Nghiên cứu các yếu tố ảnh hưởng đến quá trình tổng hợp FOS từ saccharose

2. NGUYÊN VẬT LIỆU, HÓA CHẤT, THIẾT BỊ VÀ PHƯƠNG PHÁP

3.2. Nghiên cứu các yếu tố ảnh hưởng đến quá trình tổng hợp FOS từ saccharose

(3.21)

Trong đó, k là hằng số, có giá trị là giá trị lớn nhất trong quần thể.

3.3.3.3. Lai ghép

Có nhiều phương pháp lai ghép, chúng tôi đề xuất sử dụng phương pháp lai ghép đoạn nhiễm sắc thể trong gen P và gen Q của quần thể. Phát sinh ngẫu nhiên một vị trí bắt đầu, một vị trí kết thúc của gen P, cắt đoạn nhiễm sắc thể của gen P, Q đúng vị trí bắt đầu, kết thúc đã phát sinh rồi hoán đổi hai nhiễm sắc thể của gen P và của gen Q.

Ví dụ, chọn hai gen P={P1, P2,…, P11} và Q={Q1, Q2,…, Q11} phát sinh ngẫu nhiên có vị trí bắt đầu là 02 và vị trí kết thúc là 08. Quá trình lai ghép sẽ tạo ra hai gen mới là PC={P1, Q2,…, Q8, P9, P10, P11} và QC={Q1, P2,…, P8, Q9, Q10, Q11}.

3.3.3.4. Đột biến

Trong nghiên cứu này, chúng tôi tiến hành đột biến tại một vị trí ngẫu nhiên của gen P. Gen P có thể là cá thể xấu nhất hay cá thể trung bình hay cá thể ngẫu nhiên trong quần thể được chọn sẽ tùy thuộc vào quá trình tiến hóa như thế nào.

Trong quá trình tiến hóa chúng tôi sử dụng cá thể đột biến hầu như là cá thể ngẫu nhiên hay trung bình. Nếu trong một thời gian dài quần thể không có sự thay đổi nào khác (độ lệch của hàm mục tiêu so với dữ liệu thực nghiệm không tối thiểu được nữa), chúng tôi sẽ sử dụng cá thể xấu nhất để đột biến.

Ví dụ, chọn gen P={P1, P2,…, P11} để đột biến. Tiến hành ngẫu nhiên hóa vị trí đột biến, mà tại đó có giá trị a sẽ khác nhiều với giá trị (1 – a), giả sử là vị trí 11, thì cá thể mới là X={P1, P2,…, 1- P11}.

3.3.3.5. Giải bài toán tối ưu

Việc giải bài toán này được tiến hành qua 2 giai đoạn: tạo quần thể và tìm nghiệm tối ưu.

Giai đoạn 1: Tạo quần thể bằng phương pháp ngẫu nhiên

Với mục đích tạo quần thể ban đầu, chúng tôi đề xuất thuật toán 1 để giải quyết với lưu đồ thuật toán trong hình 3.2.

Thuật toán 1. Xây dựng quần thể bằng phương pháp ngẫu nhiên

- Bước 1: Chọn một phần tử cho quần thể + Bước 1.1: Chọn ngẫu nhiên các phần tử

+ Bước 1.2: Giải hệ phương trình vi phân bằng phương pháp Runge-Kutta bậc 4 + Bước 1.3: Tính giá trị của hàm mục tiêu Ei từ công thức (3.19)

+ Bước 1.4: Tính điều kiện ràng buộc dk Nếu Kms < Kmk < Kmn thì dk = 1 Vms > Vmk > Vmn

Ngược lại thì dk = 0

+ Lặp lại bước 1.1 nếu dk=0 hoặc Ei > giá trị dừng - Bước 2: Lặp lại cho đến khi đủ số phần tử trong quần thể

Hình 3.2. Lưu đồ thuật toán xây dựng quần thể bằng phương pháp ngẫu nhiên

Kết quả quần thể thu được ở giai đoạn 1 được trình bày trong bảng 3.4.

