Construction Example for Algebra System Using  Harmony Search Algorithm

<table class="algorithm-group"><tr><td><table class="algorithm" id="alg1"><tr><td colspan="2"><b>If fitness  </b><svg height="15.1401pt" id="M74" style="vertical-align:-4.1023pt" version="1.1" viewbox="-0.0498162 -11.0378 36.3997 15.1401" width="36.3997pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0135,0,0,-0.0135,0,2.07113e-005)"><path d="M332 -241C217 -138 149 60 149 271C149 483 216 680 332 783L312 808C148 686 74 491 74 272V271C74 50 148 -146 312 -266L332 -241Z" id="g119-5"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="385" vert-adv-y="385"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,5.236,0)"><path d="M700 0V35C631 42 609 53 567 118C509 208 460 288 401 381C449 447 492 506 526 546C567 595 594 607 658 615V650H417V615C481 603 484 593 465 557C441 512 406 457 375 417C333 483 302 536 285 568C273 591 271 603 326 615V650H25V615C93 608 120 591 148 544C201 461 242 391 290 312C233 226 163 135 127 90C98 57 63 41 8 35V0H259V35C192 46 183 54 207 97C228 137 269 202 316 273C390 149 413 111 423 93C440 61 445 47 379 35V0H700Z" id="g13-86"></path><glyph.data ascent="1024" descent="-360" horiz-adv-x="693" vert-adv-y="693"></glyph.data></g><g transform="matrix(.0095,0,0,-0.0095,14.72,-5.984)"><path d="M524 0V26C466 32 460 36 460 104V297C460 393 411 449 331 449C302 449 276 437 248 419C223 402 201 387 181 372V451C137 432 90 420 42 411V388C96 378 102 374 102 310V104C102 38 97 33 29 26V0H246V26C187 32 181 36 181 104V339C211 365 250 390 290 390C357 390 381 345 381 276V109C381 40 374 32 315 26V0H524Z" id="g190-111"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="547" vert-adv-y="547"></glyph.data></g><g transform="matrix(.0095,0,0,-0.0095,19.869,-5.984)"><path d="M380 106C343 72 306 56 265 56C195 56 116 112 115 248C235 252 361 262 377 265C396 269 400 277 400 297C400 374 333 449 250 449H249C198 449 144 421 103 376S37 269 37 201C37 88 109 -12 232 -12C263 -12 332 6 395 84L380 106ZM225 412C281 412 315 364 314 312C314 297 308 292 290 292C232 290 176 289 120 289C135 370 180 412 225 412Z" id="g190-102"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="425" vert-adv-y="425"></glyph.data></g><g transform="matrix(.0095,0,0,-0.0095,23.976,-5.984)"><path d="M696 437H516V411C580 402 587 397 574 345C555 271 527 183 505 114H503C461 222 420 328 383 432H357C315 316 278 214 241 118H239C214 195 189 274 165 350C151 396 156 402 216 411V437H9V411C57 405 65 398 83 346C125 226 162 108 199 -11H227C267 100 308 199 346 300C387 195 428 97 468 -11H497C542 124 587 257 617 337C637 392 646 404 696 411V437Z" id="g190-120"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="685" vert-adv-y="685"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,31.029,2.07113e-005)"><path d="M311 271V272C311 491 237 686 73 808L53 783C169 680 236 483 236 271C236 60 168 -138 53 -241L73 -266C237 -146 311 50 311 271Z" id="g119-6"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="385" vert-adv-y="385"></glyph.data></g></svg> is be<b>tt</b>er than fitness <svg height="15.633pt" id="M75" style="vertical-align:-4.102301pt" version="1.1" viewbox="-0.0498162 -11.5307 41.5972 15.633" width="41.5972pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0135,0,0,-0.0135,0,2.07113e-005)"><path d="M332 -241C217 -138 149 60 149 271C149 483 216 680 332 783L312 808C148 686 74 491 74 272V271C74 50 148 -146 312 -266L332 -241Z" id="g119-5"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="385" vert-adv-y="385"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,5.236,0)"><path