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Data, Results and Codes: Application of NSGA-II in tourism logistics

2019-05-02 14:47:48 作者：互联网

Appendix A – Initial Dataset of Illustrative Case

No. of BS	Category of Basic Site	Location of BS	Demand in Basic Site, unit: kg		*Capacity (Ski) of supply of items A from Production Site to the current Basic Site, unit: kg*										Sum of Capacity of item A for BS
No. of BS	Category of Basic Site	Location of BS	items A	items B	PS1	PS2	PS3	PS4	PS5	PS6	PS7	PS8	PS9	PS10	Sum of Capacity of item A for BS
1	Airport	(1, 8)	DiA~N(10000, 2408)	DiB~N(15264, 5780)	0	2156	0	5389	4311	0	0	1078	3233	0	16167
2	Coach station	(82, 18)	DiA~N(2892, 250)	DiB~N(4142, 222)	0	0	0	0	1200	0	1800	0	0	600	3600
3	Coach station	(45, 4)	DiA~N(2718, 62)	DiB~N(4177, 792)	192	384	0	0	575	0	767	0	959	0	2877
4	Train station	(58, 84)	DiA~N(4185, 1010)	DiB~N(6158, 1367)	0	0	1287	0	0	1716	0	0	858	429	4290
5	Train station	(83, 81)	DiA~N(4222, 624)	DiB~N(5954, 52)	0	0	0	0	0	0	0	0	0	4813	4813
6	Train station	(87, 22)	DiA~N(4422, 1015)	DiB~N(7624, 1421)	0	0	0	0	3090	0	1030	0	0	2060	6180
7	Metro station	(6, 33)	DiA~N(586, 102)	DiB~N(1503, 286)	0	415	0	138	0	0	0	0	277	0	830
8	Metro station	(71, 57)	DiA~N(802, 79)	DiB~N(664, 118)	0	0	0	0	0	0	0	0	0	933	933
9	Metro station	(56, 44)	DiA~N(832, 43)	DiB~N(1328, 269)	0	0	613	0	0	0	0	0	0	307	920
10	Metro station	(73, 65)	DiA~N(669, 146)	DiB~N(656, 158)	0	0	0	0	0	0	0	0	0	836	836
11	Metro station	(93, 69)	DiA~N(643, 124)	DiB~N(1249, 136)	0	0	0	0	0	0	0	0	0	772	772
12	Metro station	(67, 72)	DiA~N(625, 66)	DiB~N(1059, 68)	0	0	0	0	0	0	0	0	0	692	692
13	Metro station	(37, 76)	DiA~N(845, 21)	DiB~N(961, 175)	0	0	273	0	0	182	0	0	363	91	909
14	Metro station	(76, 70)	DiA~N(583, 21)	DiB~N(974, 167)	0	0	0	0	0	0	0	0	0	623	623
15	Metro station	(95, 19)	DiA~N(899, 10)	DiB~N(1314, 309)	0	0	0	0	0	0	306	0	0	613	919
16	Metro station	(29, 8)	DiA~N(603, 5)	DiB~N(890, 203)	0	311	0	104	0	208	0	0	0	0	623
17	Restaurant	(89, 81)	DiA~N(1735, 249)	DiB~N(2742, 45)	0	0	0	0	0	0	0	0	0	2501	2501
18	Restaurant	(66, 10)	DiA~N(1994, 489)	DiB~N(1393, 164)	1388	0	0	0	925	0	0	0	463	0	2776
19	Restaurant	(95, 1)	DiA~N(1711, 347)	DiB~N(3684, 270)	0	0	0	0	618	0	927	0	0	309	1854
20	Restaurant	(58, 11)	DiA~N(1556, 29)	DiB~N(2936, 627)	221	0	442	0	111	0	0	0	553	332	1659
21	Restaurant	(91, 54)	DiA~N(2331, 130)	DiB~N(2909, 61)	0	0	0	0	875	0	0	0	0	1750	2625
22	Restaurant	(20, 75)	DiA~N(2387, 39)	DiB~N(1802, 309)	0	0	0	0	0	423	0	0	846	1268	2537
23	Restaurant	(61, 89)	DiA~N(2425, 528)	DiB~N(1731, 256)	0	0	246	0	0	983	0	0	738	492	2459
24	Restaurant	(43, 32)	DiA~N(1706, 5)	DiB~N(3174, 529)	0	0	574	862	0	0	0	0	287	0	1723
25	Restaurant	(65, 34)	DiA~N(1757, 293)	DiB~N(209, 41)	814	1220	0	0	0	0	0	0	0	407	2441
26	Restaurant	(65, 61)	DiA~N(1959, 113)	DiB~N(2935, 343)	746	0	0	1491	0	0	0	0	0	0	2237
27	Hotel	(7, 17)	DiA~N(1390, 170)	DiB~N(852, 171)	0	1196	0	0	0	0	0	0	598	0	1794
28	Hotel	(74, 39)	DiA~N(1084, 185)	DiB~N(1984, 286)	0	0	0	0	0	0	0	0	0	1518	1518
29	Hotel	(78, 54)	DiA~N(1480, 100)	DiB~N(1785, 59)	0	0	0	0	0	0	0	0	0	1657	1657
30	Hotel	(94, 65)	DiA~N(1336, 138)	DiB~N(2083, 298)	0	0	0	0	1198	0	0	0	0	599	1797
31	Hotel	(97, 27)	DiA~N(1010, 178)	DiB~N(1016, 234)	0	0	0	0	0	0	358	0	0	716	1074
32	Hotel	(94, 86)	DiA~N(1189, 215)	DiB~N(1118, 114)	0	0	0	0	884	0	0	0	0	442	1326
33	Hotel	(70, 45)	DiA~N(792, 91)	DiB~N(2001, 236)	0	609	0	0	0	0	0	0	0	304	913
34	Hotel	(90, 28)	DiA~N(1195, 122)	DiB~N(1710, 166)	0	0	0	0	0	0	941	0	0	471	1412
35	Hotel	(13, 96)	DiA~N(1375, 290)	DiB~N(753, 164)	0	0	0	0	0	985	0	0	328	657	1970
36	Hotel	(11, 62)	DiA~N(763, 5)	DiB~N(1415, 344)	0	260	0	0	0	0	0	0	520	0	780
37	Tourist attractions	(47, 40)	DiA~N(8858, 333)	DiB~N(11697, 1432)	0	0	4625	1542	0	0	0	0	3083	0	9250
38	Tourist attractions	(22, 94)	DiA~N(8202, 1975)	DiB~N(12321, 96)	0	0	0	0	0	7317	0	0	2439	4878	14634
39	Tourist attractions	(55, 63)	DiA~N(8510, 1989)	DiB~N(13844, 2765)	0	0	0	0	0	0	0	0	4981	9963	14944
40	Tourist attractions	(44, 85)	DiA~N(8247, 968)	DiB~N(11739, 87)	0	0	1022	0	0	4088	0	0	2044	3066	10220
41	Tourist attractions	(76, 41)	DiA~N(8804, 313)	DiB~N(10709, 1586)	0	0	0	0	0	0	0	0	0	9391	9391
42	Tourist attractions	(28, 98)	DiA~N(8391, 1428)	DiB~N(13323, 410)	0	0	0	0	0	2874	0	0	1437	4311	8622
43	Tourist attractions	(14, 41)	DiA~N(8312, 103)	DiB~N(11699, 754)	0	0	0	2855	0	0	0	0	5710	0	8565
44	Whole retailer/Retailer	(97, 35)	DiA~N(6295, 1289)	DiB~N(8247, 1416)	0	0	0	0	6161	0	0	0	0	3081	9242
45	Whole retailer/Retailer	(62, 1)	DiA~N(6495, 194)	DiB~N(9324, 1801)	2752	1376	0	0	2064	0	0	0	688	0	6880
46	Whole retailer/Retailer	(13, 19)	DiA~N(6492, 1429)	DiB~N(11305, 397)	0	4922	0	0	0	2461	0	0	0	0	7383
47	Whole retailer/Retailer	(31, 49)	DiA~N(6363, 895)	DiB~N(8866, 1580)	3957	989	2968	1979	0	0	0	0	0	0	9893
48	Whole retailer/Retailer	(41, 95)	DiA~N(6365, 588)	DiB~N(8637, 1225)	0	0	0	775	0	2326	0	0	3101	1551	7753
49	Whole retailer/Retailer	(7, 1)	DiA~N(7451, 1606)	DiB~N(10154, 2153)	0	6310	0	0	0	0	3155	0	0	0	9465
50	Whole retailer/Retailer	(73, 24)	DiA~N(6886, 1671)	DiB~N(10071, 1103)	0	0	0	0	1197	0	3592	0	2395	4789	11973
Location of the current PS					(55, 25)	(18, 19)	(45, 66)	(30, 40)	(73, 17)	(28, 78)	(88, 11)	(10, 85)	(15, 63)	(59, 69)