Sai

Bắt đầu

Chọn ngẫu nhiên 1 phần tử trong quần thể

dk=0 hoặc E>giá trị dừng

Tính giá trị của hàm mục tiêu E

Đúng

i=1

Giải hệ phương trình vi phân

Tính điều kiện ràng buộc dk

Sai Đủ số phần tử trong quần thể? Kết thúc Đúng i=i+1

Bảng 3.4. Quần thể được xây dựng bằng phương pháp ngẫu nhiên trong giai đoạn 1

E Kms Kmk Kmn Kigs Kigk Kign Vms Vmk Vmn Kmhn Vmhn

8.7033124e+003 3.7843173e+002 6.5074569e+002 7.9305809e+002 2.2313966e+001 2.3487415e+002 8.2953229e+001 6.3142269e+002 1.0148470e+002 3.4936958e+001 2.8690041e+002 3.4547214e+000 8.7033124e+003 3.7843173e+002 6.5074569e+002 7.9305809e+002 2.2313966e+001 2.3487415e+002 8.2953229e+001 6.3142269e+002 1.0148470e+002 3.4936958e+001 2.8690041e+002 3.4547214e+000 8.7074863e+003 2.0326471e+002 5.5564448e+002 8.8411591e+002 1.5577013e+001 2.7883533e+002 6.7629411e+001 4.7197459e+002 8.5702092e+001 4.7670694e+001 3.1678393e+002 2.9225531e+000 8.7146942e+003 3.1962116e+002 5.3670221e+002 7.6274898e+002 1.5695193e+001 2.9282603e+002 8.0527670e+001 6.8587082e+002 8.0904682e+001 2.9015542e+001 2.9893132e+002 3.3786503e+000 8.7190054e+003 3.2918185e+002 4.0463897e+002 7.6911048e+002 1.9412520e+001 2.5584467e+002 7.6782259e+001 6.1469825e+002 6.6666777e+001 3.9791661e+001 2.4069278e+002 5.8561680e-001 8.7190054e+003 3.2918185e+002 4.0463897e+002 7.6911048e+002 1.9412520e+001 2.5584467e+002 7.6782259e+001 6.1469825e+002 6.6666777e+001 3.9791661e+001 2.4069278e+002 5.8561680e-001 8.7197539e+003 1.8644731e+002 5.2941547e+002 7.5498597e+002 1.1814948e+001 2.9548435e+002 9.1381404e+001 5.3627776e+002 7.6058654e+001 3.4434023e+001 1.9639105e+002 2.3668199e-001 8.7244919e+003 2.1158162e+002 7.2419009e+002 7.4391415e+002 1.5590145e+001 2.9203713e+002 6.6902713e+001 4.9348367e+002 1.0236467e+002 3.5741324e+001 2.1237813e+002 1.8618971e+000 8.7245302e+003 4.0783717e+002 4.6002604e+002 9.4308318e+002 2.2525631e+001 2.9416960e+002 8.0562993e+001 6.4625257e+002 7.1182193e+001 4.8235790e+001 3.0123722e+002 7.4233920e-001 8.7301432e+003 2.4147073e+002 3.1278525e+002 7.2805037e+002 1.2838954e+001 2.5668978e+002 1.0037248e+002 6.4887460e+002 5.6308056e+001 3.1158139e+001 2.3338523e+002 1.8583208e+000 8.7330335e+003 1.4766049e+002 5.9676636e+002 6.1817031e+002 1.2226018e+001 2.7506344e+002 9.7194817e+001 4.4218447e+002 8.9064446e+001 2.7403313e+001 1.8998826e+002 1.8557799e+000 8.7371583e+003 2.3953874e+002 3.5600348e+002 8.8452208e+002 1.2118599e+001 2.8879676e+002 9.7237663e+001 6.4810244e+002 5.9174163e+001 4.1465691e+001 8.9651530e+001 