d="M700 0V35C631 42 609 53 567 118C509 208 460 288 401 381C449 447 492 506 526 546C567 595 594 607 658 615V650H417V615C481 603 484 593 465 557C441 512 406 457 375 417C333 483 302 536 285 568C273 591 271 603 326 615V650H25V615C93 608 120 591 148 544C201 461 242 391 290 312C233 226 163 135 127 90C98 57 63 41 8 35V0H259V35C192 46 183 54 207 97C228 137 269 202 316 273C390 149 413 111 423 93C440 61 445 47 379 35V0H700Z" id="g13-86"></path><glyph.data ascent="1024" descent="-360" horiz-adv-x="693" vert-adv-y="693"></glyph.data></g><g transform="matrix(.0095,0,0,-0.0095,14.72,-5.984)"><path d="M696 437H516V411C580 402 587 397 574 345C555 271 527 183 505 114H503C461 222 420 328 383 432H357C315 316 278 214 241 118H239C214 195 189 274 165 350C151 396 156 402 216 411V437H9V411C57 405 65 398 83 346C125 226 162 108 199 -11H227C267 100 308 199 346 300C387 195 428 97 468 -11H497C542 124 587 257 617 337C637 392 646 404 696 411V437Z" id="g190-120"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="685" vert-adv-y="685"></glyph.data></g><g transform="matrix(.0095,0,0,-0.0095,21.14,-5.984)"><path d="M257 449C165 449 37 374 37 209C37 98 119 -12 256 -12C355 -12 473 65 473 226C473 349 381 449 257 449ZM244 416C333 416 380 320 380 204C380 67 329 21 267 21C184 21 130 115 130 241C130 354 184 416 244 416Z" id="g190-112"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="510" vert-adv-y="510"></glyph.data></g><g transform="matrix(.0095,0,0,-0.0095,25.862,-5.984)"><path d="M181 342V451C133 431 89 419 40 411V388C98 381 102 377 102 311V104C102 38 95 32 33 26V0H263V26C186 32 181 38 181 104V287C203 343 235 372 261 372C277 372 289 366 304 352C310 346 318 345 330 350C349 359 362 379 362 399C362 422 338 449 304 449C256 449 213 393 183 342H181Z" id="g190-115"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="371" vert-adv-y="371"></glyph.data></g><g transform="matrix(.0095,0,0,-0.0095,29.324,-5.984)"><path d="M319 325C317 349 306 409 297 431C277 440 250 449 209 449C117 449 57 389 57 319C57 243 122 209 182 182C232 159 261 135 261 91C261 48 227 21 190 21C130 21 85 79 68 145L41 140C41 104 51 36 58 22C75 7 121 -12 172 -12C252 -12 337 35 337 126C337 195 286 231 210 262C166 281 126 304 126 348C126 388 152 417 191 417C240 417 274 378 294 318L319 325Z" id="g190-116"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="367" vert-adv-y="367"></glyph.data></g><g transform="matrix(.0095,0,0,-0.0095,32.756,-5.984)"><path d="M298 36L289 62C276 55 253 45 228 45C202 45 169 60 169 141V397H276C289 405 292 426 282 437H169V574L155 576L90 509V437H45L17 408L21 397H90V107C90 28 125 -12 188 -12C198 -12 213 -8 230 1L298 36Z" id="g190-117"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="305" vert-adv-y="305"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,36.227,2.07113e-005)"><path d="M311 271V272C311 491 237 686 73 808L53 783C169 680 236 483 236 271C236 60 168 -138 53 -241L73 -266C237 -146 311 50 311 271Z" id="g119-6"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="385" vert-adv-y="385"></glyph.data></g></svg>  <b>then</b></td></tr><tr><td colspan="2">  <svg height="11.5805pt" id="M76" style="vertical-align:-0.04979992pt" version="1.1" viewbox="-0.0498162 -11.5307 72.5075 11.5805" width="72.5075pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path d="M700 0V35C631 42 609 53 567 118C509 208 460 288 401 381C449 447 492 506 526 546C567 595 594 607 658 615V650H417V615C481 603 484 593 465 557C441 512 406 457 375 417C333 483 302 536 285 568C273 591 271 603 326 