3. Y2F Interface

YALMIP is a high-level modeling language for optimization in MATLAB. It is very convenient to use for modeling various optimization problems, including convex quadratic programs, for example. YALMIP allows you to write self-documenting code that reads very much like a mathematical description of the optimization model.

To combine the computational efficiency of FORCES Pro with the ease-of-use of YALMIP, we have created the interface Y2F. Y2F very efficiently detects the inherent structure in the optimization problem, and uses the FORCES Pro backend to generate efficient code for it. All you need to do is to replace YALMIP’s optimizer function, which pre-builds the optimization problem such that subsequent evaluations become very inexpensive, by Y2F’s optimizerFORCES function, which is fully API-compatible with optimizer.

You can read more about the concept of YALMIP’s optimizer here.

Important

The Y2F interface supports convex decision making problems, with or without binary variables.

3.1. Installing Y2F

Y2F is included in the FORCES Pro client. If optimizerFORCES is not found on your MATLAB path, you need to add the FORCES_PRO/Y2F/Y2F directory to it, e.g. by typing:

addpath /home/user/FORCES_PRO/Y2F/Y2F

on your MATLAB command prompt.

Of course, you also need a working installation of YALMIP, which you can download from https://yalmip.github.io/download/.

3.2. Generating a solver

A YALMIP model consists of a constraint object, which we name const and an objective function obj. You can create an optimizer object that has most of the work YALMIP needs to do before calling a solver (called canonicalization) already saved. The only parts missing are the parameters of the problem, which you can specify when calling optimizer:

P = optimizer(Con, Obj, Options, Parameters, WantedVariables); % YALMIP syntax

With Y2F, you can have the same syntax but creating a FORCES Pro solver:

P = optimizerFORCES(Con, Obj, Options, Parameters, WantedVariables, [ParameterNames], [OutputNames]);

where Options is a FORCES codeoptions struct (see the Solver Options section for more information). The two last arguments are optional cell arrays of strings specifying the names of the parameters and the wanted variables. These will be used for naming e.g. the in- and output ports of the generated Simulink block.

3.3. Calling the solver

There are several ways of calling the generated solver:

1. Using the optimizerFORCES object, which again is API compatible with YALMIP’s optimizer object:

[wantedVariableValues, exitflag, info = P{Parameters}; % YALMIP syntax

2. Using the generated Matlab (MEX) interface (type help solvername at the Matlab command prompt for more information):

problem.ParameterName1 = value1; problem.ParameterName2 = value2;
[output, exitflag, info] = solvername(problem);
wantedVariable = output.outputName1;

3. Via the generated Simulink block (see interfaces folder of the generated code).

3.4. Solver info

3.4.1. Exitflags

One should always check whether the solver has exited without an error before using the solution. Possible values of exitflag are presented in Table 3.1.

Table 3.1 Exitflag values
Exitflag Description
1 Optimal solution found to the requested accuracy.
2 (only branch-and-bound) A feasible point has been identified for which the objective value is no more than codeoptions.mip.mipgap*100 per cent worse than the global optimum.
0 Timeout – maximum number of iterations or maximum computation time of codeoptions.mip.timeout (only branch-and-bound) reached. The returned solution is the best one found so far.
-1 (only branch-and-bound) Infeasible problem (problems solving the root relaxation to desired accuracy).
-2 (only branch-and-bound) Out of memory – cannot fit branch and bound nodes into pre-allocated memory.
-7 The convex solver could not proceed due to stalled line search. The problem might be infeasible. Otherwise, please submit a bug report to support@embotech.com including all data necessary to reproduce the problem. You can also run FORCESdiagnostics on your problem to check for most common errors in the formulation.
-10 The convex solver could not proceed due to an internal error. The problem might be infeasible. Otherwise, please submit a bug report to support@embotech.com including all data necessary to reproduce the problem. You can also run FORCESdiagnostics on your problem to check for most common errors in the formulation.
-100 License error. If you have generated code with a simulation license, it will run only on the machine from which the code has been generated. In some cases, e.g. when connected to a VPN network, the FORCES Pro license checker produces a false negative. Re-run the code generation script in this case to make sure licensing information is correctly set.

3.4.2. Additional diagnostics

The solver returns additional information to the optimizer in the info struct. Some of the fields are described in Table 3.2. Depending on the method used, there will also be other fields describing the quality of the returned result.

Table 3.2 Info values
Info Description
info.it Number of iterations. In branch-and-bound mode this is the number of convex problems solved in total.
info.solvetime Total computation time in seconds.
info.pobj Value of the objective function.
info.it2opt (only branch-and-bound) Number of convex problems solved for finding the optimal solution. Note that often the optimal solution is found early in the search, but in order to certify (sub-)optimality, all branches have to be explored.

3.5. Performance

A performance measurement for the interface when compared to other solvers called via YALMIP and to the same problem formulated via the low-level interface of FORCES Pro (2 states, 1 input, box constraints, varying horizon) is presented in Figure 3.1. In this example, the code generated directly from YALMIP is about 10 times faster than other solvers, and only a factor 2 slower than the code generated with the low-level interface of FORCES Pro.

../_images/Y2F_performance.png

Figure 3.1 Performance comparison of the Y2F interface of FORCES Pro.

3.6. Examples

  • Y2F interface: Basic example: Learn how to formulate problems in YALMIP easily, and then use the Y2F interface to generate code with FORCES Pro.