{"id":4864,"date":"2018-04-04T22:36:16","date_gmt":"2018-04-04T19:36:16","guid":{"rendered":"https:\/\/hpc-education.unn.ru\/?page_id=4864"},"modified":"2018-12-14T10:01:56","modified_gmt":"2018-12-14T07:01:56","slug":"%d1%82%d0%b5%d1%81%d1%82%d0%be%d0%b2%d1%8b%d0%b5-%d0%b7%d0%b0%d0%b4%d0%b0%d1%87%d0%b8-%d0%b3%d0%bb%d0%be%d0%b1%d0%b0%d0%bb%d1%8c%d0%bd%d0%be%d0%b9-%d0%be%d0%bf%d1%82%d0%b8%d0%bc%d0%b8%d0%b7%d0%b0","status":"publish","type":"page","link":"https:\/\/hpc-education.unn.ru\/ru\/globopt\/%d1%82%d0%b5%d1%81%d1%82%d0%be%d0%b2%d1%8b%d0%b5-%d0%b7%d0%b0%d0%b4%d0%b0%d1%87%d0%b8-%d0%b3%d0%bb%d0%be%d0%b1%d0%b0%d0%bb%d1%8c%d0%bd%d0%be%d0%b9-%d0%be%d0%bf%d1%82%d0%b8%d0%bc%d0%b8%d0%b7%d0%b0","title":{"rendered":"\u0422\u0435\u0441\u0442\u043e\u0432\u044b\u0435 \u0437\u0430\u0434\u0430\u0447\u0438 \u0433\u043b\u043e\u0431\u0430\u043b\u044c\u043d\u043e\u0439 \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438 \u0431\u0435\u0437 \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u0438\u0439"},"content":{"rendered":"\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
\n

Ackley’s Problem<\/h3>\n<\/td>\n<\/tr>\n

\"Ackley's<\/td>\n\n

  <\/span>   <\/span>\"\[<\/p>\n<\/td>\n<\/tr>\n

\n
    \n
  • \u0420\u0430\u0437\u043c\u0435\u0440\u043d\u043e\u0441\u0442\u044c: \"n = 1, 2, \ldots, 32\".<\/li>\n
  • \u041e\u0431\u043b\u0430\u0441\u0442\u044c \u043f\u043e\u0438\u0441\u043a\u0430: \"-30 \leq x_i \leq 30\", \"i \in \{1, 2, \ldots, n\}\".<\/li>\n
  • \u0413\u043b\u043e\u0431\u0430\u043b\u044c\u043d\u044b\u0439 \u043c\u0438\u043d\u0438\u043c\u0443\u043c: \"f(0, 0, \ldots, 0) = 0\".<\/li>\n
  • \u041a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u043e \u043b\u043e\u043a\u0430\u043b\u044c\u043d\u044b\u0445 \u043c\u0438\u043d\u0438\u043c\u0443\u043c\u043e\u0432: \u043d\u0435\u0438\u0437\u0432\u0435\u0441\u0442\u043d\u043e.<\/li>\n
  • \u0418\u0441\u0442\u043e\u0447\u043d\u0438\u043a\u0438: [1, 2, 4, 5, 6, 7, 10, 11, 13, 14, 15]<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n
\n

Camel Back — 3 (Three Hump) Problem<\/h3>\n<\/td>\n<\/tr>\n

\"Camel<\/td>\n\n

  <\/span>   <\/span>\"\[<\/p>\n<\/td>\n<\/tr>\n

\n
    \n
  • \u0420\u0430\u0437\u043c\u0435\u0440\u043d\u043e\u0441\u0442\u044c: \"n = 2\".<\/li>\n
  • \u041e\u0431\u043b\u0430\u0441\u0442\u044c \u043f\u043e\u0438\u0441\u043a\u0430: \"-5 \leq x_i \leq 5\", \"i \in \{1, 2\}\".<\/li>\n
  • \u0413\u043b\u043e\u0431\u0430\u043b\u044c\u043d\u044b\u0439 \u043c\u0438\u043d\u0438\u043c\u0443\u043c: \"f(0, 0) = 0\".<\/li>\n
  • \u041a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u043e \u043b\u043e\u043a\u0430\u043b\u044c\u043d\u044b\u0445 \u043c\u0438\u043d\u0438\u043c\u0443\u043c\u043e\u0432: \"3\".<\/li>\n
  • \u0418\u0441\u0442\u043e\u0447\u043d\u0438\u043a\u0438: [1, 4, 9, 10, 11, 12, 13, 14, 16]<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n
\n

