The paper describes a procedure of solving an optimal design problem with continuous/discrete design variables. The procedure is applied to a set of design parameters of a conventional fuel injection equipment for a diesel engine. The design parameters concern the design of the cam, high pressure pump, delivery valve, snubber valve, high pressure tube and injector. By the proposed procedure the continuous/discrete optimal design problem is replaced by a finite sequence of auxiliary problems where all design variables are treated as continuous. After solving each auxiliary problem one of the discrete design variables is set equal to the closest available discrete value and eliminated from the set of design variables. This process does not guarantee that an optimal solution to the continuous/integer programming problem is located; however it does produce improved near optimal designs for conventional fuel injection equipment. The proposed procedure is illustrated with a numerical example.

1.
Arora, J. S., 1989, Introduction to Optimum Design, McGraw-Hill, New York.
2.
Belegundu
A. D.
, and
Arora
J. S.
,
1984
, “
A Recursive Quadratic Programming Method With Active Set Strategy for Optimal Design
,”
International Journal for Numerical Methods in Engineering
, Vol.
20
, pp.
803
816
.
3.
Cˇernej
A.
,
Dobovisˇek
Zˇ.
,
Jankowski
A.
,
Kegl
B.
, and
Samec
N.
,
1994
, “
Global Optimization Procedure Applied on Conventional Fuel Injection Equipment. Direct Course of Process Simulation—DCPS
,”
Archivum Combustions
, Vol.
13
, pp.
83
100
.
4.
Dhingra
A. K.
, and
Lee
B. H.
,
1994
, “
A Genetic Algorithm Approach to Single and Multiobjective Structural Optimization With Discrete-Continuous Variables
,”
International Journal for Numerical Methods in Engineering
, Vol.
37
, pp.
4059
4080
.
5.
Fleury
C.
, and
Braibant
V.
,
1986
, “
Structural Optimization: A New Dual Method Using Mixed Variables
,”
International Journal for Numerical Methods in Engineering
, Vol.
23
, pp.
409
428
.
6.
Hallman, W. P., 1990, “Sensitivity Analysis for Trajectory Optimization Problems,” AIAA Paper 90-0471.
7.
Haug, E. J., and Arora, J. S., 1979, Applied Optimal Design, John Wiley, New York.
8.
Hsieh
C. C.
, and
Arora
J. S.
,
1984
, “
Design Sensitivity Analysis and Optimization of Dynamic Response
,”
Computer Methods in Applied Mechanics and Engineering
, Vol.
43
, pp.
195
219
.
9.
Kegl
B.
,
1995
, “
Optimal Design of Conventional Inline Fuel Injection Equipment
,”
Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering
, Vol.
209
, pp.
135
141
.
10.
Kegl, B., 1995, “An Improved Mathematical Model of Conventional FIE Processes,” SAE paper 950079.
11.
Kegl, B., Zambare, V. V., Cˇernej, A., and Dobovisˇek, Zˇ., 1992, “A Parametric Study of Fuel Injection Performance by Calculation,” IMechE Seminar on Diesel Fuel Injection Systems, Birmingham, Mechanical Engineering Publications, London, pp. 65–74.
12.
Kegl
M. S.
,
Butinar
B. J.
, and
Oblak
M. M.
,
1992
, “
Optimization of Mechanical Systems: On Strategy of Non-Linear First-Order Approximation
,”
International Journal for Numerical Methods in Engineering
, Vol.
33
, pp.
223
234
.
13.
Lim
O. K.
, and
Arora
J. S.
,
1986
, “
An Active Set RQP Algorithm for Engineering Design Optimization
,”
Computer Methods in Applied Mechanics and Engineering
, Vol.
57
, pp.
51
65
.
14.
Parker, R. F., 1976, “Future Fuel Injection System Requirements of Diesel Engines for Mobile Power,” SAE paper 760125.
15.
Svanberg
K.
,
1987
, “
The Method of Moving Asymptotes—A New Method for Structural Optimization
,”
International Journal for Numerical Methods in Engineering
, Vol.
24
, pp.
359
373
.
This content is only available via PDF.
You do not currently have access to this content.