Hi.

Over the last years, one of the trends is the algorithms based on column generation. I'm working mainly on vehicle scheduling and there are more and more serious publication with this technique.

There are diversified categories of heuristic and meta-heuristic methodologies which have been dynamically studied. Of meta-heuristic type methods, Harmony search and Firefly algorithm might be considered of somehow more recent approaches, however, there are various population based approaches which have shown promising ability in optimization problems such as Ant Colony, Bee Colony, Particle Swarm Optimization (PSO as one of most prominent ones) while Simulated annealing and Travelling salesman problem might be constructive. Applied Soft Computing as a leading journal in this field can further clarify this subject with detailed information.

Dear friends,

Thanks for valuable information and your response.

Artificial immune network is another one

Actually, this is a very large-scope question. From my experience, I have faced many problems which required different optimization algorithms. To name a few, Dynamic Programming, Pontryagin's Minimum Principle, Genetic Algorithm, Particle Swarm Optimization. For stochastic systems, Stochastic Dynamic Programming plays a signification role. For complex systems with large state space and large control space, Approximate Dynamic Programming (ADP) is your choice. I think, ADP is very interesting and there has been a significant research on it in the past few years.

One of the recent success stories is hybridizing metaheuristics and mathematical programming. Details can be found under the acronym MATHEURISTICS. (See, e.g., http://en.wikipedia.org/wiki/Matheuristics). We have a conference on this (in Hamburg, Germany) which just opened the submission page:

http://iwi.econ.uni-hamburg.de/mh14/

Moreover there are special tracks at various conferences on this topic; see, e.g. the GOR Meeting in Aachen, Germany: http://www.or2014.de/

This question does not have a simple answer. Optimization is a field that is far too big for that. Depending on the type of optimization problem you face there are many new emerging technologies. Just to provide a rough classification:

You may want to find local optima or global optima

the optimization problems may be unconstrained or with various types of constraints

There are finite dimensional optimization problems (low dimensional or high dimensional) or infinite dimensional problems

for the finite dimensional ones you can have

combinatorial problems (integer problems)

continuous problems

mixed-integer problems

for every one of these you can have

special structure (linear, quadratic, etc.)

factorable problems (i.e. all functions are known by explicit formulas)

problems for which semi-local or global information is available (Lipschitz constants, convexity, automatic estimates)

problems for which only local information is available (point evaluations, derivative evaluations, etc.)

there it makes a difference, how many derivatives you get (Hessians y/n, gradients y/n?)

it also makes a huge difference, how much effort one function evaluation takes (expensive or cheap functions)

For infinite dimensional optimization problems there are also many classes

semi-infinite problems

optimal control problems

problems with differential equation constraints

For all of these problem classes there are various new emerging techniques available, depending on whether you want to find your solution with certainty (complete algorithms), provably with probability 1 eventually (asymptotically complete algorithms), or very likely (incomplete algorithms). If you provide more information on your problems, we might provide more specific information.

Algorithm References Inventor&Year

1. Ant colony optimization (ACO) ; I Dorigo and Stutzle (2004)

2. Artificial immune system optimization; Cutello and Nicosia (2002)

3. Bacterial foraging optimization ; Kim, Abraham and Cho (2007)

4. Bee optimization ; Karaboga and Bosturk (2007)

Pham et al (2006)

5. Cuckoo algorithm ; Yang and Deb (2009, 2010)

6. Differential evolution (DE) ; Storn and Price (1995, 1997)

7. Firefly optimization ; Yang (2010)

8. Fish optimization ; Huang and Zhou (2008)

9.Genetic algorithms (GA) ; Haupt and Haupt (2004)

10.Particle swarm optimization (PSO), Binary Particle Swarm Optimization (BPSO); Eberhart and Kennedy (1995)

11.Raindrop optimization ; Shah-Hosseini (2009)

12.Simulated annealing ; Kirkpatrick, Gelatt and Vecchi (1983)

