highs-sys 1.14.1

Rust binding for the HiGHS linear programming solver. See http://highs.dev.
Documentation 
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

# Multi-objective binary knapsack example
from highspy import Highs, HighsLinearObjective
import numpy as np

# Parameters
capacity = 13

# chosen such that applying each objective lexicographically gives a different solution
profit = np.asarray([
        [0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1],
        [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0],
        [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0],
        [1,1,1,1,0,1,0,0,1,1,0,0,0,1,1,1,0,0,0,0],

    ], dtype=np.float64).reshape(4, 20)

OBJECTIVES = profit.shape[0]
ITEMS = profit.shape[1]

def pretty_print(objective_values):
    return '[ ' + ', '.join(map(lambda x: "{:2.0f}".format(x), objective_values)) + ' ]'

#
# individual optimization of each objective
def individual_objectives(h, X):
    print('## Individual:\n')
    objective_values = []

    for k in range(OBJECTIVES):
        h.maximize(np.dot(X, profit[k,:]))
        print(f'  Obj {k+1}: [{"".join(map(lambda x: "{:1.0f}".format(x), profit[k,:]))}]')
        print(f'  Sol {k+1}: [{"".join(map(lambda x: "{:1.0f}".format(x), abs(h.vals(X))))}]\n')
        objective_values.append(h.getObjectiveValue())

    print(f'  OBJ: {pretty_print(objective_values)}\n\n')

#
# manual implementation of lexicographic multi-objective optimization
def manual_lexicographic(h, X):
    print('## Manual lexicographic:\n')
    cons = []
    objs = np.dot(profit, X)

    for k in range(OBJECTIVES):
        h.maximize(objs[k])
        print(f'  Obj {k+1}: [{"".join(map(lambda x: "{:1.0f}".format(x), profit[k,:]))}]')
        print(f'  Sol {k+1}: [{"".join(map(lambda x: "{:1.0f}".format(x), abs(h.vals(X))))}]\n')

        # add constraint to ensure next solution are at least as good in this objective
        cons.append(h.addConstr(np.dot(profit[k,:], X) >= h.getObjectiveValue()))

    objective_values = h.vals(objs)
    h.deleteRows(len(cons), cons)  # clean up constraints
    print(f'  SOL: [{"".join(map(lambda x: "{:1.0f}".format(x), abs(h.vals(X))))}]')
    print(f'  OBJ: {pretty_print(objective_values)}\n\n')


#
# built-in lexicographic multi-objective optimization
def highs_lexicographic(h, X):
    print('## Built-in lexicographic:\n')
    h.setOptionValue('blend_multi_objectives', False) # use lexicographic

    for k in range(OBJECTIVES):
        obj = HighsLinearObjective()
        obj.coefficients = profit[k,:].tolist()
        obj.weight = -1    # maximize
        obj.priority = -k  # higher priority for lower k
        obj.abs_tolerance = 0.01
        obj.rel_tolerance = 0.001

        h.addLinearObjective(obj)

    h.solve()
    print(f'  SOL: [{"".join(map(lambda x: "{:1.0f}".format(x), abs(h.vals(X))))}]')
    print(f'  OBJ: {pretty_print(np.dot(profit, h.vals(X)))}\n\n')

    print(f'  Number of objectives: {h.getNumLinearObjectives()}')
    for k in range(h.getNumLinearObjectives()):
        obj = h.getLinearObjective(k)
        print(f'  Obj {k+1}: weight={obj.weight}, priority={obj.priority}, abs_tol={obj.abs_tolerance}, rel_tol={obj.rel_tolerance}')
    print('\n')

    h.clearLinearObjectives()


#
# manual implementation of weighted multi-objective optimization
def manual_weighted(h, X):
    print('## Manual Weighted:\n')
    weights = np.asarray([1.0/(k+1) for k in range(OBJECTIVES)], dtype=np.float64)
    h.maximize(np.dot(weights[:,None] * profit, X).sum())

    print(f'  SOL: [{"".join(map(lambda x: "{:1.0f}".format(x), abs(h.vals(X))))}]')
    print(f'  OBJ: {pretty_print(np.dot(profit, h.vals(X)))}\n')

    print(f'  Obj: {h.getObjective()[0]}\n\n')


#
# built-in weighted multi-objective optimization
def highs_weighted(h, X):
    print('## Built-in Weighted:\n')
    h.setOptionValue('blend_multi_objectives', True) # use weighted

    for k in range(OBJECTIVES):
        obj = HighsLinearObjective()
        obj.coefficients = profit[k,:].tolist()
        obj.weight = -1.0/(k+1)

        h.addLinearObjective(obj)

    h.solve()
    print(f'  SOL: [{"".join(map(lambda x: "{:1.0f}".format(x), abs(h.vals(X))))}]')
    print(f'  OBJ: {pretty_print(np.dot(profit, h.vals(X)))}\n')

    print(f'  Number of objectives: {h.getNumLinearObjectives()}')
    for k in range(h.getNumLinearObjectives()):
        obj = h.getLinearObjective(k)
        print(f'  Obj {k+1}: weight={obj.weight}, priority={obj.priority}, abs_tol={obj.abs_tolerance}, rel_tol={obj.rel_tolerance}')
    print('\n')

    h.clearLinearObjectives()


if __name__ == "__main__":
    h = Highs()
    h.silent(True)

    X = h.addBinaries(ITEMS)
    h.addConstr(X.sum() <= capacity)

    individual_objectives(h, X)

    manual_lexicographic(h, X)
    manual_weighted(h, X)

    highs_lexicographic(h, X)
    highs_weighted(h, X)