betaRMP is an open-source benchmarking visualization tool written in MATLAB for creating β-Relative Minimization Profiles (β-RMPs), which are plots for concisely comparing optimization methods evaluated on large heterogenous sets of test problems. β-RMPs are designed to highlight the interplay and trade-offs between the following three pertinent performance attributes:
Like performance profiles and data profiles, β-RMPs can also be used in other contexts outside of optimization, such as assessing numerical accuracy of solvers under different computational budget limits.
In general, we assume that the difficulty of each test problem varies somewhat proportionally with the computational cost to solve it. Note that test problems of different types, such as linear versus non-linear, should not necessarily be grouped together in a single test set.
Each solver in a comparison has what is called its RMP curve. A point (a,b) on a given solver's RMP curve indicates that, for b% of the test problems, the solver was able to find feasible solutions such that the best (lowest) objective values attained at these feasible points were either equal to given per-problem target values or, at worst, were only higher by at most a relative difference of 10^{a}.
Per-problem target values, if known a priori, can be supplied by the user but, by default, target values are automatically extracted from the collected benchmarking data itself. In general, each per-problem target value is defined as the best (lowest) objective value known to be achievable at a feasible point, which is determined by taking the best feasible solution encountered over all the methods being compared. Feasibility is generally defined in terms of a tolerance (particularly for equality constraints, since it is unrealistic to expect them to be perfectly satisfied).
To do a comparison of methods with respect to computational budgets, we generalize the concept of the aforementioned RMP curve to a so called β-RMP curve. When β is infinity, a β-RMP curve is equivalent to the RMP curve described above, that is, the solvers are judged without any imposed per-problem computational budgets. However, when β is less than infinity, a solver's β-RMP curve is defined only in terms of the iterates that the solver was able to reach within certain per-problem budgets, specifically β times a fixed set of per-problem computational budgets.
Like the target values, the fixed per-problem computational budgets can be explicitly supplied by the user if desired. However, as the difficulty of each problem in the test set may vary significantly and it can be difficult to predict to appropriate budgets, by default, the per-problem budgets are automatically determined from the collected benchmarking data itself. The set of observed costs for running each method on a given problem can be used to estimate an appropriate budget for that problem. These fixed per-problem budget estimates can be constructed in various ways, depending on what aspect one wishes to highlight in an β-RMP benchmark; see the betaRMP documentation for more info.
For more details and discussion on β-RMPs, such as their motivation and exact definition, we refer the interested reader to the paper mentioned below.
cd your_betaRMP_install_directory
load('betaRMP_sample_data.mat');
betaRMP(sample_data.method_data,sample_data.opts);
help betaRMP
Note if this cost data cannot be collected, it may be okay to estimate it (though one must proceed with caution). For example, if elapsed wall-clock time is the cost metric and all the methods typically take many iterations before terminating, then it may then be adequate to simply record the total elapsed time and the number of iterations incurred for every problem method pair and use the average elapsed time per iterate to construct an approximation to the actual cumulative cost data.
If you publish work that either refers to or makes use of β-RMPs, please cite the following paper:
When referring to this software, please also include which version was used,
e.g. betaRMP v1.4. Note that betaRMP
, in monospaced font,
refers to the command/routine, not the name of the
software package.
betaRMP is licensed under the GNU Affero General Public License, version 3.