-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathMODI_Degen.m
238 lines (230 loc) · 7.7 KB
/
MODI_Degen.m
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
function[]= MODI_Degen(A,x)
% x: Initial Basic Feasible Solution (m*n)
% b: 1 for each basic variables 0 for nonbasic (m*n)
% A: costs (m*n)
% u: multipliers for rows (m*1)
% v: multipliers for columns (n*1)
Matrix_for_Next_Iteration = x;
[m,n]=size(x);
for i = 1:m
for j=1:n
if x(i,j)==0
b(i,j)= 0;
else
b(i,j)=1;
end
end
end
%Multiplier function like action
u=Inf*ones(m,1);
v=Inf*ones(n,1);
u(1)=0; % choose an arbitrary multiplier = 0
nr=1;
while nr<m+n-1 % until all multipliers are assigned
for row=1:m
for col=1:n
if b(row,col)>0
if (u(row)~=Inf) && (v(col)==Inf)
v(col)=A(row,col)-u(row);
u(row)=u(row);
nr=nr+1;
elseif (u(row)==Inf) && (v(col)~=Inf)
u(row)=A(row,col)-v(col);
v(col)=v(col);
nr=nr+1;
elseif (u(row)==Inf) && (v(col)==Inf)
u(row)=u(row);
v(col)=v(col);
nr=nr+1;
end
end
end
end
end
%end of multiplier
%%%Identifying the postion to place the Epsilon
b_mod=b;
loop=[];
for row=1:m
for col=1:n
if b(row,col)==0
b_mod(row,col)=0.0001;
if ((u(row)==Inf) & (v(col)~=Inf))|((u(row)~=Inf) & (v(col)==Inf))|((u(row)==Inf) & (v(col==Inf)))
xpos=row;
ypos=col;
loop=[xpos ypos;loop];
b_mod(row,col)=0;
end
end
end
end
%%%Identifying the postion to place the Epsilon ends; loop is the position
%%%of epsilon
[m1,n1]=size(loop);
b2=b;
[b2_row,b2_col]=size(b2);
% count=0;
% for h1=1:b2_row
% for h2=1:b2_col
% if b2(h1,h2)==1
% count=count+1;
% end
% end
% end
count=nnz(b2);
for i=1:m1
b2=b;
% if ((count==b2_row+b2_col-3) & m1>2)
% b2(loop(m1,1),loop(m1,2))=0.0001;
% b2(loop(m1-2,1),loop(m1-2,2))=0.0001;
% elseif (count==b2_row+b2_col-4) & m1>3
% b2(loop(m1,1),loop(m1,2))=0.0001;
% b2(loop(m1-2,1),loop(m1-2,2))=0.0001;
% b2(loop(m1-3,1),loop(m1-3,2))=0.0001;
% elseif (count<=b2_row+b2_col-5) & m1>4
% b2(loop(m1,1),loop(m1,2))=0.0001;
% b2(loop(m1-2,1),loop(m1-2,2))=0.0001;
% b2(loop(m1-3,1),loop(m1-3,2))=0.0001;
% b2(loop(m1-4,1),loop(m1-4,2))=0.0001;
% elseif count==b2_row+b2_col-2
% b2(loop(i,1),loop(i,2))=0.0001;
% end
if ((count==b2_row+b2_col-3) & i+2<=m1)
b2(loop(i,1),loop(i,2))=0.0001;
b2(loop(i+2,1),loop(i+2,2))=0.0001;
elseif ((count==b2_row+b2_col-4) & i+2<=m1)
b2(loop(i,1),loop(i,2))=0.0001;
b2(loop(i+1,1),loop(i+1,2))=0.0001;
b2(loop(i+2,1),loop(i+2,2))=0.0001;
elseif ((count==b2_row+b2_col-3) & i==m1)
b2(loop(i-1,1),loop(i-1,2))=0.0001;
b2(loop(i,1),loop(i,2))=0.0001;
elseif count==b2_row+b2_col-2
b2(loop(i,1),loop(i,2))=0.0001;
end
u=Inf*ones(m,1);
v=Inf*ones(n,1);
u(1)=0; % choose an arbitrary multiplier = 0
nr=1;
while nr<m+n % until all multipliers are assigned
for row=1:m
for col=1:n
if b2(row,col)>0
if (u(row)~=Inf) && (v(col)==Inf)
v(col)=A(row,col)-u(row);
u(row)=u(row);
nr=nr+1;
elseif (u(row)==Inf) && (v(col)~=Inf)
u(row)=A(row,col)-v(col);
v(col)=v(col);