Appendix B – Data of Good Compromise Solutions

Good Compromise Solution 1															Good Compromise Solution 2
BSi*		*bqAi /kg**		*bqBi /kg**		CDCj*		*qAj /kg**		*qBj /kg**	Qkj* /kg		PSk*		BSi*		*bqAi /kg**		*bqBi /kg**		CDCj*		*qAj /kg**			*qBj /kg**		Qkj* /kg		PSk*
1		14954		16994		2		24016		29487	1994		2		1		14735		16986		2		23776		29578			1965		2
2		3435		4699							4985		4		2		3442		4673									4912		4
22		2477		2543							6297		5		22		2474		2562									6222		5
30		1746		2960							413		6		30		1719		3023									413		6
34		1404		2286							2653		7		34		1406		2330									2658		7
											997		8															983		8
											3816		9															3772		9
											2861		10															2852		10
4		4255		9417		4		13053		23013	1277		3		4		4257		10286		4		13032		24027			1277		3
44		8797		13593							5865		5		44		8775		13739									5850		5
											1702		6															1703		6
											851		9															852		9
											3358		10															3351		10
5		4749		6041		5		27933		42197	742		1		5		4734		6065		5		27704		41958			737		1
6		6043		9904							6244		2		6		5876		9926									6289		2
17		2410		2864							1482		4		17		2303		2863									1472		4
19		1820		4107							4510		5		19		1830		4293									4427		5
26		2223		3840							5039		7		26		2208		3778									5039		7
32		1323		1417							9917		10		32		1318		1410									9741		10
49		9365		14016											49		9433		13616
7		771		2472		7		7588		15364	2727		1		7		770		2562		7		7566		15433			2718		1
45		6816		12890							1749		2		45		6796		12869									1744		2
											128		4															128		4
											2045		5															2039		5
											939		9															937		9
9		908		2315		9		1588		3623	605		3		9		903		2402		9		1576		3684			602		3
12		680		1307							983		10		12		673		1280									975		10
3		2855		5860		13		3754		7295	191		1		3		2853		5903		13		3758		7202			190		1
13		899		1433							381		2		13		905		1297									381		2
											270		3															272		3
											571		5															570		5
											180		6															181		6
											761		7															761		7
											1311		9															1312		9
											90		10															91		10
8		920		1023		14		2152		3981	310		2		8		922		1020		14		2159		3929			310		2
14		610		1439							104		4		14		615		1458									104		4
16		622		1516							208		6		16		620		1447									207		6
											1530		10															1538		10
25		2325		2350		25		16930		14924	775		1		25		2352		2350		25		15089		15003			784		1
38		14606		12572							1162		2		38		12737		12651									1176		2
											7303		6															6369		6
											2434		9															2123		9
											5256		10															4638		10
27		1742		1294		27		1742		1295	1161		2		27		1752		1293		27		1752		1294			1168		2
											581		9															584		9
10		828		1054		31		14113		21391	1348		1		10		810		1095		31		1398		21374			1304		1
15		915		2335							898		5		15		915		2322									869		5
18		2695		1766							2869		6		18		2608		1820									2861		6
31		1069		1728							661		7		31		1071		1742									662		7
42		8606		14504							1884		9		42		8583		14391									1866		9
											6454		10															6426		10
35		1764		1169		35		11155		12393	3756		1		35		1755		1132		35		10664		12699			3564		1
47		9391		11222							939		2		47		8909		11565									891		2
											2817		3															2673		3
											1879		4															1782		4
											882		6															877		6
											294		9															292		9
											588		10															585		10
23		2458		2403		36		12121		19285	5105		2		23		2452		2392		36		12147		19198			5120		2
29		1617		1997							246		3		29		1627		2018									245		3
36		778		2297							3405		6		36		777		2298									3411		6
46		7268		12584							1256		9		46		7291		12486									1254		9
											2109		10															2118		10
24		1721		4894		37		31282		43874	6172		3		24		1721		4747		37		30739		43312			6169		3
37		9187		14249							2392		4		37		9217		13984									2398		4
40		10049		11972							1032		5		40		9871		11985									993		5
50		10326		12755							4020		6		50		9930		12592									3948		6
											3098		7															2979		7
											7424		9															7319		9
											7145		10															6933		10
11		759		1779		39		12914		23449	4051		9		11		761		1758		39		13012		20680			4084		9
39		12155		21667							8862		10		39		12251		18920									8929		10
20		1629		4576		43		20402		35145	217		1		20		1632		4628		43		20352		36424			218		1
33		893		2633							596		2		33		886		2578									591		2
41		9374		14382							434		3		41		9329		15424									435		3
43		8506		13549							2835		4		43		8505		13789									2835		4
											109		5															109		5
											6214		9															6214		9
											9998		10															9951		10
21		2616		3136		48		11250		17135	715		4		21		2594		3136		48		11416		17328			733		4
28		1481		2767							872		5		28		1486		2877									865		5
48		7152		11228							2146		6		48		7335		11311									2201		6
											2861		9															2934		9
											4656		10															4684		10
Good Compromise Solution 3															Good Compromise Solution 4
BSi*	*bqAi /kg**		*bqBi /kg**		CDCj*		*qAj /kg**		*qBj /kg**			Qkj* /kg		PSk*	BSi*	*bqAi /kg**		*bqBi /kg**		CDCj*		*qAj /kg**		*qBj /kg**			Qkj* /kg		PSk*
1	15205		16957		2		24266		29454			2028		2	1	13488		17009		2		22583		29413			1799		2
2	3458		4722									5068		4	2	3464		4672									4496		4
22	2471		2534									6360		5	22	2479		2535									5912		5
30	1730		2956									412		6	30	1741		2992									413		6
