(used)e(for)h(the)g(follo)o(wing)e(reasons:)225 980 y(it)15 b(pro)o(vides)f(man)o(y)g(built)g(in)h(auxiliary)e(functions)g(useful)h(for)h(function)e(optimization;)h(it)h(is)h(completely)225 1021 y(p)q(ortable;)9b(and)h(it)g(is)h(e\016cien)o(t)f(for)g(n)o(umerical)e(computation)o(s.)13 b(The)e(genetic)e(algorithm)f(to)q(olb)q(o)o(x)g(dev)o(elop)q(ed)225 1063 y(is)15 b(tested)f(on)h(a)h(series)e(of)h(non-linear,)f(m)o(ulti-mo)q(d)o(al,)f(non-con)o(v)o(ex)g(test)h(problems)g(and)g(compared)f(with)225 1104 y(results)e(using)f(sim)o(ulated)g(annealing.)j(The)f(genetic)e(algorithm)f(using)i(a)h(\015oat)f(represen)o(tati)o(on)e(is)j(found)e(to)225 1146 y(b)q(e)g(sup)q(erior)f(to)h(b)q(oth)g(a)g(binary)f(genetic)g(algorithm)f(and)h(sim)o(ulated)g(annealing)e(in)k(terms)e(of)h(e\016ciency)g(and)2251187 y(qualit)o(y)g(of)h(solution.)j(The)e(use)f(of)h(genetic)d(algorithm)g(to)q(olb)q(o)o(x)h(as)i(w)o(ell)f(as)h(the)f(co)q(de)g(is)g(in)o(tro)q(duced)e(in)i(the)225 1229 y(pap)q(er.)2251289 y(Categories)f(and)i(Sub)r(ject)e(Descriptors:)k(G.1)d([)pFv(Numerical)i(Analysis)p Fw(]:)j(Optimization|)p Fu(Unc)n(onstr)n(aine)n(d)225 1330 y(Optimization,)d(nonline)n(ar)h(pr)n(o)n(gr)n(amming,)h(gr)n(adient)f(metho)n(ds)225 1389 y Fw(General)c(T)m(erms:)k(Optimization,)9 b(Algorithms)225 1447 y(Additional)f(Key)i(W)m(ords)f(and)g(Phrases:)k(genetic)8 b(algorithms,)g(m)o(ultimo)q(d)o(al)f(noncon)o(v)o(ex)g(functions,)h(Matlab)p 225 1505 V 2251652 a Fx(1.)20 b(INTRODUCTION)225 1720 y Ft(Algorithms)12b(for)i(function)h(optimization)c(are)k(generally)f(limited)e(to)i(con)o(v)o(ex)h(regular)f(func-)225 1770 y(tions.)24 b(Ho)o(w)o(ev)o(er,)17b(man)o(y)d(functions)i(are)g(m)o(ulti-modal,)d(discon)o(tin)o(uous,)j(and)g(nondi\013eren-)p 225 1860 V 225 1910 a Fw(Name:)f(Christopher)9b(R.)i(Houc)o(k)225 1951 y(Address:)21 b(North)14 b(Carolina)f(State)g(Univ)o(ersit)o(y)m(,)h(Bo)o(x)g(7906,)g(Raleigh,)f(NC,)j(27695-7906)o(,USA,\(91)o(9\))c(515-)225 1993 y(5188,\(919\))d(515-1543,c)n(hou)o(c)o(k)o(@eos.nc)o(su.e)o(du)225 2034 y(A\016liation:)14b(North)d(Carolina)f(State)g(Univ)o(ersit)o(y)225 2076y(Name:)15 b(Je\013ery)10 b(A.)i(Joines)225 2117 y(Address:)21b(North)14 b(Carolina)f(State)g(Univ)o(ersit)o(y)m(,)h(Bo)o(x)g(7906,)g(Raleigh,)f(NC,)j(27695-7906)o(,USA,\(91)o(9\))c(515-)2252159 y(5188,\(919\))d(515-1543,j)o(join)o(e@eos.)o(ncsu)o(.ed)o(u)2252200 