FAQ - Frequently Asked Questions


How to cite MIDACO


If you wish to cite the MIDACO software, please use:


Schlueter M., Erb S., Gerdts M., Kemble S., Rückmann  J.J.
MIDACO on MINLP Space Applications
Advances in Space Research (Elsevier), Vol 51, Issue 7, Pages 1116–1131 (2013)  [BibTex]


If you wish to particularly cite the ACO algorithm within MIDACO, please use: 


Schlueter M., Egea J.A., Banga J.R.
Extended Ant Colony Optimization for non-convex Mixed Integer Nonlinear Programming
Computers & Operations Research (Elsevier), Vol. 36 , Issue 7, Pages 2217-2229 (2009)  [BibTex] 

If you wish to particularly cite the constraint handling technique of MIDACO, please use:


Schlueter M., Gerdts, M. 
The Oracle Penalty Method 
Journal of Global Optimization (Springer), Vol. 47, Issue 2, Pages 293-325 (2010)  [BibTex]


Thank you for citing MIDACO


How to transform a maximization problem into a minimization problem

A maximization problem can easily be transformed into a minimization problem by
switching the sign of the objective function:

F(X) = - F(X)


How to select the lower and upper bounds (XL & XU)

Selecting the lower and upper bounds (XL and XU) for a problem is always application specific. In general, the bounds have a significant influence on the MIDACO performance and should be set as tight as possible. If applicable, it is recommended to use the "BOUNDS-PROFIL" in order to identify, which bounds should be shrinked and which should be enlarged.

Does MIDACO require the variable bounds to be scaled between zero and one?

No. While some algorithms (in esp. SQP) require the bounds to be scaled zero and one, MIDACO does not have any such scaling restrictions. Lower and upper bounds can freely be chosen to any value. However, note that a large search space normally implies a slower convergence, as MIDACO will sample the entire search space. The bounds should therefore be chosen as tight as possible.

How to select a starting point

In general, the starting point (also called initial point or initial solution) has only a low influence on the MIDACO performance. If a good starting point is available, it should be used in combination with the FOCUS parameter (see user manual). Using specific starting points is recommended for solution refinement (e.g. improving the precision of the feasibility of constraints).

How to set a variable to be binary

Set the type of variable to be "integer" in the problem dimension step. The set the lower bound XL = 0.0 and the upper bound XU = 1.0

How to transform two-sided constraints to one-sided constraints

Constraints of the form  LOWER < G(X) < UPPER  can be transformed into two individual constraints:

 G(X) >  LOWER
-G(X) > -UPPER

What means "Violation of constraints G(X)"?

The "violation of G(X)" (VIO) measures the feasibility of the constraints. In particular, VIO is the L1-Norm (sum of all absolute values) over all entries of G(X) that are not feasible.

If VIO = 0, all constraints are feasible due to the default accuracy (0.001) or the user specified accuracy, defined by PARAM(1).

How to solve problems, where a variable must be in a discrete set (e.g. catalog)

If an optimization variable should take a value from some discrete set (e.g. catalog) a variable transformation is necessary. For example, consider that the variable X(i) should be restricted to one of the following four values: 0.3, 0.5, 0.7 or 1.2.

Then the following mapping transforms this variable from an
integer { 1, 2, 3, 4 } set to a custom value set { 0.3, 0.5, 0.7, 1.2 }:

IF( X(i) == 1 ):   X(i) = 0.3
IF( X(i) == 2 ):   X(i) = 0.5
IF( X(i) == 3 ):   X(i) = 0.7
IF( X(i) == 4 ):   X(i) = 1.2

Note that it is recommended to change the variable name from X(i) to some other (e.g. "Z"):

IF( X(i) == 1 ):   Z1= 0.3
IF( X(i) == 2 ):   Z1= 0.5
IF( X(i) == 3 ):   Z1= 0.7
IF( X(i) == 4 ):   Z1= 1.2

Otherwise, if the variable name is not changed, a re-transformation of the form:

IF( X(i) == 0.3 ): X(i) = 1
IF( X(i) == 0.5 ): X(i) = 2
IF( X(i) == 0.7 ): X(i) = 3
IF( X(i) == 1.2 ): X(i) = 4

is necessary in many languages (like C/C++ or Fortran) for return argument reasons.

How to set MIDACO parameters

Please see the User Manual on how to set MIDACO parameters. Note that MIDACO runs by default in some kind of "Autopilot" mode and it is not necessary to tune the parameters.