34	1403		2279									2664		7	34	1411		2201									2672		7
												1014		8													899		8
												3865		9													3524		9
												2856		10													2867		10
4	4254		9306		4		13095		21801			1276		3	4	4255		10284		4		13381		22974			1277		3
44	8840		12493									5893		5	44	9126		12688									6084		5
												1702		6													1702		6
												851		9													851		9
												3373		10													3468		10
5	4724		6034		5		27679		42237			740		1	5	4790		6069		5		27444		42331			743		1
6	6061		9849									6132		2	6	5767		9840									6122		2
17	2337		2861									1480		4	17	2342		2872									1485		4
19	1818		4192									4518		5	19	1815		4209									4367		5
26	2220		3810									4985		7	26	2228		3995									4930		7
32	1322		1417									9825		10	32	1318		1444									9796		10
49	9197		14067												49	9184		13895
7	769		2454		7		7577		15202			2723		1	7	765		2559		7		7568		15289			2721		1
45	6808		12745									1746		2	45	6803		12728									1743		2
												128		4													127		4
												2043		5													2041		5
												938		9													936		9
9	896		2253		9		1572		3558			597		3	9	902		2335		9		1579		3668			601		3
12	676		1303									975		10	12	677		1330									978		10
3	2849		5879		13		3752		7288			190		1	3	2848		6170		13		3757		7465			190		1
13	903		1406									380		2	13	909		1292									380		2
												271		3													273		3
												569		5													569		5
												181		6													182		6
												760		7													759		7
												1310		9													1312		9
												90		10													91		10
8 14 16 0	921 613 621 0		1023 1449 1518 0		14 0 0 0		2154 0 0 0		3992 0 0 0			310		2	8	917		1038		14		2153		3963			310		2
												104		4	14	615		1453									104		4
												207		6	16 0	621 0		1469 0									207		6
												1533		10													1532		10
25	2310		2351		25		14904		14927			770		1	25	2268		2349		25		15218		14945			757		1
38	12594		12573									1155		2	38	12949		12594									1134		2
												6297		6													6475		6
												2099		9													2158		9
												4583		10													4695		10
27	1718		1281		27		1718		1282			1146		2	27	1752		1355		27		1752		1356			1168		2
												573		9													584		9
10	827		1094		31		14128		21578			1349		1	10	813		1085		31		14086		21451			1337		1
15	916		2374									899		5	15	915		2324									891		5
18	2697		1735									2874		6	18	2674		1798									2871		6
31	1067		1797									661		7	31	1070		1750									662		7
42	8621		14573									1887		9	42	8614		14489									1882		9
												6460		10													6444		10
35	1762		1160		35		11258		12043			3798		1	35 47	1747 9274		1161 11186		35		11021		12349			3710		1
47	9496		10882									949		2													927		2
												2849		3													2782		3
												1900		4													1855		4
												881		6													873		6
												293		9													291		9
												588		10													583		10
23	2456		2375		36		12125		19273			5103		2	23	2453		2393		36		12101		19258			5089		2
29	1627		1992									246		3	29	1626		2015									246		3
36	777		2290									3404		6	36	777		2272									3396		6
46	7266		12612									1255		9	46	7245		12574									1254		9
												2118		10													2117		10
24	1721		4971		37		31165		43395			6170		3	24	1721		4791		37		30712 0 0 0 0 0 0		43717 0 0 0 0 0 0			6150		3
37	9207		13920									2396		4	37	9214		14108									2397		4
40	9934		11971									1030		5	40	9697		11971									1008		5
50	10303		12529									3974		6	50 0 0 0	10080 0 0 0		12843 0 0 0									3879		6
												3091		7													3024		7
												7403		9													7314		9
												7101		10													6941		10
11	759		1711		39		12605		20855			3949		9	11	760		1750		39		12828		19852			4022		9
39	11846		19142									8657		10	39	12067		18100									8806		10
20	1624		4691		43		20385		35073			216		1	20	1628		4640		43		20349		34897			217		1
33	889		2629									593		2	33	889		2616									593		2
41	9365		14150									433		3	41	9336		13869									434		3
43	8508		13599									2836		4	43 0 0 0	8497 0 0 0		13768 0 0 0									2832		4
												109		5													109		5
												6213		9													6207		9
												9986		10													9958		10
21	2608		3140		48		11494		17814			740		4	21	2596		3131		48		11475		17054			739		4
28	1484		2788									870		5	28	1485		2893									865		5
48	7402		11882									2221		6	48	7394		11027									2218		6
												2961		9													2958		9
												4704		10													4695		10
* the solutions for each good compromise solution

Appendix C – MATLAB Code of NSGA II

The following four parts of the code are written down on our own including, Data input, Values of objective functions and constraints errors, variables normalisation and judgement of whether solutions feasible or infeasible.

Dataset input

%% dataset of TL case

num_bs=50; % number of BSs

num_cdc=num_bs;

num_ps=10;

V=num_bs*num_cdc+num_ps*num_cdc+num_cdc+num_bs*2+num_cdc*2+num_ps*num_cdc; % sum of variables

mu_ddpt_A=Demand_all(:,1)'; % ddpt~N(mu,sigma) and the number related to every BS

sigma_ddpt_A=Demand_all(:,2)';

mu_ddpt_B=Demand_B(:,1)';

sigma_ddpt_B=Demand_B(:,2)';

S_pb=supply';

W_pb=(S_pb>0);

loc_bs=loc_bs; % locations of BSs

loc_ps=loc_ps;

loc_cdc=loc_bs;

alph_A=4; % cost for Items A increasing per unit

alph_B=3;

beta_cdc=100000; % cost for opening a CDC

gam_AB=12000; % unit cost of transport

gam_A=8400;

gam_B=5900;