615V650H25V615C93 608 120 591 148 544C201 461 242 391 290 312C233 226 163 135 127 90C98 57 63 41 8 35V0H259V35C192 46 183 54 207 97C228 137 269 202 316 273C390 149 413 111 423 93C440 61 445 47 379 35V0H700Z" id="g13-86"></path><glyph.data ascent="1024" descent="-360" horiz-adv-x="693" vert-adv-y="693"></glyph.data></g><g transform="matrix(.0095,0,0,-0.0095,9.484,-5.984)"><path d="M696 437H516V411C580 402 587 397 574 345C555 271 527 183 505 114H503C461 222 420 328 383 432H357C315 316 278 214 241 118H239C214 195 189 274 165 350C151 396 156 402 216 411V437H9V411C57 405 65 398 83 346C125 226 162 108 199 -11H227C267 100 308 199 346 300C387 195 428 97 468 -11H497C542 124 587 257 617 337C637 392 646 404 696 411V437Z" id="g190-120"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="685" vert-adv-y="685"></glyph.data></g><g transform="matrix(.0095,0,0,-0.0095,15.904,-5.984)"><path d="M257 449C165 449 37 374 37 209C37 98 119 -12 256 -12C355 -12 473 65 473 226C473 349 381 449 257 449ZM244 416C333 416 380 320 380 204C380 67 329 21 267 21C184 21 130 115 130 241C130 354 184 416 244 416Z" id="g190-112"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="510" vert-adv-y="510"></glyph.data></g><g transform="matrix(.0095,0,0,-0.0095,20.627,-5.984)"><path d="M181 342V451C133 431 89 419 40 411V388C98 381 102 377 102 311V104C102 38 95 32 33 26V0H263V26C186 32 181 38 181 104V287C203 343 235 372 261 372C277 372 289 366 304 352C310 346 318 345 330 350C349 359 362 379 362 399C362 422 338 449 304 449C256 449 213 393 183 342H181Z" id="g190-115"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="371" vert-adv-y="371"></glyph.data></g><g transform="matrix(.0095,0,0,-0.0095,24.088,-5.984)"><path d="M319 325C317 349 306 409 297 431C277 440 250 449 209 449C117 449 57 389 57 319C57 243 122 209 182 182C232 159 261 135 261 91C261 48 227 21 190 21C130 21 85 79 68 145L41 140C41 104 51 36 58 22C75 7 121 -12 172 -12C252 -12 337 35 337 126C337 195 286 231 210 262C166 281 126 304 126 348C126 388 152 417 191 417C240 417 274 378 294 318L319 325Z" id="g190-116"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="367" vert-adv-y="367"></glyph.data></g><g transform="matrix(.0095,0,0,-0.0095,27.521,-5.984)"><path d="M298 36L289 62C276 55 253 45 228 45C202 45 169 60 169 141V397H276C289 405 292 426 282 437H169V574L155 576L90 509V437H45L17 408L21 397H90V107C90 28 125 -12 188 -12C198 -12 213 -8 230 1L298 36Z" id="g190-117"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="305" vert-adv-y="305"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,34.776,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z" id="g117-34"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="587" vert-adv-y="587"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,46.514,0)"><path d="M700 0V35C631 42 609 53 567 118C509 208 460 288 401 381C449 447 492 506 526 546C567 595 594 607 658 615V650H417V615C481 603 484 593 465 557C441 512 406 457 375 417C333 483 302 536 285 568C273 591 271 603 326 615V650H25V615C93 608 120 591 148 544C201 461 242 391 290 312C233 226 163 135 127 90C98 57 63 41 8 35V0H259V35C192 46 183 54 207 97C228 137 269 202 316 273C390 149 413 111 423 93C440 61 445 47 379 35V0H700Z" id="g13-86"></path><glyph.data ascent="1024" descent="-360" horiz-adv-x="693" vert-adv-y="693"></glyph.data></g><g transform="matrix(.0095,0,0,-0.0095,55.998,-5.984)"><path d="M524 0V26C466 32 460 36 460 104V297C460 393 411 449 331 449C302 449 276 437 248 419C223 402 201 387 181 372V451C137 432 90 420 42 411V388C96 378 102 374 102 