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
|
#ifndef SimTK_SIMMATH_OPTIMIZER_SYSTEMS_H_
#define SimTK_SIMMATH_OPTIMIZER_SYSTEMS_H_
/* -------------------------------------------------------------------------- *
* Simbody(tm): SimTKmath *
* -------------------------------------------------------------------------- *
* This is part of the SimTK biosimulation toolkit originating from *
* Simbios, the NIH National Center for Physics-Based Simulation of *
* Biological Structures at Stanford, funded under the NIH Roadmap for *
* Medical Research, grant U54 GM072970. See https://simtk.org/home/simbody. *
* *
* Portions copyright (c) 2006-14 Stanford University and the Authors. *
* Authors: Chris Dembia *
* Contributors: *
* *
* Licensed under the Apache License, Version 2.0 (the "License"); you may *
* not use this file except in compliance with the License. You may obtain a *
* copy of the License at http://www.apache.org/licenses/LICENSE-2.0. *
* *
* Unless required by applicable law or agreed to in writing, software *
* distributed under the License is distributed on an "AS IS" BASIS, *
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. *
* See the License for the specific language governing permissions and *
* limitations under the License. *
* -------------------------------------------------------------------------- */
// These websites list test functions for optimization.
// https://en.wikipedia.org/wiki/Test_functions_for_optimization
// http://www.sfu.ca/~ssurjano/optimization.html
#include "SimTKmath.h"
using SimTK::Vector;
using SimTK::Real;
using SimTK::OptimizerSystem;
using SimTK::Pi;
using SimTK::square;
using SimTK::sqrt;
class TestOptimizerSystem : public OptimizerSystem {
public:
TestOptimizerSystem(int nParameters)
: OptimizerSystem(nParameters) {}
virtual Real optimalValue() const {
Real f;
objectiveFunc(optimalParameters(), true, f);
return f;
}
virtual Vector optimalParameters() const = 0;
};
// This function come from Nikolaus Hansen's source code
// (https://github.com/cma-es). I think it is supposed to be cigar-shaped.
class Cigtab : public TestOptimizerSystem {
public:
Cigtab(int nParameters) : TestOptimizerSystem(nParameters) {}
int objectiveFunc(const Vector& x, bool new_parameters,
Real& f) const override {
f = 1e4 * x[0] * x[0] + 1e-4 * x[1] * x[1];
for (int i = 0; i < getNumParameters(); ++i) {
f += x[i] * x[i];
}
return 0;
}
Vector optimalParameters() const override {
Vector x(getNumParameters());
x.setToZero();
return x;
}
};
// A function with many local minima. http://www.sfu.ca/~ssurjano/ackley.html
class Ackley : public TestOptimizerSystem {
public:
Ackley(int nParameters) : TestOptimizerSystem(nParameters),
a(20), b(0.2), c(2 * Pi) {
// The website above says this function usually has the following
// bounds:
Vector limits(nParameters);
limits.setTo(32.768);
setParameterLimits(-limits, limits);
}
int objectiveFunc(const Vector& x, bool new_parameters, Real& f) const override {
const Real n = getNumParameters();
Real sumcos = 0;
for (int i = 0; i < n; ++i) {
sumcos += cos(c * x[i]);
}
f = -a * exp(-b * x.normRMS()) - exp(sumcos / n) + a + SimTK::E;
return 0;
}
Vector optimalParameters() const override {
Vector x(getNumParameters());
x.setToZero();
return x;
}
private:
const Real a;
const Real b;
const Real c;
};
// A very complex 2D function http://www.sfu.ca/~ssurjano/drop.html
class DropWave : public TestOptimizerSystem {
public:
DropWave() : TestOptimizerSystem(2) {
// The website above says this function usually has the following
// bounds:
Vector limits(getNumParameters());
limits.setTo(5.12);
setParameterLimits(-limits, limits);
}
int objectiveFunc(const Vector& x, bool new_parameters, Real& f) const override {
const Real dotprod = x[0] * x[0] + x[1] * x[1];
f = -(1 + cos(12 * sqrt(dotprod))) / (0.5 * dotprod + 2);
return 0;
}
Vector optimalParameters() const override {
Vector x(getNumParameters());
x.setToZero();
return x;
}
};
// Looks like a curved valley.
// https://en.wikipedia.org/wiki/Test_functions_for_optimization
class Rosenbrock : public TestOptimizerSystem {
public:
Rosenbrock(int nParameters) : TestOptimizerSystem(nParameters) {}
int objectiveFunc(const Vector& x, bool new_parameters, Real& f) const override {
f = 0;
for (int i = 0; i < getNumParameters() - 1; ++i) {
f += 100.0 * square(x[i+1] - square(x[i])) + square(x[i] - 1);
}
return 0;
}
Vector optimalParameters() const override {
Vector x(getNumParameters());
x.setTo(1);
return x;
}
};
// http://www.sfu.ca/~ssurjano/schwef.html
class Schwefel : public TestOptimizerSystem {
public:
Schwefel(int nParameters) : TestOptimizerSystem(nParameters) {
// The website above says this function usually has the following
// bounds:
Vector limits(nParameters);
limits.setTo(500);
setParameterLimits(-limits, limits);
}
int objectiveFunc(const Vector& x, bool new_parameters, Real& f) const override {
Real sum = 0;
for (int i = 0; i < getNumParameters(); ++i) {
sum += x[i] * sin(sqrt(std::abs(x[i])));
}
f = 418.9829 * getNumParameters() -sum;
return 0;
}
Vector optimalParameters() const override {
Vector x(getNumParameters());
x.setTo(420.9687);
return x;
}
};
class Easom : public TestOptimizerSystem {
public:
Easom() : TestOptimizerSystem(2) {
// The website above says this function usually has the following
// bounds:
Vector limits(getNumParameters());
limits.setTo(100);
setParameterLimits(-limits, limits);
}
int objectiveFunc(const Vector& x, bool new_parameters, Real& f) const override {
f = -cos(x[0]) * cos(x[1]) *
exp(-pow(x[0] - Pi, 2) - pow(x[1] - Pi, 2));
return 0;
}
Vector optimalParameters() const override {
Vector x(getNumParameters());
x.setTo(Pi);
return x;
}
};
#endif // SimTK_SIMMATH_OPTIMIZER_SYSTEMS_H_
|