Objective Functions and Constraints errors

function [fit,err,err2]=TL_case(x)

global num_bs num_cdc num_ps mu_ddpt_A sigma_ddpt_A mu_ddpt_B sigma_ddpt_B

global S_pb alph_A alph_B beta_cdc gam_AB gam_A gam_B

global loc_bs loc_cdc loc_ps

%% code starts

c=[];

pA=0;

pB=0;

num_f3=num_bs*num_cdc+num_ps*num_cdc+num_cdc;

x(:,1:num_f3)=round(x(:,1:num_f3));

% establish a new S_pb for judgement

%x1-xij, x2-ykj, x3-zj, x4-bqAi, x5-bqBi, x6-qAj, x7-qBj, x8-Qkj.

x1=x(:,1:num_bs*num_cdc); %('0010000100001000001000010'); % Decision variables, xij, ykj, zj should automatically be processed here is for trial.

x2=x(:,num_bs*num_cdc+1:num_bs*num_cdc+num_ps*num_cdc); % ('001000010000010'); % The rule of string is that from left to right, y11, 12, 13, 14, 15, 21, 22, 23, 24, 25, 31, 32, 33, 34, 35 % binary string represented by a decimal value for bitget

x3=x(:,num_bs*num_cdc+num_ps*num_cdc+1:num_f3); % ('00110');

x4=x(:,num_f3+1:num_f3+num_bs); % the number is capacity of every BS and should be processed by compute automatically, here is for trial

x5=x(:,num_f3+1+num_bs:num_f3+num_bs+num_bs);

x6=x(:,num_f3+1+num_bs+num_bs:num_f3+num_bs+num_bs+num_cdc); % the number is capacity of every potential CDC

x7=x(:,num_f3+1+num_bs+num_bs+num_cdc:num_f3+num_bs+num_bs+num_cdc+num_cdc); % for items B

x8=x(:,num_f3+1+num_bs+num_bs+num_cdc+num_cdc:num_f3+num_bs+num_bs+num_cdc+num_cdc+num_ps*num_cdc);

%% Handling constraints

%% Constraint 1 and 2

for hci=1:num_bs

cons_1=sum(x1(:,(hci-1)*num_cdc+1:hci*num_cdc),2);

c(:,hci)=cons_1-1.1; %initially normalisaiton of constraints xij (uniform is <=0)

c(:,num_bs+hci)=0.9-cons_1; % first num_bs columns save constraint 1

% constraints 1 and 2 in which sum of xij <=0, i.e. 0.9<=sum of xij <=1.1

end

%% Constraint 3 and 4

for jj=1:num_cdc % Must notice the order of loop who is first and then.

cons_3=0;

cons_4=0;

for ii=1:num_bs % Who is inner will be first loop.

o_bc_ctf=(ii-1)*num_cdc+jj; % the location of current BS on the string

xx1_bc_ctf=x1(:,o_bc_ctf);

cons_3=cons_3+xx1_bc_ctf.*x4(:,ii);

cons_4=cons_4+xx1_bc_ctf.*x5(:,ii);

end

c(:,num_bs+num_bs+jj)=cons_3-x6(:,jj)-num_bs-2; % num_bs and 2 are used to compensate variance from round function

c(:,num_bs+num_bs+num_cdc+jj)=cons_4-x7(:,jj)-num_bs-2;

end

%% Contraint 5: Q<=S

for kkkkk=1:num_ps

for jjjjj=1:num_cdc

cons_5=0;

o_pc_c5=(kkkkk-1)*num_cdc+jjjjj;

for iiiii=1:num_bs

o_bc_c5=(iiiii-1)*num_cdc+jjjjj;

xx1_bc_c5=x1(:,o_bc_c5);

cons_5=cons_5+S_pb(kkkkk,iiiii).*xx1_bc_c5;

end

c(:,num_bs+num_bs+num_bs+num_bs+o_pc_c5)=x8(:,o_pc_c5)-cons_5-num_ps-3;

end

%% Constrain 6: qAj<=sum of Qkj

for jjjj=1:num_cdc

cons_6=0;

for kkkk=1:num_ps

o_pc_c6=(kkkk-1)*num_cdc+jjjj;

cons_6=cons_6+x8(:,o_pc_c6)*x3(:,jjjj);

end

c(:,num_bs+num_bs+num_cdc+num_cdc+num_cdc*num_ps+jjjj)=x6(:,jjjj)-cons_6-num_ps-2;

end

%% CSL

for i =1:num_bs

pA_temp =normcdf(x4(:,i), mu_ddpt_A(:,i), sigma_ddpt_A(:,i)); %probability of Items A in BSi

pB_temp=normcdf(x5(:,i), mu_ddpt_B(:,i), sigma_ddpt_B(:,i));

pA=pA+pA_temp; %probability across the whole network

pB=pB+pB_temp;

end

% TOC

%% Facility Cost includes PFC and POC

fc_bs=0;

fc_cdc=0;

fc_pfc_cdc=0;

for i=1:num_bs

fc_bs_temp=alph_A*x4(:,i)+alph_B*x5(:,i);

fc_cdc_temp=alph_A*x6(:,i)+alph_B*x7(:,i);

fc_pfc_cdc_temp=beta_cdc*x3(:,i);

fc_bs=fc_bs+fc_bs_temp; %sum of facility cost of BS

fc_cdc=fc_cdc+fc_cdc_temp;

fc_pfc_cdc=fc_pfc_cdc+fc_pfc_cdc_temp; % sum of periodic fixed cost for opening a CDC

end

fc_total=fc_bs+fc_cdc+fc_pfc_cdc;

%%Transportation cost, TCij, TCkj, TChj

tc_bs=0;

tc_ps=0;

tc_cdc=0;

%% transport cost of BS-CDC

for i=1:num_bs

for j =1:num_cdc

d_bs=sqrt( (loc_bs (i, 1)-loc_cdc(j,1))^2+(loc_bs (i, 2)-loc_cdc(j,2))^2);

o_bc=(i-1)*num_cdc+j; % the location of current BS on the string

xx1_bc=x1(:,o_bc); % Extract the value of current x1, i.e. xij, the rule of extract is from high to low position, i.e. left to right of the string

tc_bs_temp=d_bs*gam_AB*xx1_bc;

tc_bs=tc_bs+tc_bs_temp; %Cumulative transport costs of BS

end

%% transport cost of PS-CDC-CDC

for jjj=1:num_cdc

% transport cost of PS-CDC

for kkk=1:num_ps

d_ps=sqrt( (loc_cdc (jjj, 1)-loc_ps(kkk,1))^2+(loc_cdc(jjj, 2)-loc_ps(kkk,2))^2);

o_pc=(kkk-1)*num_cdc+jjj;

xx2_pc=x2(:,o_pc);

tc_ps_temp=d_ps*gam_A.*xx2_pc;

tc_ps=tc_ps+tc_ps_temp;

end

%% transport cost of CDC-CDC

for h=1:num_cdc

d_cdc_12=sqrt( (loc_cdc(jjj, 1)-loc_cdc(h,1))^2+(loc_cdc (jjj, 2)-loc_cdc(h,2))^2);

o_cdc_1=jjj;

o_cdc_2=h;

xx3_cdc_1=x3(:,o_cdc_1);

xx3_cdc_2=x3(:,o_cdc_2);

tc_cdc_temp=d_cdc_12.*gam_B.*xx3_cdc_1.*xx3_cdc_2;

tc_cdc=tc_cdc+tc_cdc_temp;

end

tc_total=tc_bs+tc_ps+tc_cdc;

f1=-(pA+pB)/(2*num_bs); % for both minised optimisation hereby using minus CSL

f2=fc_total+tc_total;

err2=c;

err=(c>0); % (c>0) if c(1,1)<=0, output c(1,1)=0;if c(1,2)>0, output c(1,2)=1.

