Job machine scheduling like job shop, open shop and more than three machine flow shop problems are quite challenging to solve because they are all NP Hard problems.  So researchers have tried to solve these problems with heuristics and metaheuristics methods. Even there are good number of algorithm exist to solve these class of problems but still lot more research can be done considering the solution quality and computational speed. 

To me, the most challenging optimization problem I've ever tackled with is network routing. Finding the shortest path in a network with the presence of change in traffic pattern or network structure. ANTNET is a robust algorithm which can adapt the routing tables to the changing environment in a reasonable time. We've improved ANTNET from different perspectives like learning, adaptability etc.

http://www.sciencedirect.com/science/article/pii/S1084804514001271

http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=5548215&url=http%3A%2F%2Fieeexplore.ieee.org%2Fxpls%2Fabs_all.jsp%3Farnumber%3D5548215

What I found as a problem is the convergence time and fitness value in the application of wireless communication systems. The convergence time represented by how long optimization algorithm requires to reach to an acceptable solution. Also the value of this solution and the local optima are another problems in the communication systems, where the parameters will represent a best configuration to apply in order to achieve the link objectives

Really it was a great question. However according to my point of view traffic stress and electricity shortages, optimization problem is most challenging problem which we all are facing daily in our real life (especially in india) and also have some price money for solve this problem from Mahindra Group . The problem only can be solved by robust Metaheuristic/Evolutionary Algorithms like (PSO), GA  or some others. http://timesofindia.indiatimes.com/india/Mahindras-1-million-bounty-awaits-desi-innovators/articleshow/31062876.cms

As far as now, control of non-linear dynamical systems

for my case, it is multi-document summarization... I have spent a lot of time to implement that using MSFLA!!

I have solved a portfolio optimization problem using ACO and I am very satisfied with its performance. Coding the same in MATLAB was really a challenge for me and it was taking almost 48 hrs to perform a single execution..

I have been informed of the publication of a book edited by Springer:

Applications of Metaheuristics in Process Engineering

Editors: Jayaraman Valadi, Patrick Siarry

ISBN: 978-3-319-06507-6 (Print) 978-3-319-06508-3 (Online)

There is a historial review chapter in there. Process Engineering has a lot of challenging optimization problems to deal with, irrespective of the solution methods.

Indeed, I have been informed by a citation alert since they cite an article we've written a couple of years ago - it's on RG - on the use of a simulated annealing algorithm for the constrained dynamic optimization of an emulsion polymerization process.

We were very satisfied with the obtained solution "the best known solution", since it confirmed results obtained with other - deterministic - techniques.

Backtracking search algorithm is also an effective one.

http://www.sciencedirect.com/science/article/pii/S0096300313001380

As a matter of fact, many. For example the assembling of some, previously unknown  3D 8*8*8 English crosswords with no black field at all. This is my newest, several weeks old feat.

http://www.critticall.com/cubus_maximus/test.html

Supply Chain Network Problems can be really tough, specially in real big reall world scenarios. I've been facing many problems regarding execution time when compared to exact algorithms, such IBM CPLEX.

Hi,

I suggest Ant-Q algorithm for handling NP-hard problem. The  Ant-Q algorithm is an agent based algorithm that combines Ant colony based methods  with the

reinforcement learning technique.

Personnaly I have used the Ant-Q as hyperheuristic for solving the cutting stock problem and I have reached good results.

https://www.researchgate.net/publication/224247371_Ant-Q_hyper-heuristic_approach_for_solving_2-dimensional_Cutting_Stock_Problem

Good luck. 

Conference Paper Ant-Q hyper-heuristic approach for solving 2-dimensional Cut...

Relays coordination problem.....

https://www.researchgate.net/publication/280244004_A_comparative_study_of_metaheuristic_optimization_approaches_for_directional_overcurrent_relays_coordination?ev=prf_pub

Article A comparative study of metaheuristic optimization approaches...

Probabilistic Satisfiability (PSAT) has been the hardest problem I have solved. :) Logical formula we want to satisfy has to be converted to a linear system whose number of variables exponentially increases with the number of propositional variables in the original formula. My master thesis solved this problem with the Bee Colony Optimization algorithm. I found it more complex than Boolean SAT or continuous optimization because formulation of PSAT as an optimization problem is not as straightforward as it might seem and requires careful preprocessing. Moreover, PSAT is not pure combinatorial or continuous problem, but a mix of the two types because you have to deal with discrete values for propositional letters (True and False), and real values for the probabilities. 

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

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

Code Codes in MATLAB for Particle Swarm Optimization

Dear All,

I hope you can read our recent work addressing challenging optimization problems https://github.com/ThangLe-duc or https://sites.google.com/site/nguyenxuanhungsite/software?authuser=0. BCMO provided a less-parameter optimization technique.

Thank you,

Hung