1.9485556e-001 8.7371583e+003 2.3953874e+002 3.5600348e+002 8.8452208e+002 1.2118599e+001 2.8879676e+002 9.7237663e+001 6.4810244e+002 5.9174163e+001 4.1465691e+001 8.9651530e+001 1.9485556e-001 8.7381300e+003 4.4337023e+002 4.9633555e+002 6.2937778e+002 2.3881015e+001 2.9032499e+002 1.0257193e+002 6.9714459e+002 7.7220300e+001 2.4302709e+001 5.7731134e+001 1.6909047e+000 8.7425368e+003 3.7578532e+002 5.9436535e+002 5.9438004e+002 1.9238459e+001 2.8616330e+002 9.2376477e+001 6.9597561e+002 8.8127790e+001 2.4536973e+001 1.6000034e+002 1.4671351e+000 8.7457798e+003 3.1062929e+002 3.6769817e+002 6.3677243e+002 1.8527504e+001 2.3091943e+002 7.8516216e+001 6.1565309e+002 6.7063666e+001 2.9993850e+001 2.3679635e+002 3.8372565e+000 8.7488407e+003 1.8987829e+002 3.5792396e+002 7.9815543e+002 1.0212053e+001 2.9289367e+002 6.6288691e+001 6.1023211e+002 6.0065256e+001 5.1690421e+001 2.0671047e+002 6.7156363e-001 8.7495495e+003 2.5600708e+002 5.6858639e+002 6.9825535e+002 1.4407826e+001 2.7448065e+002 9.2700379e+001 5.9967103e+002 8.5439052e+001 2.7508592e+001 1.0079180e+002 1.1029927e+000 8.7560121e+003 3.3424678e+002 4.4942499e+002 8.4100773e+002 2.3287262e+001 2.7577283e+002 6.7316551e+001 5.5303056e+002 7.4497823e+001 3.8552184e+001 2.2299642e+002 3.9756233e+000 8.7568852e+003 4.9058048e+002 5.1770808e+002 5.9756518e+002 3.0139224e+001 3.8484249e+002 1.7944399e+002 6.4394894e+002 7.7410976e+001 2.1764258e+001 1.1819890e+002 2.7209286e+000 8.7596021e+003 3.1577372e+002 4.4445323e+002 8.2758326e+002 1.8923435e+001 2.8848429e+002 1.0517713e+002 6.0988946e+002 7.1457115e+001 4.2453869e+001 3.1621882e+002 1.9017512e+000 8.7639747e+003 2.8704206e+002 7.0821218e+002 7.6805307e+002 1.6228222e+001 2.7144796e+002 6.1544340e+001 6.2594539e+002 1.0222949e+002 4.4393865e+001 2.7572330e+002 1.3742235e+000 8.7724465e+003 3.6697357e+002 4.9497047e+002 5.9746225e+002 2.1714520e+001 2.2261809e+002 9.7736952e+001 6.1813104e+002 8.0769023e+001 2.7139785e+001 2.7819222e+002 6.2943611e-001 8.7724465e+003 3.6697357e+002 4.9497047e+002 5.9746225e+002 2.1714520e+001 2.2261809e+002 9.7736952e+001 6.1813104e+002 8.0769023e+001 2.7139785e+001 2.7819222e+002 6.2943611e-001 8.7759126e+003 4.4647079e+002 6.1047175e+002 8.5135170e+002 2.3381068e+001 2.1414982e+002 1.0462618e+002 6.9266741e+002 9.6469966e+001 3.0214028e+001 7.6321318e+001 1.1399812e+000 8.7787708e+003 3.0010055e+002 3.1737777e+002 9.0139474e+002 1.8815428e+001 2.8719801e+002 8.3259936e+001 5.9599279e+002 5.6493942e+001 4.3836498e+001 2.4276524e+002 2.4706342e+000 