fit=[f1,f2];

end

Variables Normalisation

%% This function is going to normalise the data of decision variables which are generated in the part of Main Loop as so to incorporate binary and decimal data at same time.

function [x]=variables_normalised(x_temp)

global num_bs num_cdc num_ps pop_size W_pb S_pb

%% Making a population feasible is to

% 1, ensure the sum of zj>=1;

% 2, randomly allocate bs to cdc while cdc's bs is only linked itself.

% 3, allocate ps to cdc.

% 4, other constraints are fulfilled.

% Notes: the variables really out of control is x3, x4 and x5, others'

% value are determined by these three measures.

no_x1=num_bs*num_cdc; % number of xij

no_x12=num_bs*num_cdc+num_cdc*num_ps; %xij+ykj

no_x123=num_bs*num_cdc+num_cdc*num_ps+num_cdc; %xij+ykj+zj

no_x14=no_x123+num_bs;

no_x15=no_x14+num_bs;

no_x16=no_x15+num_cdc;

no_x17=no_x16+num_cdc;

no_x18=no_x17+num_ps*num_cdc;

x=[];

for p=1:pop_size

%% Step 1 - ensure at least one cdc is open

for jjj=1:num_cdc

if x_temp(p,no_x12+1:no_x123)<0.5 %Loop for zj<0.5

x_temp(p,no_x12+1:no_x123)=x_temp(p,no_x12+1:no_x123)./3;

ccc=randperm(num_cdc);

x_temp(p,no_x12+ccc(1))= x_temp(p,no_x12+ccc(1))+0.5;

end

% step 2 - Allocate BS

for tj=1:num_cdc % zj=1, xjj==1, the others in the same vector is 0.1;

if x_temp(p,no_x12+tj)>=0.5 % ensure a bs which is opening as cdc is only linked itself

x_temp(p,(tj-1)*num_cdc+1:tj*num_cdc)=0.1; % sum of xij =1

x_temp(p,(tj-1)*num_cdc+tj)=0.9;

else

% zj=0, x1j,y1j....xij,ykj==0

for tti=1:num_bs

x_temp(p,(tti-1)*num_cdc+tj)=0.1;

end

for ttk=1:num_ps

x_temp(p,no_x1+(ttk-1)*num_cdc+tj)=0.1;

end

%zj=0, allocate the other BSs in the same vector to available CDC

one_cdc=find(x_temp(p,no_x12+1:no_x123)>=0.5);

leng_o=length(one_cdc); % length of columns where cdc is 1.

for ttj=1:num_cdc % zj=0, allocate other BSs besides above

if x_temp(p,no_x12+ttj)<0.5

tc=randperm(leng_o); % for random assignment of CDC opened to a bs

tjj=one_cdc(tc(1)); % randomly pick up a cdc who is open

if x_temp(p,(ttj-1)*num_cdc+1:ttj*num_cdc)<0.5 % here for xij, tj refers to i, tjj refers to j

x_temp(p,(ttj-1)*num_cdc+tjj)=0.9; % random choose one cdc from opening depots to aasign to bs

else

one_bs=find(x_temp(p,(ttj-1)*num_cdc+1:ttj*num_cdc)>=0.5);

leng_obs=length(one_bs);

tcc=randperm(leng_obs); % random choose one bs which has been assigned to a cdc opened

tii=one_bs(tcc(1));

x_temp(p,(ttj-1)*num_cdc+1:ttj*num_cdc)=0.1; % ensure sum of xij==1

x_temp(p,(ttj-1)*num_cdc+tii)=0.9; % enable the bs picked up to assign to an available cdc

end

% Step 3 - Allocate PS to cdc

for apk=1:num_ps

for j=1:num_cdc

for ii=1:num_bs

round_bc=round(x_temp(p,(ii-1)*num_cdc+j));

tpu1=round_bc;

tpu2=W_pb(apk,ii);

tempuse=tpu1*tpu2;

if tempuse>0

x_temp(p,no_x1+(apk-1)*num_cdc+j)=0.9;

end

%% Ensure others are fulfilled

xsave=x_temp;

x_temp(:,1:no_x123)=round(x_temp(:,1:no_x123));

for othsj=1:num_cdc

% if zj=0, qAj,qBj, Qkj=0;

if x_temp(p,no_x12+othsj)<0.5

x_temp(p,no_x15+othsj)=0.1;

x_temp(p,no_x16+othsj)=0.1;

for tempk=1:num_ps

x_temp(p,no_x17+(tempk-1)*num_cdc+othsj)=0.1;

end

% for constraint 4 ==> Qkj=sum of Qki which is <= S_pb(k,i) and

% calculated with bqAi.

for othsk=1:num_ps

Qkj=0.1;

for othsi=1:num_bs

Qki=x_temp(p,no_x123+othsi).*S_pb(othsk,othsi)./sum(S_pb(:,othsi));

Qkj_temp=Qki*x_temp(p,(othsi-1)*num_cdc+othsj);

Qkj=Qkj+Qkj_temp;

end

x_temp(p,no_x17+(othsk-1)*num_cdc+othsj)=Qkj;

end

% qAj,qBj

for tempj=1:num_cdc

% sum of qAi*xij,qBi*xij

sum_bsA=0.1;

sum_bsB=0.1;

for tempi=1:num_bs

bsA_temp=x_temp(p,(tempi-1)*num_cdc+tempj)*x_temp(p,no_x123+tempi);

bsB_temp=(x_temp(p,(tempi-1)*num_cdc+tempj))*(1+x_temp(p,no_x14+tempi));

sum_bsA=sum_bsA+bsA_temp;

sum_bsB=sum_bsB+bsB_temp;

end

% qAj,qBj == sum of qAi*xij == sum of Qkj

x_temp(p,no_x15+tempj)=sum_bsA;

x_temp(p,no_x16+tempj)=sum_bsB;

end

x=[x;x_temp(p,:)];

x(p,1:no_x123)=xsave(p,1:no_x123);

x=real(x);

end

Judgemant

%% This function is to judgem how many and which solutions generated are feasible and suitable to our case.

function [no_fea_solutions,fea_solutions,Errors]=judge(xx_temp)

%% This function is second part of initialisation of population

% In a population, find solutuions which ensure a opening cdc is

% connected only one bs and at least one ps, and a closing cdc is linking

% to nothing.