Camel Back — 6 (Six Hump) Problem<\/h3>\n<\/td>\n<\/tr>\n

\"Camel<\/td>\n\n

  <\/span>   <\/span>\"\[<\/p>\n<\/td>\n<\/tr>\n

\n
    \n
  • \u0420\u0430\u0437\u043c\u0435\u0440\u043d\u043e\u0441\u0442\u044c: \"n = 2\".<\/li>\n
  • \u041e\u0431\u043b\u0430\u0441\u0442\u044c \u043f\u043e\u0438\u0441\u043a\u0430: \"-5 \leq x_i \leq 5\", \"i \in \{1, 2\}\".<\/li>\n
  • \u0413\u043b\u043e\u0431\u0430\u043b\u044c\u043d\u044b\u0439 \u043c\u0438\u043d\u0438\u043c\u0443\u043c: \"f(0.089842, -0.712656) = f(-0.089842, 0.712656) = -1.0316\".<\/li>\n
  • \u041a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u043e \u043b\u043e\u043a\u0430\u043b\u044c\u043d\u044b\u0445 \u043c\u0438\u043d\u0438\u043c\u0443\u043c\u043e\u0432: \"6\".<\/li>\n
  • \u0418\u0441\u0442\u043e\u0447\u043d\u0438\u043a\u0438: [1, 2, 4, 6, 7, 9, 10, 12, 13, 14, 16]<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n
\n

Griewank Problem<\/h3>\n<\/td>\n<\/tr>\n

\"Griewank<\/td>\n\n

  <\/span>   <\/span>\"\[<\/p>\n<\/td>\n<\/tr>\n

\n
    \n
  • \u0420\u0430\u0437\u043c\u0435\u0440\u043d\u043e\u0441\u0442\u044c: \"n = 1, 2, \ldots, 32\".<\/li>\n
  • \u041e\u0431\u043b\u0430\u0441\u0442\u044c \u043f\u043e\u0438\u0441\u043a\u0430: \"-600 \leq x_i \leq 600\", \"i \in \{1, 2, \ldots, n\}\".<\/li>\n
  • \u0413\u043b\u043e\u0431\u0430\u043b\u044c\u043d\u044b\u0439 \u043c\u0438\u043d\u0438\u043c\u0443\u043c: \"f(0, 0, \ldots, 0) = 0\".<\/li>\n
  • \u041a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u043e \u043b\u043e\u043a\u0430\u043b\u044c\u043d\u044b\u0445 \u043c\u0438\u043d\u0438\u043c\u0443\u043c\u043e\u0432: \u043d\u0435\u0438\u0437\u0432\u0435\u0441\u0442\u043d\u043e; \u043f\u0440\u0438 \"n = 2\" \u043e\u043a\u043e\u043b\u043e \"500\".<\/li>\n
  • \u0418\u0441\u0442\u043e\u0447\u043d\u0438\u043a\u0438: [1, 2, 4, 5, 6, 7, 10, 11, 13, 14, 16]<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n
\n

Levy and Montavlo 1 Problem<\/h3>\n<\/td>\n<\/tr>\n

\"Levy<\/td>\n\n

  <\/span>   <\/span>\"\[<\/p>\n

\u0433\u0434\u0435 \"y_i = 1 + \frac 1 4 (x_i+1)\".<\/td>\n<\/tr>\n

\n
    \n
  • \u0420\u0430\u0437\u043c\u0435\u0440\u043d\u043e\u0441\u0442\u044c: \"n = 1, 2, \ldots, 32\".<\/li>\n
  • \u041e\u0431\u043b\u0430\u0441\u0442\u044c \u043f\u043e\u0438\u0441\u043a\u0430: \"-10 \leq x_i \leq 10\", \"i \in \{1, 2, \ldots, n\}\".<\/li>\n
  • \u0413\u043b\u043e\u0431\u0430\u043b\u044c\u043d\u044b\u0439 \u043c\u0438\u043d\u0438\u043c\u0443\u043c: \"f(-1, -1, \ldots, -1) = 0\".<\/li>\n
  • \u041a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u043e \u043b\u043e\u043a\u0430\u043b\u044c\u043d\u044b\u0445 \u043c\u0438\u043d\u0438\u043c\u0443\u043c\u043e\u0432: \"\approx 5^n\".<\/li>\n
  • \u0418\u0441\u0442\u043e\u0447\u043d\u0438\u043a\u0438: [1, 10, 13, 14, 15]<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n
\n

McCormick Problem<\/h3>\n<\/td>\n<\/tr>\n

\"McCormick<\/td>\n\n

  <\/span>   <\/span>\"\[<\/p>\n<\/td>\n<\/tr>\n

\n
    \n
  • \u0420\u0430\u0437\u043c\u0435\u0440\u043d\u043e\u0441\u0442\u044c: \"n = 2\".<\/li>\n
  • \u041e\u0431\u043b\u0430\u0441\u0442\u044c \u043f\u043e\u0438\u0441\u043a\u0430: \"-1.5 \leq x_1 \leq 4\", \"-3 \leq x_2 \leq 3\".<\/li>\n
  • \u0413\u043b\u043e\u0431\u0430\u043b\u044c\u043d\u044b\u0439 \u043c\u0438\u043d\u0438\u043c\u0443\u043c: \"f(-0.547, -1.547) \approx -1.9133\".<\/li>\n
  • \u041a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u043e \u043b\u043e\u043a\u0430\u043b\u044c\u043d\u044b\u0445 \u043c\u0438\u043d\u0438\u043c\u0443\u043c\u043e\u0432: \"2\".<\/li>\n
  • \u0418\u0441\u0442\u043e\u0447\u043d\u0438\u043a\u0438: [1, 4, 10, 13, 14]<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n
\n