nr=nr+1;
elseif (u(row)~=Inf) && (v(col)~=Inf)
u(row)=u(row);
v(col)=v(col);
nr=nr+1;
end
end
end
end
end
for row=1:m
for col=1:n
if b2(row,col)==0
if (u(row)~=Inf)&&(v(col)~=Inf)
e(row,col)=A(row,col)-u(row)-v(col); %% computing opportunity cost for the unoccupied cells
end
end
end
end
opportunity_cost_matrix = e;
minval = min(min(e));
for k=1:m
for j=1:n
if e(k,j)==minval
xpos=k;
ypos=j;
end
end
end
x2=x;
if ((count==b2_row+b2_col-3) & i+2<=m1)
x2(loop(i,1),loop(i,2))=0.0001;
x2(loop(i+2,1),loop(i+2,2))=0.0001;
fprintf('Epsilon Position: %d, %d, and, %d, %d ', loop(i,1), loop(i,2),loop(i+2,1),loop(i+2,2));
fprintf('\n');
elseif ((count==b2_row+b2_col-3) & i==m1)
x2(loop(i-1,1),loop(i-1,2))=0.0001;
x2(loop(i,1),loop(i,2))=0.0001;
fprintf('Epsilon Position: %d, %d, and, %d, %d ', loop(i,1), loop(i,2),loop(i-1,1),loop(i-2,2));
fprintf('\n');
elseif count==b2_row+b2_col-2
x2(loop(i,1),loop(i,2))=0.0001;
fprintf('Epsilon Position: %d, %d', loop(i,1), loop(i,2));
fprintf('\n');
end
% if ((count==b2_row+b2_col-3) & m1>2)
% x2(loop(m1,1),loop(m1,2))=0.0001;
% x2(loop(m1-2,1),loop(m1-2,2))=0.0001;
% % x2(loop(i,1),loop(i,2))=0.0001;
% % x2(loop(i+2,1),loop(i+2,2))=0.0001;
% % fprintf('Epsilon Position: %d, %d', loop(m1,1),loop(m1,2));
% % fprintf('\n');
% % fprintf('Epsilon Position: %d, %d', loop(m1-2,1),loop(m1-2,2));
% % fprintf('\n');
% elseif (count==b2_row+b2_col-4) & m1>3
% x2(loop(m1,1),loop(m1,2))=0.0001;
% x2(loop(m1-2,1),loop(m1-2,2))=0.0001;
% x2(loop(m1-3,1),loop(m1-3,2))=0.0001;
% elseif (count<=b2_row+b2_col-5) & m1>4
% x2(loop(m1,1),loop(m1,2))=0.0001;
% x2(loop(m1-2,1),loop(m1-2,2))=0.0001;
% x2(loop(m1-3,1),loop(m1-3,2))=0.0001;
% x2(loop(m1-4,1),loop(m1-4,2))=0.0001;
% elseif count==b2_row+b2_col-2
% x2(loop(i,1),loop(i,2))=0.0001;
% end
%x2(loop(i,1),loop(i,2))=0.0001;
%if (i<=m)
%fprintf('Epsilon Position: %d, %d', loop(i,1), loop(i,2));
%fprintf('\n');
if minval<0
fprintf('Optimum Solution At this iteration: ');
try
x1=cycle(x2,xpos,ypos,b2);
x3=int64(x1)
A=int64(A);
x=int64(x);
Optimal_Cost_matrix = x3.*A;
Optimal_Cost_value = sum(sum(x3.*A))
fprintf('Cost Reduced By : %d',sum(sum(x.*A))-sum(sum( x3.*A)));
fprintf('\n');
if (sum(sum(x.*A))-sum(sum( x3.*A)))>0
fprintf('\nNext Iteration:');
fprintf('\n');
if (nnz(x3)==m+n-1)
fprintf('\nMODI Function Called:');
fprintf('\n');
MODI_2(A,x3,x);
elseif (nnz(x3)<m+n-1)
fprintf('\nMODI Degeneration Function Called:');
fprintf('\n');
MODI_Degen(A,x3);
end
end
catch
disp('Index exceeds matrix dimensions Occured but Execution will continue.');
disp('Next Epsilon Assignment');
end
elseif minval==0
fprintf('Alternate Optimum Solution :');
x1=cycle(x2,xpos,ypos,b2);
x3=int64(x1)
A=int64(A);
x=int64(x);
Optimal_Cost_matrix = x3.*A;
Optimal_Cost_value = sum(sum( x3.*A))
fprintf('Cost Reduced By : %d',sum(sum(x.*A))-sum(sum( x3.*A)));
fprintf('No Change in Cost');
fprintf('\n');
end
end