About the Software

VTMOP [1] is a Fortran 2008 package containing a robust, portable solver and a flexible framework for solving multiobjective optimization problems (MOPs). Designed for efficiency and scalability to an arbitrary number of objectives, VTMOP attempts to generate uniformly spaced points on a (possibly nonconvex) Pareto front with minimal cost function evaluations using the adaptive weighting scheme described in [2]. The driver subroutine is VTMOP_SOLVE, which can be run both serially and with parallel function evaluations. Minimal subsets of dependencies such as VTDIRECT, QNSTOP, SHEPPACK, DELAUNAYSPARSE, SLATEC, LAPACK, and BLAS are also provided. Comments at the top of each subroutine document their usage, and examples demonstrating the driver's usage are given in the sample drivers samples.f90 and samplep.f90.

A Python interface for VTMOP is also available through the libEnsemble library [3,4], which can be used to dynamically coordinate the distribution of simulation evaluations over extreme-scale resources.

VTMOP has been used to solve problems in the areas of HPC library auto-tuning [5,6], particle accelerator optimization [1], and cell biology [7].

Read the User Guide »

Publications

[1] T. H. Chang, L. T. Watson, J. Larson, N. Neveu, W. I. Thacker, S. Deshpande, and T. C. H. Lux. "Algorithm 1028: VTMOP: Solver for Blackbox Multiobjective Optimization Problems", ACM Trans. Math. Software, 48(3), Article 34 (2022), 1-34.

[2] S. Deshpande, L. T. Watson, and R. A. Canfield. "Multiobjective optimization using an adaptive weighting scheme", Optimization Methods and Software, 31(1), (2016), 110-133.

[3] T. H. Chang, J. Larson, L. T. Watson, and T. C. H. Lux. "Managing computationally expensive blackbox multiobjective optimization problems with libEnsemble", In Proc. 2020 Spring Simulation Conference (SpringSim '20), Society for Modeling and Simulation International, virtual event, 2020, Article No. 31.

[4] S. Hudson, J. Larson, J.-L. Navarro, and S. Wild. "libEnsemble: A library to coordinate the concurrent evaluation of dynamic ensembles of calculations", IEEE Trans. Parallel and Distributed Systems, 33(4), (2022), 977-988.

[5] T. H. Chang, J. Larson, and L. T. Watson. "Multiobjective optimization of the variability of the high-performance Linpack solver", In Proc. 2020 Winter Simulation Conference (WSC 2020), virtual event, 2020, pp. 3081-3092.

[6] T. H. Chang, "Mathematical Software for Multiobjective Optimization Problems". Ph.D. thesis, Virginia Polytechnic Institute and State University, Blacksburg, VA, USA, 2020.

[7] C. Xu, H. Hollis, M. Dai, X. Yao, L. T. Watson, Y. Cao, and M. Chen. "Modeling the temporal dynamics of master regulators and CtrA proteolysis in Caulobacter crescentus cell cycle", PLOS Computational Biology, 18(1), (2022), 1-25.