Modified Langerman Problem<\/h3>\n<\/td>\n<\/tr>\n

\"Modified<\/td>\n\n

  <\/span>   <\/span>\"\[<\/p>\n

\u0433\u0434\u0435 \"d_j = \sum_{i=1}^n (x_i - a_{ji})^2\" \u0438 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \"c_j\" \u0438 \"a_{ji}\" \u043f\u0440\u0438\u0432\u0435\u0434\u0435\u043d\u044b \u0432 \u0422\u0430\u0431\u043b\u0438\u0446\u0435 1.<\/td>\n<\/tr>\n

\n
    \n
  • \u0420\u0430\u0437\u043c\u0435\u0440\u043d\u043e\u0441\u0442\u044c: \"n = 5, 10\".<\/li>\n
  • \u041e\u0431\u043b\u0430\u0441\u0442\u044c \u043f\u043e\u0438\u0441\u043a\u0430: \"0 \leq x_1 \leq 10\", \"i \in \{1, 2, \ldots, n\}\".<\/li>\n
  • \u0413\u043b\u043e\u0431\u0430\u043b\u044c\u043d\u044b\u0439 \u043c\u0438\u043d\u0438\u043c\u0443\u043c:\n
      \n
    • \"f(8.074, 8.777, 3.467, 1.867, 6.708) = -0.965\" \u0434\u043b\u044f \"n = 5\";<\/li>\n
    • \"f(8.074, 8.777, 3.467, 1.867, 6.708, 6.349, 4.534, 0.276, 7.633, 1.567) = -0.965\" \u0434\u043b\u044f \"n = 10\".<\/li>\n<\/ul>\n<\/li>\n
    • \u041a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u043e \u043b\u043e\u043a\u0430\u043b\u044c\u043d\u044b\u0445 \u043c\u0438\u043d\u0438\u043c\u0443\u043c\u043e\u0432: \u043d\u0435\u0438\u0437\u0432\u0435\u0441\u0442\u043d\u043e.<\/li>\n
    • \u0418\u0441\u0442\u043e\u0447\u043d\u0438\u043a\u0438: [1, 4, 9, 10]<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n
\u0422\u0430\u0431\u043b\u0438\u0446\u0430 1. \u0414\u0430\u043d\u043d\u044b\u0435 \u0434\u043b\u044f \u0437\u0430\u0434\u0430\u0447\u0438 Modified Langerman Problem<\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
\"j\"<\/td>\n\"c_j\"<\/td>\n\"a_{ji}\"<\/td>\n<\/tr>\n
\"i=1\"<\/td>\n2<\/td>\n3<\/td>\n4<\/td>\n5<\/td>\n6<\/td>\n7<\/td>\n8<\/td>\n9<\/td>\n10<\/td>\n<\/tr>\n
1<\/td>\n0.806<\/td>\n9.681<\/td>\n0.667<\/td>\n4.783<\/td>\n9.095<\/td>\n3.517<\/td>\n9.325<\/td>\n6.544<\/td>\n0.211<\/td>\n5.122<\/td>\n2.020<\/td>\n<\/tr>\n
2<\/td>\n0.517<\/td>\n9.400<\/td>\n2.041<\/td>\n3.788<\/td>\n7.931<\/td>\n2.882<\/td>\n2.672<\/td>\n3.568<\/td>\n1.284<\/td>\n7.033<\/td>\n7.374<\/td>\n<\/tr>\n
3<\/td>\n0.100<\/td>\n8.025<\/td>\n9.152<\/td>\n5.114<\/td>\n7.621<\/td>\n4.564<\/td>\n4.711<\/td>\n2.996<\/td>\n6.126<\/td>\n0.734<\/td>\n4.982<\/td>\n<\/tr>\n
4<\/td>\n0.908<\/td>\n2.196<\/td>\n0.415<\/td>\n5.649<\/td>\n6.979<\/td>\n9.510<\/td>\n9.166<\/td>\n6.304<\/td>\n6.054<\/td>\n9.377<\/td>\n1.426<\/td>\n<\/tr>\n
5<\/td>\n0.965<\/td>\n8.074<\/td>\n8.777<\/td>\n3.467<\/td>\n1.867<\/td>\n6.708<\/td>\n6.349<\/td>\n4.534<\/td>\n0.276<\/td>\n7.633<\/td>\n1.567<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/td>\n<\/tr>\n
\n