How to solve non-linear equation systems with MIDACO

MIDACO has the capability to solve problems with a significant number of (non-linear) equality constraints (see Benchmarks). Therefore MIDACO can also be applied to find solutions to general non-linear equation systems (NLES), where no objective function F(X) is present. In order to solve a NLES with MIDACO, the objective function can either be given a constant value (e.g. F(X)=0), or one of the (equality) constraints is formulated as objective (e.g. F(X) = |G(1)|). It is recommended, that the most difficult constraint is formulated as objective (rather than as constraint) and MIDACO is called with the ORACLE parameter. As in such a scenario the objective function actually expresses an equality constraint, an appropriate ORACLE parameter is easy to select close to zero (e.g. 0.05 or 0.1).

How to run MIDACO silently  [ disable all printing ]

Set the option PRINTEVAL= 0 and SAVE2FILE = 0. This will disable all printing commands.

How to pass additional input / output arguments to the problem function

A common way to pass additional arguments to the problem function is using global variables. This approach is independent of the MIDACO infrastructure and works well in many cases.

Another way to pass additional input/output arguments to the problem function can be realized by directly modifying the problem function call. An advantage of this approach is that it might result in (slightly) faster execution times, than using global variables. In the user manual, this direct modification approach is explained in detail in Section 1.3.

How to rename the problem function

The problem function can easily be renamed to any name. See user manual Section 1.3

How to measure MIDACO run-time in milliseconds instead of seconds

In most programming languages the MIDACO run-time is displayed in seconds rather than in milliseconds. However, for many problems (esp. small-scale and benchmarks) MIDACO will reach a solution in less than a second. In case the runtime is desired in milliseconds in such cases, a simple approximation can be done.

For example: A problem requires 12,345 evaluation to be solved and the runtime is displayed as 0 seconds. Then a (much) larger number of evaluation (e.g. 10,000,000 evaluation) should be performed and the corresponding runtime should be noted (e.g. 30 seconds for 10,000,000 evaluation). Then the CPU runtime for the original (small) number of function evaluation can be approximated in milliseconds as follows:

12345 * ( 30 / 10000000 ) = 0.037035 seconds = 37 milliseconds


Matlab / Octave: Is the MEX command required ever time, when running MIDACO?

No. The MEX command "mex midacox.c" is required only once to create the library file. Once the MIDACO DLL/MEX library file is generated on your system, you will not need to perform this command again.

Multi-Objective: Does MIDACO require the objective functions to be scaled?

No. The objective function values can be passed "as is" to MIDACO. For example, the values of the first objective may vary somewhere between 0 and 1, while the second objective function values may vary drastically between -100000 and 100000. MIDACO will fully-automatically scale those values for its internal algorithmic process.

Multi-Objective: Assignment of balanced solution along the pareto front

The assignment (placement) of the MIDACO solution along the pareto front is done fully automatically and on-the-fly during the optimization process. This means that during the optimization process it can temporarily happen that the MIDACO solution is placed on a different part of the pareto front, as the expected one. For example, MIDACO is run by default and the solution is therefore expected to be placed in the centre of the pareto front, but it is instead placed somewhere close to the edge of the front. These miss-placements are part of the algorithmic process and will normally be quickly corrected by MIDACO. However, especially during the first ten's or hundred's of evaluation, those miss-placements may temporarily occur.

Multi-Objective: PlotTool.exe is detected by Antivirus Software

Some antivirus software might detect / block the PlotTool.exe. This is a false positive, the PlotTool does not contain any harmful code and it will not upload/download any data. However, as a general disclaimer for the PlotTool and any other material offered on this webpage:  




Does MIDACO support parallelization for multi-objective optimization?

Yes. MIDACO's parallelization feature is fully available for all problem types, including multi-objective, large-scale and mixed integer problems. This means that in the extreme case, MIDACO can be used to solve:


Many-objective large-scale MINLP's with massive parallelization


( See here for examples of many-objective large-scale MINLP's solved by MIDACO )

Should parallelization be used?

Parallelization can be very effective, if the objectives and/or constraints evaluation is CPU-time expensive. This means that a single evaluation of F(X) and/or G(X) requires significant time. However, in case those evaluation is not CPU-time expensive, parallelization is normally not recommended. In fact, for CPU-time cheap problems, parallelization can even increase the overall time, due to the overhead introduced by the parallelization scheduler. In case of CPU-time cheap problems, executing several independent MIDACO runs with different random-seeds is normally more effective.

A special case occurs if the CPU-time for an evaluation can drastically vary. For example some evaluation may take up to some seconds/minutes, while others only take few milliseconds. In such case, parallel-overclocking with MIDACO can be a promising strategy (see user manual, section 8.8).