Nonlinear Network Programming on Vector Supercomputers: A Study on the CRAY X-MP

The parallelism built into vector supercomputers raises several challenging issues for designers of optimization algorithms. We survey recent trends in parallel computer systems and study the impact of vector computing on nonlinear network programming. We propose a general framework for migrating fortran optimization software to a vector computer, and apply it in the context of two nonlinear network codes: NLPNETG, based on the primal truncated Newton algorithm, and GNSD, based on the simplicial decomposition method. We include computational experiments on a CRAY X-MP/24 system that tested the nonlinear network codes and compared the results with those of MINOS, a general purpose optimizer. Our experience indicates that vectorized codes can achieve significant improvements in performance as much as 80% for primal truncated Newton, but achieve only modest improvements 15% for simplicial decomposition for other algorithms.

[1]  Balder Von Hohenbalken,et al.  Simplicial decomposition in nonlinear programming algorithms , 1977, Math. Program..

[2]  Kai Hwang,et al.  Supercomputers - Design and Applications , 1984 .

[3]  Ira W. Cotton.  Technologies for Local Area Computer Networks , 1980, Comput. Networks.

[4]  Janusz S. Kowalik.  High-Speed Computation , 1984 .

[5]  John L. Larson.  Multitasking on the Cray X-MP-2 Multiprocessor , 1984, Computer.

[6]  Michael J. Flynn,et al.  Some Computer Organizations and Their Effectiveness , 1972, IEEE Transactions on Computers.

[7]  Burton J. Smith.  Architecture And Applications Of The HEP Multiprocessor Computer System , 1982, Optics & Photonics.

[8]  Udo Schendel,et al.  Introduction to Numerical Methods for Parallel Computers , 1984 .

[9]  Michael Florian,et al.  A Method for Computing Network Equilibrium with Elastic Demands , 1974 .

[10]  Leon S. Lasdon,et al.  Feature Article - Survey of Nonlinear Programming Applications , 1980, Oper. Res..

[11]  Jack J. Dongarra,et al.  Unrolling loops in fortran , 1979, Softw. Pract. Exp..

[12]  John M. Mulvey,et al.  Nonlinear programming on generalized networks , 1987, TOMS.

[13]  S A Zenios.  SEQUENTIAL AND PARALLEL ALGORITHMS FOR CONVEX GENERALIZED NETWORK PROBLEMS AND RELATED APPLICATIONS , 1986 .

[14]  Stavros Andrea Zenios.  Sequential and parallel algorithms for convex generalized network problems and related applications (optimization, nonlinear, air-traffic) , 1986 .

[15]  Richard E. Rosenthal,et al.  A Nonlinear Network Flow Algorithm for Maximization of Benefits in a Hydroelectric Power System , 1981, Oper. Res..

[16]  Charles L. Lawson,et al.  Basic Linear Algebra Subprograms for Fortran Usage , 1979, TOMS.

[17]  Narendra Karmarkar,et al.  A new polynomial-time algorithm for linear programming , 1984, Comb..

[18]  Charles L. Seitz,et al.  The cosmic cube , 1985, CACM.

[19]  Iain S. Duff.  The use of supercomputers in Europe , 1985 .

[20]  J. G. Klincewicz,et al.  A scaled reduced gradient algorithm for network flow problems with convex separable costs , 1981 .

[21]  J. M. Mulvey,et al.  Integrated risk/cost planning models for the US Air Traffic system , 1985 .

[22]  Philip E. Gill,et al.  Practical optimization , 1981 .

[23]  Jack J. Dongarra.  Performance of various computers using standard linear equations software in a Fortran environment , 1984, SGNM.

[24]  Robert B. Schnabel,et al.  Parallel Computing in Optimization , 1985 .