Neumaier 2 Problem<\/h3>\n<\/td>\n<\/tr>\n

\"Neumaier<\/td>\n\n

  <\/span>   <\/span>\"\[<\/p>\n

\u0433\u0434\u0435 \"b = (8, 18, 44, 114)\".<\/td>\n<\/tr>\n

\n
    \n
  • \u0420\u0430\u0437\u043c\u0435\u0440\u043d\u043e\u0441\u0442\u044c: \"n = 4\".<\/li>\n
  • \u041e\u0431\u043b\u0430\u0441\u0442\u044c \u043f\u043e\u0438\u0441\u043a\u0430: \"0 \leq x_i \leq i\", \"i \in \{1, 2, \ldots, n\}\".<\/li>\n
  • \u0413\u043b\u043e\u0431\u0430\u043b\u044c\u043d\u044b\u0439 \u043c\u0438\u043d\u0438\u043c\u0443\u043c: \"f(1, 2, 2, 3) = 0\".<\/li>\n
  • \u041a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u043e \u043b\u043e\u043a\u0430\u043b\u044c\u043d\u044b\u0445 \u043c\u0438\u043d\u0438\u043c\u0443\u043c\u043e\u0432: \u043d\u0435\u0438\u0437\u0432\u0435\u0441\u0442\u043d\u043e.<\/li>\n
  • \u0418\u0441\u0442\u043e\u0447\u043d\u0438\u043a\u0438: [1, 10, 13, 14, 15, 16]<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n
\n

Neumaier 3 Problem<\/h3>\n<\/td>\n<\/tr>\n

\"Neumaier<\/td>\n\n

  <\/span>   <\/span>\"\[<\/p>\n<\/td>\n<\/tr>\n

\n
    \n
  • \u0420\u0430\u0437\u043c\u0435\u0440\u043d\u043e\u0441\u0442\u044c: \"n = 2, 3, \ldots, 32\".<\/li>\n
  • \u041e\u0431\u043b\u0430\u0441\u0442\u044c \u043f\u043e\u0438\u0441\u043a\u0430: \"-n^2 \leq x_i \leq n^2\", \"i \in \{1, 2, \ldots, n\}\".<\/li>\n
  • \u0413\u043b\u043e\u0431\u0430\u043b\u044c\u043d\u044b\u0439 \u043c\u0438\u043d\u0438\u043c\u0443\u043c: \"f(x^*) = - \frac{n(n+4)(n-1)}{6}\", \"x^*_i = i(n+1-i)\".<\/li>\n
  • \u041a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u043e \u043b\u043e\u043a\u0430\u043b\u044c\u043d\u044b\u0445 \u043c\u0438\u043d\u0438\u043c\u0443\u043c\u043e\u0432: \u043d\u0435\u0438\u0437\u0432\u0435\u0441\u0442\u043d\u043e.<\/li>\n
  • \u0418\u0441\u0442\u043e\u0447\u043d\u0438\u043a\u0438: [1, 10, 13, 16]<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n
\n

Paviani Problem<\/h3>\n<\/td>\n<\/tr>\n

\"Paviani<\/td>\n\n

  <\/span>   <\/span>\"\[<\/p>\n<\/td>\n<\/tr>\n

\n
    \n
  • \u0420\u0430\u0437\u043c\u0435\u0440\u043d\u043e\u0441\u0442\u044c: \"n = 10\".<\/li>\n
  • \u041e\u0431\u043b\u0430\u0441\u0442\u044c \u043f\u043e\u0438\u0441\u043a\u0430: \"2 \leq x_i \leq 10\", \"i \in \{1, 2, \ldots, 10\}\".<\/li>\n
  • \u0413\u043b\u043e\u0431\u0430\u043b\u044c\u043d\u044b\u0439 \u043c\u0438\u043d\u0438\u043c\u0443\u043c: \"f(x^*) \approx - 45.778\", \"x^*_i \approx 9.351\".<\/li>\n
  • \u041a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u043e \u043b\u043e\u043a\u0430\u043b\u044c\u043d\u044b\u0445 \u043c\u0438\u043d\u0438\u043c\u0443\u043c\u043e\u0432: \u043d\u0435\u0438\u0437\u0432\u0435\u0441\u0442\u043d\u043e.<\/li>\n
  • \u0418\u0441\u0442\u043e\u0447\u043d\u0438\u043a\u0438: [1, 4, 10, 12, 13, 14]<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n
\n

Rosenbrock Problem<\/h3>\n<\/td>\n<\/tr>\n

\"Rosenbrock<\/td>\n\n

  <\/span>   <\/span>\"\[<\/p>\n<\/td>\n<\/tr>\n

\n
    \n
  • \u0420\u0430\u0437\u043c\u0435\u0440\u043d\u043e\u0441\u0442\u044c: \"n = 2, 3, \ldots, 32\".<\/li>\n
  • \u041e\u0431\u043b\u0430\u0441\u0442\u044c \u043f\u043e\u0438\u0441\u043a\u0430: \"-30 \leq x_i \leq 30\", \"i \in \{1, 2, \ldots, n\}\".<\/li>\n
  • \u0413\u043b\u043e\u0431\u0430\u043b\u044c\u043d\u044b\u0439 \u043c\u0438\u043d\u0438\u043c\u0443\u043c: \"f(1, 1, \ldots, 1) = 0\".<\/li>\n
  • \u041a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u043e \u043b\u043e\u043a\u0430\u043b\u044c\u043d\u044b\u0445 \u043c\u0438\u043d\u0438\u043c\u0443\u043c\u043e\u0432: \"1\".<\/li>\n
  • \u0418\u0441\u0442\u043e\u0447\u043d\u0438\u043a\u0438: [1, 2, 4, 5, 6, 7, 8, 9, 10, 13, 14, 15, 16]<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n
\n