8.7793698e+003 1.6421120e+002 5.0442026e+002 7.0701068e+002 1.0599724e+001 2.9645526e+002 6.0958887e+001 5.1828122e+002 7.4169149e+001 3.4993737e+001 2.9311371e+002 2.2056922e+000 8.7816514e+003 3.8037136e+002 6.9723409e+002 8.8505761e+002 2.2401803e+001 2.6876978e+002 6.8350870e+001 6.2311470e+002 1.0539544e+002 4.4665358e+001 2.2850154e+002 3.8368112e+000 8.7837574e+003 3.1356554e+002 3.9957086e+002 7.5360394e+002 2.3263119e+001 2.9757115e+002 9.8978948e+001 5.2170391e+002 6.6714647e+001 2.8245400e+001 1.7488622e+002 2.6210529e+000 8.7837574e+003 3.1356554e+002 3.9957086e+002 7.5360394e+002 2.3263119e+001 2.9757115e+002 9.8978948e+001 5.2170391e+002 6.6714647e+001 2.8245400e+001 1.7488622e+002 2.6210529e+000 8.7837574e+003 3.1356554e+002 3.9957086e+002 7.5360394e+002 2.3263119e+001 2.9757115e+002 9.8978948e+001 5.2170391e+002 6.6714647e+001 2.8245400e+001 1.7488622e+002 2.6210529e+000 8.7898763e+003 1.5125777e+002 7.1762753e+002 7.9282144e+002 1.1552500e+001 2.8748690e+002 9.6024279e+001 4.5837876e+002 1.0084677e+002 3.1871256e+001 2.2696988e+002 2.6316622e+000 8.7941503e+003 1.8277109e+002 5.7831536e+002 8.1752141e+002 1.1727977e+001 2.8202515e+002 7.1360069e+001 5.4232901e+002 8.3139481e+001 4.6320986e+001 2.0748949e+002 1.5255559e-001 8.7941503e+003 1.8277109e+002 5.7831536e+002 8.1752141e+002 1.1727977e+001 2.8202515e+002 7.1360069e+001 5.4232901e+002 8.3139481e+001 4.6320986e+001 2.0748949e+002 1.5255559e-001 8.7941503e+003 1.8277109e+002 5.7831536e+002 8.1752141e+002 1.1727977e+001 2.8202515e+002 7.1360069e+001 5.4232901e+002 8.3139481e+001 4.6320986e+001 2.0748949e+002 1.5255559e-001 8.7941503e+003 1.8277109e+002 5.7831536e+002 8.1752141e+002 1.1727977e+001 2.8202515e+002 7.1360069e+001 5.4232901e+002 8.3139481e+001 4.6320986e+001 2.0748949e+002 1.5255559e-001 8.7967496e+003 4.1644177e+002 5.0833452e+002 8.7306849e+002 2.2313254e+001 2.5107932e+002 1.0951711e+002 6.8184152e+002 8.3008243e+001 3.1748437e+001 2.8611976e+002 3.0622499e+000 8.7967496e+003 4.1644177e+002 5.0833452e+002 8.7306849e+002 2.2313254e+001 2.5107932e+002 1.0951711e+002 6.8184152e+002 8.3008243e+001 3.1748437e+001 2.8611976e+002 3.0622499e+000 8.8024588e+003 4.2402399e+002 5.5906497e+002 9.1617491e+002 2.2625883e+001 2.2546298e+002 6.8069077e+001 6.8749271e+002 9.0226178e+001 5.6957960e+001 1.8495715e+002 1.6206751e+000 8.8058159e+003 2.7338772e+002 4.0716076e+002 7.4578687e+002 1.6063196e+001 2.7015504e+002 5.5599114e+001 5.9334495e+002 6.4734553e+001 5.3523312e+001 1.0130565e+002 2.0906202e-002