% Save these solutions into another matrix;

global num_bs num_cdc num_ps pop_size V M

no_x1=num_bs*num_cdc; % number of xij

no_x12=num_bs*num_cdc+num_cdc*num_ps; %xij+ykj

no_x123=num_bs*num_cdc+num_cdc*num_ps+num_cdc; %xij+ykj+zj

xave=xx_temp;

xx_temp=round(xx_temp);

nfs=0; % number of feasible solutions in the population

fea_temp=[]; %save feasible solutions

err_records=[];

for p=1:pop_size

temp_bc=0;

temp_pc=0;

temp_pop=0;

% for value of cdc==0 to keep 0 for all bs-cdc and ps-cdc

zero_cdc=find(xx_temp(p,no_x12+1:no_x123)==0);

leng_z=length(zero_cdc);

for pos_vcdc=1:leng_z

j=zero_cdc(pos_vcdc); % columns of cdc whose value is 0

for i=1:num_bs

pos_bc=(i-1)*num_cdc+j;

temp_bc=temp_bc+xx_temp(p,pos_bc);

end

for k=1:num_ps

poS_pb=no_x1+(k-1)*num_cdc+j;

temp_pc=temp_pc+xx_temp(p,poS_pb);

end

temp_pop=temp_pc+temp_bc;

end

% for value of cdc==1 to ensure an opening cdc is connected with at least one ps

one_cdc=find(xx_temp(p,no_x12+1:no_x123)==1);

leng_o=length(one_cdc);

temp_pc11=0; % if a cdc is connected with at least one ps, 1 and 0 otherwise

temp_bc11=0;

for pos_v1cdc=1:leng_o

jj=one_cdc(pos_v1cdc); % columns of cdc whose value is 1

temp_pc1=0; % sum of values of ps which is linked to a opening cdc

for kk=1:num_ps

poS_pb1=no_x1+(kk-1)*num_cdc+jj;

temp_pc1=temp_pc1+xx_temp(p,poS_pb1); % so temp_pc1 is the sum of ps linked to an opening cdc

end

if temp_pc1==0

temp_pc11=temp_pc11+0;

else

temp_pc11=temp_pc11+1; % no matter how many ps are connected, the solution is feasible

end

% Check - sum of xij==1

for ii=1:num_bs

temp_bc1=0;

for jjj=1:num_cdc

pos_bc1=(ii-1)*num_cdc+jjj;

temp_bc1=temp_bc1+xx_temp(p,pos_bc1);

end

if temp_bc1==1

temp_bc11=temp_bc11+1;

else

temp_bc11=temp_bc11+0;

end

% judge on errs determined in TL_case

temp_err=xx_temp(p,V+M+1);

if temp_pop==0 && temp_pc11~=0 && temp_bc11==num_bs && temp_err==0

nfs=nfs+1;

fea_temp=[fea_temp,p];

end

% Output errors

if temp_pop~=0

err_records=[err_records;[p,1]];

elseif temp_pc11==0

err_records=[err_records;[p,3]];

elseif temp_bc11~=num_bs

err_records=[err_records;[p,2]];

elseif temp_err~=0

err_records=[err_records;[p,4]];

end

no_fea_solutions=nfs;

fea_solutions=xave(fea_temp,:);

Errors=err_records;

end

The following seven parts of the code are written down based on (Selvaraj, 2015) and other open accesses of resources online.

Main Loop

clear

clc

global V M etac etam pop_size pm xl xu W_pb num_bs num_cdc num_ps

global mu_ddpt_A sigma_ddpt_A mu_ddpt_B sigma_ddpt_B S_pb

global alph_A alph_B beta_cdc gam_AB gam_A gam_B

global loc_bs loc_cdc loc_ps

load('[SDD]ALL_needed1.mat') % read/load the dataset used here， SDD=standardisation

%% code starts

pop_size=1000; % Population size

gen_max=10; % Max number of generations - stopping criteria, for a population evolving

M=2;

no_runs=1; % Number of runs, for new solutions.

etac = 2; % distribution index for crossover

etam = 5; % distribution index for mutation / mutation constant

fname='TL_case'; % Objective function and constraint evaluation

%% Data used

num_bs=num_bs;num_cdc=num_bs;num_ps=num_ps;mu_ddpt_A=mu_ddpt_A;

sigma_ddpt_A=sigma_ddpt_A;mu_ddpt_B=mu_ddpt_B;sigma_ddpt_B=sigma_ddpt_B;

S_pb=S_pb;W_pb=W_pb;alph_A=alph_A;alph_B=alph_B;beta_cdc=beta_cdc;

gam_AB=gam_AB;gam_A=gam_A;gam_B=gam_B;loc_bs=loc_bs;loc_cdc=loc_cdc;

loc_ps=loc_ps;

%% Lower and Upper bound of variables

%x1,2,3

lx_bpc=zeros(1,num_bs*num_cdc+num_ps*num_cdc+num_cdc);

ux_bpc=ones(1,num_bs*num_cdc+num_ps*num_cdc+num_cdc);

%x4,5,6,7

lx4=mu_ddpt_A;

lx5=mu_ddpt_B;

lx6=zeros(1,num_cdc);

lx7=zeros(1,num_cdc);

ux4=[];

for ux_temp=1:num_cdc

ux4=[ux4,sum(S_pb(:,ux_temp))]; % under limited supply

end

ux5=mu_ddpt_B+4.*sigma_ddpt_B; % for max CSL==1

ux6=repmat(sum(ux4(:)),1,num_cdc);

ux7=repmat(sum(ux5(:)),1,num_cdc);

lx8=zeros(1,num_ps*num_cdc);

ux8=[];

for k_pc=1:num_ps

for j_pc=1:num_cdc

cap_pc=sum(S_pb(k_pc,:));

ps_pc=(k_pc-1)*num_cdc+j_pc;

ux8(1,ps_pc)=cap_pc;

end

xl=[lx_bpc lx4 lx5 lx6 lx7 lx8]; % lower bound vector

xu=[ux_bpc ux4 ux5 ux6 ux7 ux8]; % upper bound vectorfor i=1:NN

%% Previous value of objectives and temporary xl and xu

[Pre_CSL,Pre_TOC]=previous(num_bs,num_ps);

xl_temp=repmat(xl, pop_size,1);

xu_temp=repmat(xu, pop_size,1);

%% Other parameters used in the simulation

pm= 1/V; % Mutation Probability

Q=[];