Salomon Problem<\/h3>\n<\/td>\n<\/tr>\n

\"Salomon<\/td>\n\n

  <\/span>   <\/span>\"\[<\/p>\n

\u0433\u0434\u0435 \"\|x\| = \sqrt{\sum_{i=1}^n x_i^2}\".<\/td>\n<\/tr>\n

\n
    \n
  • \u0420\u0430\u0437\u043c\u0435\u0440\u043d\u043e\u0441\u0442\u044c: \"n = 1, 2, \ldots, 32\".<\/li>\n
  • \u041e\u0431\u043b\u0430\u0441\u0442\u044c \u043f\u043e\u0438\u0441\u043a\u0430: \"-100 \leq x_i \leq 100\", \"i \in \{1, 2, \ldots, n\}\".<\/li>\n
  • \u0413\u043b\u043e\u0431\u0430\u043b\u044c\u043d\u044b\u0439 \u043c\u0438\u043d\u0438\u043c\u0443\u043c: \"f(x^*) = 0\", \"x^*_i = 0\".<\/li>\n
  • \u041a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u043e \u043b\u043e\u043a\u0430\u043b\u044c\u043d\u044b\u0445 \u043c\u0438\u043d\u0438\u043c\u0443\u043c\u043e\u0432: \u043d\u0435\u0438\u0437\u0432\u0435\u0441\u0442\u043d\u043e.<\/li>\n
  • \u0418\u0441\u0442\u043e\u0447\u043d\u0438\u043a\u0438: [1, 4, 10, 11, 12, 13, 14]<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n
\n

Schwefel Problem<\/h3>\n<\/td>\n<\/tr>\n

\"Schwefel<\/td>\n\n

  <\/span>   <\/span>\"\[<\/p>\n<\/td>\n<\/tr>\n

\n
    \n
  • \u0420\u0430\u0437\u043c\u0435\u0440\u043d\u043e\u0441\u0442\u044c: \"n = 1, 2, \ldots, 32\".<\/li>\n
  • \u041e\u0431\u043b\u0430\u0441\u0442\u044c \u043f\u043e\u0438\u0441\u043a\u0430: \"-500 \leq x_i \leq 500\", \"i \in \{1, 2, \ldots, n\}\".<\/li>\n
  • \u0413\u043b\u043e\u0431\u0430\u043b\u044c\u043d\u044b\u0439 \u043c\u0438\u043d\u0438\u043c\u0443\u043c: \"f(x^*) = -418.9829n\", \u0433\u0434\u0435 \"x^*_i \approx 420.97\".<\/li>\n
  • \u041a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u043e \u043b\u043e\u043a\u0430\u043b\u044c\u043d\u044b\u0445 \u043c\u0438\u043d\u0438\u043c\u0443\u043c\u043e\u0432: \u043d\u0435\u0438\u0437\u0432\u0435\u0441\u0442\u043d\u043e.<\/li>\n
  • \u0418\u0441\u0442\u043e\u0447\u043d\u0438\u043a\u0438: [1, 2, 4, 5, 7, 10, 12]<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n
\n

Shekel 5 Problem<\/h3>\n<\/td>\n<\/tr>\n

\"Shekel<\/td>\n\n

  <\/span>   <\/span>\"\[<\/p>\n

\u0433\u0434\u0435 \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u044b \"a_{ij}\" \u0438 \"c_i\" \u043f\u0440\u0438\u0432\u0435\u0434\u0435\u043d\u044b \u0432 \u0422\u0430\u0431\u043b\u0438\u0446\u0435 2.<\/td>\n<\/tr>\n

