Tak a look at: http://www.sce.carleton.ca/faculty/chinneck/po/Chapter13.pdf

If it is binary then it is always discrete. It is probably better to say "optimization of pseudo-Boolean functions".  For example:

http://www.sciencedirect.com/science/article/pii/S0166218X01003419

The term "binary discrete optimization" is almost never used. The terms "combinatorial optimization", "discrete optimization" and "integer programming" are much more common.  For more on this, see:

"https://www.researchgate.net/post/What_is_the_meaning_of_combinatorial_optimization

Dear Professor Letchford,

I would like to know whether Bilevel Programming, MPEC and EPEC are "combinatorial optimization" or not.

Any help and useful papers would be appreciated.

Regards,

Morteza Shabanzadeh

http://mortezash.blogfa.com/

BLP, MPEC and EPEC are usually regarded as nonlinear optimisation problems (i.e., problems with continuous variables and nonlinear constraints).  They are however NP-hard in general, since the complementarity constraints are non-convex.

See for example here:

http://www.neos-guide.org/content/optimization-taxonomy

http://jesr.journal.fatih.edu.tr/jesr.tasgetiren-liang.pdf

http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6653754

http://www.hindawi.com/journals/mpe/2014/569580/

I suggest that you look at the Mathematical Programming Glossary that is published by INFORMS.  

http://glossary.computing.society.informs.org/ver2/mpgwiki/index.php?title=Main_Page

Here is also a nice paper related to a particle swarm optimization algorithm, defined "cat swarm optimization", for binary combinatorial (or discrete) optimization:

http://dx.doi.org/10.1109/IC4.2013.6653754

http://www.inf.ufpr.br/aurora/disciplinas/topicosia2/livros/search/integer.pdf

Hello,

When it comes to Binary Optimization, then we should take into account that the decision variable can take just two descrete values, namely "zero" and "one". For example in Traveling Salesman Problem the  decision variable (xij) takes one when the salesman travels from city i to city j and otherwise zero.

Regards,

Arian

You can see the topic with a simple level in http://www.amsterdamoptimization.com/pdf/minlp.pdf. With this document, you can also copy and paste the sample codes in GAMS. Note that you can download GAMS free for describing optimization model, and use many MINLP/MILP solvers in http://www.neos-server.org/neos/solvers/index.html to solve your defined problem. Best regards, Pham Duc Dai.

https://www.researchgate.net/publication/296636431_Codes_in_MATLAB_for_Particle_Swarm_Optimization

Code Codes in MATLAB for Particle Swarm Optimization

https://www.researchgate.net/publication/297245624_Particle_Swarm_Optimization_Algorithm_and_its_Codes_in_MATLAB

Research Particle Swarm Optimization: Algorithm and its Codes in MATLAB