13.Biogeography-based optimization (BBO),

14. Chemical reaction optimization (CRO)

15. A group search optimizer (GSO),

16. Imperialist algorithm

17. Swine flow Optimization Algorithm.

18. Teaching Learning Based Optimization(TLBO)

19. Bayesian Optimization Algorithms (BOA)

20. Population-based incremental learning (PBIL)

21. Evolution strategy with covariance matrix adaptation (CMA-ES)

22. Charged system search Optimization Algorithm

23. Continuous scatter search (CSS) Optimization Algorithm

24. Tabu search Continuous Optimization

25. Evolutionary programming

26. League championship algorithm

27. Harmony search Optimization algorithm

28. Gravitational search algorithm Optimization

29. Evolution strategies Optimization

30. Firework algorithm, Ying Tan, 2010

31. Big-bang big-crunch Optimization algorithm, OK Erol, 2006

32. Artificial bee colony optimization (ABC), Karaboga,2005

33. Backtracking Search Optimization algorithm (BSA)

34. Differential Search Algorithm (DSA) (A modernized particle swarm optimization algorithm)

35. Hybrid Particle Swarm Optimization and Gravitational Search Algorithm (PSOGSA)

36. Multi-objective bat algorithm (MOBA) Binary Bat Algorithm (BBA)

37. Flower Pollination Algorithm

38. The Wind Driven Optimization (WDO) algorithm

39. Grey Wolf Optimizer (GWO)

40. Generative Algorithms

41. Hybrid Differential Evolution Algorithm With Adaptive Crossover Mechanism

42.Lloyd's Algorithm

43.One Rank Cuckoo Search (ORCS) algorithm: An improved cuckoo search optimization algorithm

44. Huffman Algorithm

45. Active-Set Algorithm (ASA)

46. Random Search Algorithm

47. Alternating Conditional Expectation algorithm (ACE)

48. Normalized Normal Constraint (NNC) algorithm

Which is the latest Optimization technique for Power system problem solving? - ResearchGate. Available from: https://www.researchgate.net/post/Which_is_the_latest_Optimization_technique_for_Power_system_problem_solving2 [accessed Nov 16, 2015].

Kindly note that the existance of the large number of these algorithms can be seen quite critically. A good example exemplifying that is:

K. Sörensen (2015) Metaheuristics—the metaphor exposed

International Transactions in Operational Research 22, 3-18

DOI: 10.1111/itor.12001

MATLAB programming codes for PSO

https://www.researchgate.net/publication/296636431_Codes_in_MATLAB_for_Particle_Swarm_Optimization?ev=prf_pub

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

Code Codes in MATLAB for Particle Swarm Optimization

Article A comparative study of metaheuristic optimization approaches...

Another promising direction for optimization is called Bayesian optimization.

Bayesian optimization is very helpful when we donot know the function form and derivative.

Disaster Resilience and Sustainable Development

Grey world optimizer.

The recent meta-heuristic optimization algorithms are :

salp swarm algorithm (SSA),

moth–flame optimization (MFO),

ant lion optimizer (ALO),

multi verse optimizer (MVO),

grey wolf optimizer (GWO),

evaporation rate water cycle algorithm (ER-WCA),

and mine blast algorithm (MBA).

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Swarm Intelligence (SI)-based algorithms:

Ant Colony Optimization,

Ant Lion Optimization,

Artificial Bee Colony,

Bacterial foraging,

Bacterial-GA Foraging,

Bat Algorithm,

BeeHive,

Bumblebees,

Cat swarm,

Consultant-guided search

Cuckoo Search,

Krill Herd,

Monkey search,

Particle Swarm Optimisation,

Weightless Swarm Algorithm.

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Bio-inspired (not SI-based) algorithms:

Atmosphere clouds model,

Biogeography based Optimization,

Brain Storm Optimization,

Differential Evolution,

Dolphin echolocation,

Japanese tree frogs calling,

Eco-inspired evolutionary algorithm,

Egyptian Vulture,

Fish-school Search,

Flower pollination Algorithm,

Firefly Algorithms,

Gene expression.

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Physics and Chemistry based algorithms:

Big bang-big Crunch,

Black hole,

Central force optimization,

Charged system search,

Electro-magnetism optimization,

Galaxy-based search algorithm,

Gravitational search,

Harmony Search,

Intelligent water drop,

River formation dynamics,

Self-propelled particles,

Simulated Annealing,

Stochastic diffusion search,

Spiral optimization,

Water cycle algorithm.

Evolutionary Nature and Bio-Inspired Optimization algorithms are the new trends which are used extensively for solving/optimizing real world problems.

Some of these include:

Ant Lion Optimizer (based on the hunting mechanism of ant-lions in nature)

Dragonfly Optimization Algorithm (based on the foraging method of dragonflies)

Grey Wolf Optimizer (inspired from the hunting technique of grey wolves)

Whale Optimization Algorithm,Moth-Flame Optimization,Binary Bat Algorithm,Cuckoo Search Algorithm,Spotted Hyena Optimization,Particle Swarm Optimization, Ant Bee Colony,Grasshopper Optimizer etc.

A wide variety of applications of these algorithms are available in literature.

Nowadays, nature inspired optimisation are the trending once. AI plays signicant role when it comes to the methods