\n
    \n
  • \u0420\u0430\u0437\u043c\u0435\u0440\u043d\u043e\u0441\u0442\u044c: \"n = 4\".<\/li>\n
  • \u041e\u0431\u043b\u0430\u0441\u0442\u044c \u043f\u043e\u0438\u0441\u043a\u0430: \"0 \leq x_i \leq 10\", \"i \in \{1, 2, 3, 4\}\".<\/li>\n
  • \u0413\u043b\u043e\u0431\u0430\u043b\u044c\u043d\u044b\u0439 \u043c\u0438\u043d\u0438\u043c\u0443\u043c: \"f(4, 4, 4, 4) \approx -10.1499\".<\/li>\n
  • \u041a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u043e \u043b\u043e\u043a\u0430\u043b\u044c\u043d\u044b\u0445 \u043c\u0438\u043d\u0438\u043c\u0443\u043c\u043e\u0432: \"5\".<\/li>\n
  • \u0418\u0441\u0442\u043e\u0447\u043d\u0438\u043a\u0438: [1, 2, 4, 6, 8, 10, 12, 13, 14, 16]<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n
\u0422\u0430\u0431\u043b\u0438\u0446\u0430 2. \u0414\u0430\u043d\u043d\u044b\u0435 \u0434\u043b\u044f \u0437\u0430\u0434\u0430\u0447 Shekel Problems<\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
\"i\"<\/td>\n\"a_{ij}\"<\/td>\n\"c_{ij}\"<\/td>\n<\/tr>\n
\"j = 1\"<\/td>\n\"j = 2\"<\/td>\n\"j = 3\"<\/td>\n\"j = 4\"<\/td>\n<\/tr>\n
1<\/td>\n4<\/td>\n4<\/td>\n4<\/td>\n4<\/td>\n0.1<\/td>\n<\/tr>\n
2<\/td>\n1<\/td>\n1<\/td>\n1<\/td>\n1<\/td>\n0.2<\/td>\n<\/tr>\n
3<\/td>\n8<\/td>\n8<\/td>\n8<\/td>\n8<\/td>\n0.2<\/td>\n<\/tr>\n
4<\/td>\n6<\/td>\n6<\/td>\n6<\/td>\n6<\/td>\n0.4<\/td>\n<\/tr>\n
5<\/td>\n3<\/td>\n7<\/td>\n3<\/td>\n7<\/td>\n0.4<\/td>\n<\/tr>\n
6<\/td>\n2<\/td>\n9<\/td>\n2<\/td>\n9<\/td>\n0.6<\/td>\n<\/tr>\n
7<\/td>\n5<\/td>\n5<\/td>\n3<\/td>\n3<\/td>\n0.3<\/td>\n<\/tr>\n
8<\/td>\n8<\/td>\n1<\/td>\n8<\/td>\n1<\/td>\n0.7<\/td>\n<\/tr>\n
9<\/td>\n6<\/td>\n2<\/td>\n6<\/td>\n2<\/td>\n0.5<\/td>\n<\/tr>\n
10<\/td>\n7<\/td>\n3.6<\/td>\n7<\/td>\n3.6<\/td>\n0.5<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/td>\n<\/tr>\n
\n

Shekel 7 Problem<\/h3>\n<\/td>\n<\/tr>\n

\"Shekel<\/td>\n\n

  <\/span>   <\/span>\"\[<\/p>\n

\u0433\u0434\u0435 \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u044b \"a_{ij}\" \u0438 \"c_i\" \u043f\u0440\u0438\u0432\u0435\u0434\u0435\u043d\u044b \u0432 \u0422\u0430\u0431\u043b\u0438\u0446\u0435 2.<\/td>\n<\/tr>\n

\n
    \n
  • \u0420\u0430\u0437\u043c\u0435\u0440\u043d\u043e\u0441\u0442\u044c: \"n = 4\".<\/li>\n
  • \u041e\u0431\u043b\u0430\u0441\u0442\u044c \u043f\u043e\u0438\u0441\u043a\u0430: \"0 \leq x_i \leq 10\", \"i \in \{1, 2, 3, 4\}\".<\/li>\n
  • \u0413\u043b\u043e\u0431\u0430\u043b\u044c\u043d\u044b\u0439 \u043c\u0438\u043d\u0438\u043c\u0443\u043c: \"f(4, 4, 4, 4) \approx -10.3999\".<\/li>\n
  • \u041a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u043e \u043b\u043e\u043a\u0430\u043b\u044c\u043d\u044b\u0445 \u043c\u0438\u043d\u0438\u043c\u0443\u043c\u043e\u0432: \"7\".<\/li>\n
  • \u0418\u0441\u0442\u043e\u0447\u043d\u0438\u043a\u0438: [1, 2, 4, 6, 8, 10, 12, 13, 14, 16]<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n
\n

Shekel 10 Problem<\/h3>\n<\/td>\n<\/tr>\n

\"Shekel<\/td>\n\n

  <\/span>   <\/span>\"\[<\/p>\n

\u0433\u0434\u0435 \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u044b \"a_{ij}\" \u0438 \"c_i\" \u043f\u0440\u0438\u0432\u0435\u0434\u0435\u043d\u044b \u0432 \u0422\u0430\u0431\u043b\u0438\u0446\u0435 2.<\/td>\n<\/tr>\n

\n
    \n
  • \u0420\u0430\u0437\u043c\u0435\u0440\u043d\u043e\u0441\u0442\u044c: \"n = 4\".<\/li>\n
  • \u041e\u0431\u043b\u0430\u0441\u0442\u044c \u043f\u043e\u0438\u0441\u043a\u0430: \"0 \leq x_i \leq 10\", \"i \in \{1, 2, 3, 4\}\".<\/li>\n
  • \u0413\u043b\u043e\u0431\u0430\u043b\u044c\u043d\u044b\u0439 \u043c\u0438\u043d\u0438\u043c\u0443\u043c: \"f(4, 4, 4, 4) \approx -10.5319\".<\/li>\n
  • \u041a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u043e \u043b\u043e\u043a\u0430\u043b\u044c\u043d\u044b\u0445 \u043c\u0438\u043d\u0438\u043c\u0443\u043c\u043e\u0432: \"10\".<\/li>\n
  • \u0418\u0441\u0442\u043e\u0447\u043d\u0438\u043a\u0438: [1, 2, 4, 6, 8, 10, 12, 13, 14, 16]<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n
\n