8.8526433e+003 3.7855923e+002 5.9785680e+002 8.2750888e+002 1.9115540e+001 2.5102984e+002 7.7214938e+001 6.8685427e+002 9.0875004e+001 3.5993726e+001 1.1458065e+002 9.3697357e-001 8.8526433e+003 3.7855923e+002 5.9785680e+002 8.2750888e+002 1.9115540e+001 2.5102984e+002 7.7214938e+001 6.8685427e+002 9.0875004e+001 3.5993726e+001 1.1458065e+002 9.3697357e-001 8.8526433e+003 3.7855923e+002 5.9785680e+002 8.2750888e+002 1.9115540e+001 2.5102984e+002 7.7214938e+001 6.8685427e+002 9.0875004e+001 3.5993726e+001 1.1458065e+002 9.3697357e-001 8.8558377e+003 4.1106240e+002 5.6556523e+002 6.2644059e+002 2.1740246e+001 2.4548611e+002 5.0010842e+001 6.7427926e+002 8.6946691e+001 4.4313357e+001 2.9656419e+002 3.5300928e-001 8.8656307e+003 3.4543012e+002 4.6791317e+002 7.5816591e+002 1.9041568e+001 2.8187761e+002 9.0667865e+001 6.5118221e+002 7.6660404e+001 2.4637925e+001 3.1376035e+002 6.0675393e+000 8.8843237e+003 4.3209587e+002 8.0446251e+002 8.1547099e+002 2.2112247e+001 3.9397108e+002 9.6818968e+001 7.1034604e+002 1.0244979e+002 4.0125473e+001 3.9741934e+002 3.9356546e+000 8.8843237e+003 4.3209587e+002 8.0446251e+002 8.1547099e+002 2.2112247e+001 3.9397108e+002 9.6818968e+001 7.1034604e+002 1.0244979e+002 4.0125473e+001 3.9741934e+002 3.9356546e+000 8.8843237e+003 4.3209587e+002 8.0446251e+002 8.1547099e+002 2.2112247e+001 3.9397108e+002 9.6818968e+001 7.1034604e+002 1.0244979e+002 4.0125473e+001 3.9741934e+002 3.9356546e+000 8.8954674e+003 2.6376205e+002 5.0016727e+002 6.1360477e+002 1.6105373e+001 2.5507922e+002 5.4205247e+001 5.7633937e+002 8.3046142e+001 3.3146355e+001 3.0731303e+002 5.0795193e+000 8.8954674e+003 2.6376205e+002 5.0016727e+002 6.1360477e+002 1.6105373e+001 2.5507922e+002 5.4205247e+001 5.7633937e+002 8.3046142e+001 3.3146355e+001 3.0731303e+002 5.0795193e+000 8.8954674e+003 2.6376205e+002 5.0016727e+002 6.1360477e+002 1.6105373e+001 2.5507922e+002 5.4205247e+001 5.7633937e+002 8.3046142e+001 3.3146355e+001 3.0731303e+002 5.0795193e+000 8.9018283e+003 3.2612625e+002 5.3072951e+002 9.4245796e+002 1.7832005e+001 3.9118678e+002 1.2949963e+002 6.4949981e+002 7.5199509e+001 3.5226095e+001 2.8213806e+002 1.0300801e+000 8.9018283e+003 3.2612625e+002 5.3072951e+002 9.4245796e+002 1.7832005e+001 3.9118678e+002 1.2949963e+002 6.4949981e+002 7.5199509e+001 3.5226095e+001 2.8213806e+002 1.0300801e+000 8.9064860e+003 1.9069648e+002 4.9545721e+002 9.4634626e+002 1.4155920e+001 2.3916044e+002 5.6846280e+001 4.8089091e+002 7.9645419e+001 5.8377964e+001 2.6919912e+002 2.6059889e+000 8.9292638e+003 3.5163537e+002 5.4467115e+002 8.4188635e+002 1.8715503e+001 2.6063126e+002 1.0403907e+002 6.6287631e+002 8.1891642e+001 3.0944456e+001 1.3079846e+002 2.6688186e-001 8.9292638e+003 3.5163537e+002 5.4467115e+002 8.4188635e+002 1.8715503e+001 2.6063126e+002 1.0403907e+002 6.6287631e+002 8.1891642e+001 3.0944456e+001 1.3079846e+002 2.6688186e-001 8.9292638e+003 3.5163537e+002 5.4467115e+002 8.4188635e+002 1.8715503e+001 2.6063126e+002 1.0403907e+002 6.6287631e+002 8.1891642e+001 3.0944456e+001 1.3079846e+002 2.6688186e-001 8.9312004e+003 2.3791283e+002 4.1101175e+002 7.3756994e+002 1.3479088e+001 2.9309741e+002 9.3371369e+001 5.9567978e+002 6.5906490e+001 3.2850798e+001 2.0573664e+002 2.8944660e+000 8.9334708e+003 2.8939066e+002 4.4691078e+002 6.9132841e+002 1.4865582e+001 1.9532775e+002 8.5282383e+001 6.6415766e+002 7.6178518e+001 2.9752233e+001 2.9388439e+002 2.3362043e-001 8.9391624e+003 1.2915156e+002 6.6157533e+002 9.7071771e+002 1.0619566e+001 2.2816454e+002 1.4695049e+002 4.4834150e+002 1.0582775e+002 2.9920644e+001 2.0573409e+002 3.2432895e+000 8.9505640e+003 2.4832385e+002 3.0591734e+002 7.2886804e+002 1.3098201e+001 2.3026822e+002 6.1640510e+001 6.6249779e+002 5.7402211e+001 4.1039236e+001 1.7213606e+002 1.6914487e+000 8.9538500e+003 3.6557999e+002 4.4487928e+002 5.1345830e+002 2.5195045e+001 2.9723028e+002 8.0855423e+001 5.6426785e+002 7.4679121e+001 2.7472517e+001 6.1276266e+001 2.3735669e+000 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