The objective of this study was to evaluate the performance of different multivariate optimization algorithms by solving a “tracking” problem using a forward dynamic model of pedaling. The tracking problem was defined as solving for the muscle controls (muscle stimulation onset, offset, and magnitude) that minimized the error between experimentally collected kinetic and kinematic data and the simulation results of pedaling at 90 rpm and 250 W. Three different algorithms were evaluated: a downhill simplex method, a gradient-based sequential quadratic programming algorithm, and a simulated annealing global optimization routine. The results showed that the simulated annealing algorithm performed far superior to the conventional routines by converging more rapidly and avoiding local minima.

1.
Anderson
F. C.
,
Ziegler
J. M.
,
Pandy
M. G.
, and
Whalen
R. T.
,
1995
, “
Application of high-performance computing to numerical simulation of human movement
,”
ASME JOURNAL OF BIOMECHANICAL ENGINEERING
,
117
:
155
157
.
2.
Audu
M. L.
, and
Davy
D. T.
,
1988
, “
A comparison of optimal control algorithms for complex bioengineering studies
,”
Optimal Control Applications & Methods
,
9
:
101
106
.
3.
Bogert, A. J. van den, and Socst, A. J. van, 1993, “Optimization of power production in cycling using direct dynamics simulations,” Proc. 4th Int. Symp. Comp. Sim. in Biomech., Paris-Montligon, BMG2–14-BMG2–17.
4.
Buchanan
T. S.
, and
Shreeve
D. A.
,
1996
, “
An evaluation of optimization techniques for the prediction of muscle activation patterns during isometric tasks
,”
ASME JOURNAL OF BIOMECHANICAL ENGINEERING
,
118
:
565
574
.
5.
Corana
A.
,
Marchesi
M.
,
Martini
C.
, and
Ridella
S.
,
1987
, “
Minimizing multimodal functions of continuous variables with the simulated annealing algorithm
,”
ACM Trans Math Software
,
13
:
262
280
.
6.
Davy
D. T.
, and
Audu
M. L.
,
1987
, “
A dynamic optimization technique for predicting muscle forces in the swing phase of gait
,”
J. Biomech.
,
20
:
187
201
.
7.
Delp
S. L.
,
Loan
J. P.
,
Hoy
M. G.
,
Zajac
F. E.
,
Topp
E. L.
, and
Rosen
J. M.
,
1990
, “
An interactive graphics-based model of the lower extremity to study orthopædic surgical procedures
,”
IEEE Trans. Biomed. Eng.
,
37
:
757
767
.
8.
Desai, R., and Patil, R., 1996, “SALO: combining simulated annealing and local optimization for efficient global optimization,” presented at the 9th Florida AI Research Symposium.
9.
Fregly, B. J., 1993, “The significance of crank load dynamics to steady-state pedaling biomechanics: an experimental and computer modeling study,” Ph.D. Thesis, Department of Mechanical Engineering, Stanford University.
10.
Goffe
W. L.
,
Ferrier
G. D.
, and
Rogers
J.
,
1994
, “
Global optimization of statistical functions with simulated annealing
,”
J. Econometrics
,
60
:
65
99
.
11.
Gonzalez
R. V.
,
Andritsos
M. J.
,
Barr
R. E.
, and
Abraham
L. D.
,
1993
, “
Comparison of experimental and predicted muscle activation patterns in ballistic elbow joint movements
,”
Biomed. Sci. Instrum.
,
29
:
9
16
.
12.
Hannaford
B.
, and
Stark
L.
,
1987
, “
Late agonist activation burst (PC) required for optimal head movement: a simulation study
,”
Biol. Cybern.
,
57
:
321
330
.
13.
Ingber
L.
,
Wehner
M. F.
,
Jabbour
G. M.
, and
Barnhill
T. M.
,
1991
, “
Application of statistical mechanics methodology to term-structure bond-pricing models
,”
J. Math. Comp. Mod.
,
15
:
77
98
.
14.
Ingber
L.
,
1993
, “
Simulated annealing: practice verses theory
,”
J. Math. Comp. Mod.
,
8
:
29
57
.
15.
Kirkpatrick
S.
,
Gelatt
C. D.
, and
Vecchi
M. P.
,
1983
, “
Optimization by simulated annealing
,”
Science
,
220
:
671
680
.
16.
Lawrence, C. T., Zhou, J. L., and Tits, A. L., 1997, “User’s Guide for CFSQP Version 2.5: A C Code for Solving (Large Scale) Constrained Nonlinear (Minimax) Optimization Problems, Generating Iterates Satisfying All Inequality Constraints,” Institute for Systems Research, University of Maryland, Tech Report TR-94–16rl.
17.
Nelder
X. X.
, and
Mead
Y. Y.
,
1965
,
The Computer Journal
,
7
:
308
313
.
18.
Neptune
R. R.
, and
Hull
M. L.
,
1998
, “
Evaluation of Performance Criteria for Simulation of Submaximal Steady-State Cycling Using a Forward Dynamic Model
,”
ASME JOURNAL OF BIOMECHANICAL ENGINEERING
, Vol.
120
, pp.
334
341
.
19.
Pandy
M. G.
,
Anderson
F. C.
, and
Hull
D. G.
,
1992
, “
A parameter optimization approach for the optimal control of large-scale musculoskeletal systems
,”
ASME JOURNAL OF BIOMECHANICAL ENGINEERING
,
114
:
450
460
.
20.
Press, W. H, Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P., 1992, Numerical Recipes in Fortran: The Art of Scientific Computing, 2nd ed., Cambridge University Press, New York.
21.
Raasch
C. C.
,
Zajac
F. E.
,
Ma
B.
, and
Levine
W. S.
,
1997
, “
Muscle coordination of maximum-speed pedaling
,”
Journal of Biomechanics
,
30
:
595
602
.
22.
Zajac
F. E.
,
1989
, “
Muscle and tendon: Properties, models, scaling, and application to biomechanics and motor control
,”
Crit. Rev. Biomed. Eng.
,
17
:
359
411
.
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