Shubert Problem<\/h3>\n<\/td>\n<\/tr>\n

\"Shubert<\/td>\n\n

  <\/span>   <\/span>\"\[<\/p>\n<\/td>\n<\/tr>\n

\n
    \n
  • \u0420\u0430\u0437\u043c\u0435\u0440\u043d\u043e\u0441\u0442\u044c: \"n = 2\".<\/li>\n
  • \u041e\u0431\u043b\u0430\u0441\u0442\u044c \u043f\u043e\u0438\u0441\u043a\u0430: \"-10 \leq x_i \leq 10\", \"i \in \{1, 2\}\".<\/li>\n
  • \u0413\u043b\u043e\u0431\u0430\u043b\u044c\u043d\u044b\u0439 \u043c\u0438\u043d\u0438\u043c\u0443\u043c: 18 \u0442\u043e\u0447\u0435\u043a \u0433\u043b\u043e\u0431\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u043c\u0438\u043d\u0438\u043c\u0443\u043c\u0430, \"f^* \approx -186.7309\".<\/li>\n
  • \u0422\u043e\u0447\u043a\u0438 \u0433\u043b\u043e\u0431\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u043c\u0438\u043d\u0438\u043c\u0443\u043c\u0430 \u043f\u0440\u0438\u0432\u0435\u0434\u0435\u043d\u044b \u0432 \u0422\u0430\u0431\u043b\u0438\u0446\u0435 3.<\/li>\n
  • \u041a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u043e \u043b\u043e\u043a\u0430\u043b\u044c\u043d\u044b\u0445 \u043c\u0438\u043d\u0438\u043c\u0443\u043c\u043e\u0432: \"760\".<\/li>\n
  • \u0418\u0441\u0442\u043e\u0447\u043d\u0438\u043a\u0438: [1, 2, 4, 6, 8, 10, 12, 13]<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n
\u0422\u0430\u0431\u043b\u0438\u0446\u0430 3. \u0422\u043e\u0447\u043a\u0438 \u0433\u043b\u043e\u0431\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u043c\u0438\u043d\u0438\u043c\u0443\u043c\u0430 \u0434\u043b\u044f \u0437\u0430\u0434\u0430\u0447\u0438 Shubert Problem<\/p>\n\n\n\n\n\n\n\n
(-7.0835, 4.8580)<\/td>\n(-7.0835, -7.7083)<\/td>\n(-1.4251, -7.0835)<\/td>\n(5.4828, 4.8580)<\/td>\n(-1.4251, -0.8003)<\/td>\n(4.8580, 5.4828)<\/td>\n<\/tr>\n
(-7.7083, -7.0835)<\/td>\n(-7.0835, -1.4251)<\/td>\n(-7.7083, -0.8003)<\/td>\n(-7.7083, 5.4828)<\/td>\n(-0.8003, -7.7083)<\/td>\n(-0.8003, -1.4251)<\/td>\n<\/tr>\n
(-0.8003, 4.8580)<\/td>\n(-1.4251, 5.4828)<\/td>\n(5.4828, -7.7083)<\/td>\n(4.8580, -7.0835)<\/td>\n(5.4828, -1.4251)<\/td>\n(4.8580, -0.8003)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/td>\n<\/tr>\n
\n

\u0418\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u043d\u043d\u044b\u0435 \u0438\u0441\u0442\u043e\u0447\u043d\u0438\u043a\u0438<\/h3>\n<\/td>\n<\/tr>\n