%% Runs

for run = 1:no_runs

%% Initial population

x_temp=xl_temp+((xu_temp-xl_temp).*rand(pop_size,V));

x=variables_normalised(x_temp); % normalise data of variables

%% Evaluate objective function

for i =1:pop_size

[ff(i,:),err(i,:),err2(i,:)] =feval(fname, x(i,:)); % Objective function evaulation

end

error_norm_off=normalisation(err); % Normalisation of the constraint violation

population_init=[x ff error_norm_off];

[nfs_x,fea_x,errs_x]=judge(population_init); % check of feasible solutions

[population,front]=NDS_CD_cons(population_init); % Non domination Sorting on initial population only for sorting

%% Genetic operations Start----one iteration is one-time evolvement(parent>offspring and parent+offspring>new population)

for gen_count=1:gen_max

% selection (Parent Pt of 'N' pop size)

parent_selected=tour_selection(population);% 10 Tournament selection

%% Reproduction (Offspring Qt of 'N' pop size)

% SBX crossover and polynomial mutation

%for generating offspring population

% so individuals in population has been changed

child_offspring = genetic_operator(parent_selected(:,1:V));

child_offspring=variables_normalised(child_offspring); % normalise data of variables

for ii = 1:pop_size

[fff(ii,:),errr(ii,:),errr2(ii,:)]=feval(fname, child_offspring(ii,:)); % objective function evaluation for offspring

end

error_norm_off=normalisation(errr);

child_offspring=[child_offspring fff error_norm_off];

%% Intermediate population (Rt= Pt U Qt of 2N size)

population_inter=[population(:,1:V+M+1) ; child_offspring(:,1:V+M+1)];

[population_inter_sorted,front]=NDS_CD_cons(population_inter); % Non domination Sorting on offspring

%% Replacement - N

new_pop=replacement(population_inter_sorted,front);

new_pop(:,1:V)=new_pop(:,1:V);

population=new_pop;

end

new_pop=sortrows(new_pop,V+1);

paretoset(run).trial=new_pop(:,1:V+M+1);

Q = [Q; paretoset(run).trial]; % Combining Pareto solutions obtained in each run

end

%% Judgement of solutions

[nfs_Q,fea_Q,Err_Q]=judge(Q); % check of feasibility of Q

%% Result and Pareto plot

Q(:,1:V)=round(Q(:,1:V));

new_pop(:,1:V)=round(new_pop(:,1:V)); % Translation

if run==1

plot(new_pop(:,V+1),new_pop(:,V+2),'*')

else

[pareto_filter,front]=NDS_CD_cons(Q); % Applying non domination sorting on the combined Pareto solution set

rank1_index=find(pareto_filter(:,V+M+2)==1); % Filtering the best solutions of rank 1 Pareto

pareto_rank1=pareto_filter(rank1_index,1:V+M);

plot(pareto_rank1(:,V+1),pareto_rank1(:,V+2),'*') % Final Pareto plot

save solution5(TL_trial).txt pareto_rank1 -ASCII

end

xlabel('OF1-Minus CSL')

ylabel('OF2-TOC')

Fast Elitist Non-Dominated Sorting and Crowding Distance Assignment

%% function begins

function [chromosome_NDS_CD front] = NDS_CD_cons(population)

global V M problem_type

%% Initialising structures and variables

chromosome_NDS_CD1=[];

infpop=[];

front.fr=[];

struct.sp=[];

rank=1;

%% Segregating feasible and infeasible solutions

if all(population(:,V+M+1)==0)

problem_type=0;

chromosome=population(:,1:V+M); % All Feasible chromosomes;

pop_size1=size(chromosome,1);

elseif all(population(:,V+M+1)~=0)

problem_type=1;

pop_size1=0;

infchromosome=population; % All InFeasible chromosomes;

else

problem_type=0.5;

feas_index=find(population(:,V+M+1)==0);

chromosome=population(feas_index,1:V+M); % Feasible chromosomes;

pop_size1=size(chromosome,1);

infeas_index=find(population(:,V+M+1)~=0);

infchromosome=population(infeas_index,1:V+M+1); % infeasible chromosomes;

end

%% Handling feasible solutions

if problem_type==0 | problem_type==0.5

pop_size1 = size(chromosome,1);

f1 = chromosome(:,V+1); % objective function values

f2 = chromosome(:,V+2);

%Non- Domination Sorting

% First front

for p=1:pop_size1

struct(p).sp=find(((f1(p)-f1)<0 &(f2(p)-f2)<0) | ((f2(p)-f2)==0 &(f1(p)-f1)<0) | ((f1(p)-f1)==0 &(f2(p)-f2)<0));

n(p)=length(find(((f1(p)-f1)>0 &(f2(p)-f2)>0) | ((f2(p)-f2)==0 &(f1(p)-f1)>0) | ((f1(p)-f1)==0 &(f2(p)-f2)>0)));

end

front(1).fr=find(n==0);

% Creating subsequent fronts

while (~isempty(front(rank).fr))

front_indiv=front(rank).fr;

n(front_indiv)=inf;

chromosome(front_indiv,V+M+1)=rank;

rank=rank+1;

front(rank).fr=[];

for i = 1:length(front_indiv)

temp=struct(front_indiv(i)).sp;

n(temp)=n(temp)-1;

end

q=find(n==0);

front(rank).fr=[front(rank).fr q];

end

chromosome_sorted=sortrows(chromosome,V+M+1); % Ranked population

%Crowding distance Assignment

rowsindex=1;

for i = 1:length(front)-1

l_f=length(front(i).fr);

if l_f > 2

sorted_indf1=[];

sorted_indf2=[];

sortedf1=[];

sortedf2=[];

% sorting based on f1 and f2;

[sortedf1 sorted_indf1]=sortrows(chromosome_sorted(rowsindex:(rowsindex+l_f-1),V+1));