310V104C102 38 97 33 29 26V0H246V26C187 32 181 36 181 104V339C211 365 250 390 290 390C357 390 381 345 381 276V109C381 40 374 32 315 26V0H524Z" id="g190-111"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="547" vert-adv-y="547"></glyph.data></g><g transform="matrix(.0095,0,0,-0.0095,61.148,-5.984)"><path d="M380 106C343 72 306 56 265 56C195 56 116 112 115 248C235 252 361 262 377 265C396 269 400 277 400 297C400 374 333 449 250 449H249C198 449 144 421 103 376S37 269 37 201C37 88 109 -12 232 -12C263 -12 332 6 395 84L380 106ZM225 412C281 412 315 364 314 312C314 297 308 292 290 292C232 290 176 289 120 289C135 370 180 412 225 412Z" id="g190-102"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="425" vert-adv-y="425"></glyph.data></g><g transform="matrix(.0095,0,0,-0.0095,65.254,-5.984)"><path d="M696 437H516V411C580 402 587 397 574 345C555 271 527 183 505 114H503C461 222 420 328 383 432H357C315 316 278 214 241 118H239C214 195 189 274 165 350C151 396 156 402 216 411V437H9V411C57 405 65 398 83 346C125 226 162 108 199 -11H227C267 100 308 199 346 300C387 195 428 97 468 -11H497C542 124 587 257 617 337C637 392 646 404 696 411V437Z" id="g190-120"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="685" vert-adv-y="685"></glyph.data></g></svg>; (<svg height="11.5805pt" id="M77" style="vertical-align:-0.04979992pt" version="1.1" viewbox="-0.0498162 -11.5307 31.126 11.5805" width="31.126pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path d="M700 0V35C631 42 609 53 567 118C509 208 460 288 401 381C449 447 492 506 526 546C567 595 594 607 658 615V650H417V615C481 603 484 593 465 557C441 512 406 457 375 417C333 483 302 536 285 568C273 591 271 603 326 615V650H25V615C93 608 120 591 148 544C201 461 242 391 290 312C233 226 163 135 127 90C98 57 63 41 8 35V0H259V35C192 46 183 54 207 97C228 137 269 202 316 273C390 149 413 111 423 93C440 61 445 47 379 35V0H700Z" id="g13-86"></path><glyph.data ascent="1024" descent="-360" horiz-adv-x="693" 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342V451C133 431 89 419 40 411V388C98 381 102 377 102 311V104C102 38 95 32 33 26V0H263V26C186 32 181 38 181 104V287C203 343 235 372 261 372C277 372 289 366 304 352C310 346 318 345 330 350C349 359 362 379 362 399C362 422 338 449 304 449C256 449 213 393 183 342H181Z" id="g190-115"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="371" vert-adv-y="371"></glyph.data></g><g transform="matrix(.0095,0,0,-0.0095,24.088,-5.984)"><path d="M319 325C317 349 306 409 297 431C277 440 250 449 209 449C117 449 57 389 57 319C57 243 122 209 182 182C232 159 261 135 261 91C261 48 227 21 190 21C130 21 85 79 68 145L41 140C41 104 51 36 58 22C75 7 121 -12 172 -12C252 -12 337 35 337 126C337 195 286 231 210 262C166 281 126 304 126 348C126 388 152 417 191 417C240 417 274 378 294 318L319 325Z" id="g190-116"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="367" vert-adv-y="367"></glyph.data></g><g transform="matrix(.0095,0,0,-0.0095,27.521,-5.984)"><path d="M298 36L289 62C276 55 253 45 228 45C202 45 169 60 169 141V397H276C289 405 292 426 282 437H169V574L155 576L90 509V437H45L17 408L21 397H90V107C90 28 125 -12 188 -12C198 -12 213 -8 230 1L298 36Z" id="g190-117"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="305" vert-adv-y="305"></glyph.data></g></svg> is the worst harmony vector in HM).</td></tr><tr><td colspan="2"><b>EndIf</b></td></tr></table></td></tr></table>

Mathematical Problems in Engineering

alg1

Algorithm 1

Algorithm 1: Construction Example for Algebra System Using  Harmony Search Algorithm 