\n
    \n
  1. M.M. Ali, C. Khompatraporn, Z.B. Zabinsky. A numerical evaluation of several stochastic algorithms on selected continuous global optimization test problems. Journal of Global Optimization, 31(4), 635-672. (2005)<\/li>\n
  2. M. Laguna, R. Marti. Experimental Testing of Advanced Scatter Search Designs for Global Optimization of Multimodal Functions, Journal of Global Optimization, V. 33, 235-255. (2005)<\/li>\n
  3. H.E. Romeijn, R.L. Smith. Simulated annealing for constrained global optimization. Journal of Global Optimization 5(2): 101-126. (1994)<\/li>\n
  4. M. Jamil and X.S. Yang. A literature survey of benchmark functions for global optimization problems, Int. Journal of Mathematical Modelling and Numerical Optimization, Vol. 4, \u21162, 150-194. (2013)<\/li>\n
  5. J. Teo. Global Optimization Accuracy and Evolutionary Dynamics of the Generalized Generation Gap Algorithm with Adaptive Mutation. Malaysian Journal of Computer Science, 19(2): 159-167. (2006)<\/li>\n
  6. Q. Tao, X. Huang, S. Wang, L. Li. Adaptive block coordinate DIRECT algorithm. Journal of Global Optimization. 69:4, 797-822. (2017)<\/li>\n
  7. X.S. Yang. Test Problems in Optimization. Engineering Optimization: An Introduction with Metaheuristic Applications, John Wiley & Sons. (2010)<\/li>\n
  8. R. Paulavicius, J. Zilinskas, A. Grothey. Investigation of selection strategies in branch and bound algorithm with simplicial partitions and combination of Lipschitz bounds. Optimization Letters, 4:173-183. (2010)<\/li>\n
  9. Z. Nedelkova, P. Lindroth, M. Patriksson, A.B. Stromberg. Efficient solution of many instances of a simulation-based optimization problem utilizing a partition of the decision space. Annals of Operation Research, 1-26. (2017)<\/li>\n
  10. K. M. Mullen. Continuous Global Optimization in R. Journal of Statistical Software, 60:6, 1-45. (2014)<\/li>\n
  11. N.S. Teng, M.H.A. Hijazi and J. Teo. Self-adaptive Scaling Factor in Differential Evolution. Regional Conference on Computational Science and Technologies (RCCST 2007), 112-116. (2007)<\/li>\n
  12. Y. Alipouri, J. Poshtan, H. Alipouri. Improvement of Classical Evolutionary Programming using State Feedback Controller. Int. J. of Innovative Computing, Information and Control, Vol.10, \u2116 4, 1413-1433. (2014)<\/li>\n
  13. N. Henderson, M. Sa Rego, W.F. Sacco, R.A. Rodrigues. A new look at the topographical global optimization method and its application to the phase stability analysis of mixtures. Chemical Engineering Science. 127: 151-174. (2015)<\/li>\n
  14. F. Shahzad, S. Masood, N. K. Khan. Probabilistic opposition-based particle swarm optimization with velocity clamping, Knowledge and Information Systems, Vol. 39, Issue 3, 703-737. (2014)<\/li>\n
  15. Q. Abbas, J. Ahmad, H. Jabeen. A novel tournament selection based differential evolution variant for continuous optimization problems. Mathematical Problems in Engineering, Article ID 205709, 21pp. (2015)<\/li>\n
  16. L. G. Casado, I. Garcia, T. Csendes, V.G. Ruiz. Heuristic Rejection in Interval Global Optimization. Journal of Optimization Theory and Applications, Vol. 118, \u21161, 27-43. (2003)<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"

    Ackley’s Problem     \u0420\u0430\u0437\u043c\u0435\u0440\u043d\u043e\u0441\u0442\u044c: . \u041e\u0431\u043b\u0430\u0441\u0442\u044c \u043f\u043e\u0438\u0441\u043a\u0430: , . \u0413\u043b\u043e\u0431\u0430\u043b\u044c\u043d\u044b\u0439 \u043c\u0438\u043d\u0438\u043c\u0443\u043c: . \u041a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u043e \u043b\u043e\u043a\u0430\u043b\u044c\u043d\u044b\u0445 \u043c\u0438\u043d\u0438\u043c\u0443\u043c\u043e\u0432: \u043d\u0435\u0438\u0437\u0432\u0435\u0441\u0442\u043d\u043e. \u0418\u0441\u0442\u043e\u0447\u043d\u0438\u043a\u0438: [1, 2, 4, 5, 6, 7, 10, 11, 13, 14, 15] Camel Back — 3 (Three Hump) Problem     \u0420\u0430\u0437\u043c\u0435\u0440\u043d\u043e\u0441\u0442\u044c: . … \u0427\u0438\u0442\u0430\u0442\u044c \u0434\u0430\u043b\u0435\u0435 →<\/span><\/a><\/p>\n","protected":false},"author":40,"featured_media":0,"parent":4491,"menu_order":21,"comment_status":"closed","ping_status":"closed","template":"","meta":{"ngg_post_thumbnail":0},"_links":{"self":[{"href":"https:\/\/hpc-education.unn.ru\/ru\/wp-json\/wp\/v2\/pages\/4864"}],"collection":[{"href":"https:\/\/hpc-education.unn.ru\/ru\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/hpc-education.unn.ru\/ru\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/hpc-education.unn.ru\/ru\/wp-json\/wp\/v2\/users\/40"}],"replies":[{"embeddable":true,"href":"https:\/\/hpc-education.unn.ru\/ru\/wp-json\/wp\/v2\/comments?post=4864"}],"version-history":[{"count":2,"href":"https:\/\/hpc-education.unn.ru\/ru\/wp-json\/wp\/v2\/pages\/4864\/revisions"}],"predecessor-version":[{"id":5240,"href":"https:\/\/hpc-education.unn.ru\/ru\/wp-json\/wp\/v2\/pages\/4864\/revisions\/5240"}],"up":[{"embeddable":true,"href":"https:\/\/hpc-education.unn.ru\/ru\/wp-json\/wp\/v2\/pages\/4491"}],"wp:attachment":[{"href":"https:\/\/hpc-education.unn.ru\/ru\/wp-json\/wp\/v2\/media?parent=4864"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}