[sortedf2 sorted_indf2]=sortrows(chromosome_sorted(rowsindex:(rowsindex+l_f-1),V+2));

f1min=chromosome_sorted(sorted_indf1(1)+rowsindex-1,V+1);

f1max=chromosome_sorted(sorted_indf1(end)+rowsindex-1,V+1);

chromosome_sorted(sorted_indf1(1)+rowsindex-1,V+M+2)=inf;

chromosome_sorted(sorted_indf1(end)+rowsindex-1,V+M+2)=inf;

f2min=chromosome_sorted(sorted_indf2(1)+rowsindex-1,V+2);

f2max=chromosome_sorted(sorted_indf2(end)+rowsindex-1,V+2);

chromosome_sorted(sorted_indf2(1)+rowsindex-1,V+M+3)=inf;

chromosome_sorted(sorted_indf2(end)+rowsindex-1,V+M+3)=inf;

for j = 2:length(front(i).fr)-1

if (f1max - f1min == 0) | (f2max - f2min == 0)

chromosome_sorted(sorted_indf1(j)+rowsindex-1,V+M+2)=inf;

chromosome_sorted(sorted_indf2(j)+rowsindex-1,V+M+3)=inf;

else

chromosome_sorted(sorted_indf1(j)+rowsindex-1,V+M+2)=(chromosome_sorted(sorted_indf1(j+1)+rowsindex-1,V+1)-chromosome_sorted(sorted_indf1(j-1)+rowsindex-1,V+1))/(f1max-f1min);

chromosome_sorted(sorted_indf2(j)+rowsindex-1,V+M+3)=(chromosome_sorted(sorted_indf2(j+1)+rowsindex-1,V+2)-chromosome_sorted(sorted_indf2(j-1)+rowsindex-1,V+2))/(f2max-f2min);

end

else

chromosome_sorted(rowsindex:(rowsindex+l_f-1),V+M+2:V+M+3)=inf;

end

rowsindex = rowsindex + l_f;

end

chromosome_sorted(:,V+M+4) = sum(chromosome_sorted(:,V+M+2:V+M+3),2);

chromosome_NDS_CD1 = [chromosome_sorted(:,1:V+M) zeros(pop_size1,1) chromosome_sorted(:,V+M+1) chromosome_sorted(:,V+M+4)]; % Final Output Variable

end

%% Handling infeasible solutions

if problem_type==1 | problem_type==0.5

infpop=sortrows(infchromosome,V+M+1);

infpop=[infpop(:,1:V+M+1) (rank:rank-1+size(infpop,1))' inf*(ones(size(infpop,1),1))];

for kk = (size(front,2)):(size(front,2))+(length(infchromosome))-1;

front(kk).fr= pop_size1+1;

end

chromosome_NDS_CD = [chromosome_NDS_CD1;infpop];

Binary Tournament Selection

function [parent_selected] = tour_selection(pool)

%% Binary Tournament Selection

[pop_size, distance]=size(pool);

rank=distance-1;

candidate=[randperm(pop_size);randperm(pop_size)]';

for i = 1: pop_size

parent=candidate(i,:); % Two parents indexes are randomly selected

if pool(parent(1),rank)~=pool(parent(2),rank) % For parents with different ranks

if pool(parent(1),rank)<pool(parent(2),rank) % Checking the rank of two individuals

mincandidate=pool(parent(1),:);

elseif pool(parent(1),rank)>pool(parent(2),rank)

mincandidate=pool(parent(2),:);

end

parent_selected(i,:)=mincandidate; % Minimum rank individual is selected finally

else % for parents with same ranks

if pool(parent(1),distance)>pool(parent(2),distance) % Checking the distance of two parents

maxcandidate=pool(parent(1),:);

elseif pool(parent(1),distance)< pool(parent(2),distance)

maxcandidate=pool(parent(2),:);

else

temp=randperm(2);

maxcandidate=pool(parent(temp(1)),:);

end

parent_selected(i,:)=maxcandidate; % Maximum distance individual is selected finally

end

Genetic Operations

%We operate genetic process using SBX (Simulate Binary Crossover) and Polynomial Mutation.

function child_offspring = genetic_operator(parent_selected)

global V xl xu etac

%% SBX cross over operation incorporating boundary constraint

[N] = size(parent_selected,1);

xl1=xl';

xu1=xu';

rc=randperm(N);

for i=1:(N/2)

parent1=parent_selected((rc(2*i-1)),:);

parent2=parent_selected((rc(2*i)),:);

if (isequal(parent1,parent2))==1 & rand(1)>0.5

child1=parent1;

child2=parent2;

else

for j = 1: V

if parent1(j)<parent2(j)

beta(j)= 1 + (2/(parent2(j)-parent1(j)))*(min((parent1(j)-xl1(j)),(xu1(j)-parent2(j))));

else

beta(j)= 1 + (2/(parent1(j)-parent2(j)))*(min((parent2(j)-xl1(j)),(xu1(j)-parent1(j))));

end

u=rand(1,V);

alpha=2-beta.^-(etac+1);

betaq=(u<=(1./alpha)).*(u.*alpha).^(1/(etac+1))+(u>(1./alpha)).*(1./(2 - u.*alpha)).^(1/(etac+1));

child1=0.5*(((1 + betaq).*parent1) + (1 - betaq).*parent2);

child2=0.5*(((1 - betaq).*parent1) + (1 + betaq).*parent2);

end

child_offspring((rc(2*i-1)),:)=poly_mutation(child1); % polynomial mutation

child_offspring((rc(2*i)),:)=poly_mutation(child2); % polynomial mutation

end

Polynomial Mutation Operations

function mutated_child = poly_mutation(y)

global V xl xu etam pm

%% Polynomial mutation including boundary constraint

del=min((y-xl),(xu-y))./(xu-xl);

t=rand(1,V);

loc_mut=t<pm;

u=rand(1,V);

delq=(u<=0.5).*((((2*u)+((1-2*u).*((1-del).^(etam+1)))).^(1/(etam+1)))-1)+(u>0.5).*(1-((2*(1-u))+(2*(u-0.5).*((1-del).^(etam+1)))).^(1/(etam+1)));

c=y+delq.*loc_mut.*(xu-xl);

mutated_child=c;

Replacement for Iterations

function new_pop=replacement(population_inter_sorted, front)

global pop_size

%% code starts

index=0;

ii=1;

while index < pop_size

l_f=length(front(ii).fr);

if index+l_f < pop_size

new_pop(index+1:index+l_f,:)= population_inter_sorted(index+1:index+l_f,:);

index=index+l_f;

else

temp1=population_inter_sorted(index+1:index+l_f,:);

temp2=sortrows(temp1,size(temp1,2));

new_pop(index+1:pop_size,:)= temp2(l_f-(pop_size-index)+1:l_f,:);

index=index+l_f;

end

ii=ii+1;

end

Constraints errors normalisation

function err_norm = normalisation(error_pop)

%% Description

% 1. This function normalises the constraint violation of various individuals, since the range of

% constraint violation of every chromosome is not uniform. The methods of handling such a

% problem is to put the solutions of which constraints errors are all zero forward.

% 2. Input is in the matrix error_pop with size [pop_size, number of constraints].

% 3. Output is a normalised vector, err_norm of size [pop_size,1]

%% Error Nomalisation for inequation (<=0)

[N,nc]=size(error_pop);

con_max=0.00001+max(error_pop); % max([]) returns to the maximum of each column, e.g. max([1 7;2 3])=[2 7]

con_maxx=repmat(con_max,N,1);

cc=error_pop./con_maxx;

err_norm=sum(error_pop,2); % finally sum up all violations sum(A,1) sum of column, sum(A,2) sum of row

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来源： https://blog.csdn.net/weixin_43051257/article/details/89761381