y(A\016liation:)14 b(North)d(Carolina)f(State)g(Univ)o(ersit)o(y)225 2242 y(Name:)15 b(Mic)o(hael)10 b(G.)h(Ka)o(y)2252283 y(Address:)21 b(North)14 b(Carolina)f(State)g(Univ)o(ersit)o(y)m(,)h(Bo)o(x)g(7906,)g(Raleigh,)f(NC,)j(27695-7906)o(,USA,\(91)o(9\))c(515-)225 2325 y(2008,\(919\))d(515-1543,k)m(a)o(y@eo)o(s.nc)o(su.e)o(du)225 2366 y(A\016liation:)14 b(North)d(Carolina)f(State)g(Univ)o(ersit)o(y)225 2408 y(Sp)q(onsor:)j(This)e(researc)o(h)e(w)o(as)i(funded)e(in)h(part)g(b)o(y)g(the)g(National)f(Science)g(F)m(oundation)f(under)i(gran)o(t)f(n)o(um-)225 2449 y(b)q(er)i(DMI-9322834.)peop%%Page: 2 22 1 bop 225 125 a Fs(2)71 b Fr(\001)78 b Fs(C.)12 b(Houck)h(et)g(al.)225 233 y Ft(tiable.)25 b(Sto)q(c)o(hastic)17 b(sampling)d(metho)q(ds)i(ha)o(v)o(e)h(b)q(een)g(used)h(to)e(optimize)f(these)j(functions.)225283 y(Whereas)e(traditional)d(searc)o(h)j(tec)o(hniques)g(use)g(c)o(haracteristics)g(of)f(the)g(problem)f(to)g(deter-)225332 y(mine)f(the)i(next)h(sampling)c(p)q(oin)o(t)i(\(e.g.,)f(gradien)o(ts,)i(Hessians,)g(linearit)o(y)m(,)e(and)i(con)o(tin)o(uit)o(y\),)225382 y(sto)q(c)o(hastic)f(searc)o(h)g(tec)o(hniques)g(mak)o(e)d(no)i(suc)o(h)h(assumptions.)i(Instead,)e(the)f(next)h(sampled)225432 y(p)q(oin)o(t\(s\))e(is\(are\))g(determined)f(based)i(on)e(sto)q(c)o(hastic)i(sampling/decision)c(rules)j(rather)g(than)225482 y(a)i(set)g(of)g(deterministic)f(decision)h(rules.)267532 y(Genetic)21 b(algorithms)d(ha)o(v)o(e)i(b)q(een)i(used)f(to)g(solv)o(e)f(di\016cult)g(problems)g(with)g(ob)r(jectiv)o(e)225582 y(functions)13 b(that)h(do)f(not)h(p)q(ossess)h(\\nice")e(prop)q(erties)i(suc)o(h)f(as)g(con)o(tin)o(uit)o(y)m(,)d(di\013eren)o(tiabilit)o(y)m(,)225 631 y(satisfaction)18 b(of)f(the)i(Lipsc)o(hitz)f(Condition,)g(etc.[Da)o(vis)f(1991;)i(Goldb)q(erg)f(1989;)h(Holland)225681 y(1975;)c(Mic)o(halewicz)h(1994].)22 b(These)c(algorithms)13b(main)o(tain)g(and)j(manipulate)e(a)h(family)m(,)d(or)225731 y(p)q(opulation,)h(of)g(solutions)h(and)g(implemen)o(t)e(a)i(\\surviv)n(al)e(of)i(the)h(\014ttest")g(strategy)g(in)f(their)225781 y(searc)o(h)h(for)e(b)q(etter)i(solutions.)i(This)c(pro)o(vides)h(an)f(implicit)e(as)i(w)o(ell)g(as)g(explicit)g(parallelism)225831 y(that)i(allo)o(ws)e(for)i(the)g(exploitation)e(of)h(sev)o(eral)i(promising)c(areas)j(of)g(the)g(solution)f(space)h(at)225880 y(the)g(same)e(time.)19 b(The)14 b(implicit)e(paral