1. Amortized complexity and online algorithms1.

2. Ant Colony Optimization (ACO)

3. Bounded-error Probabilistic Polynomial-time (BPP) Algorithms2.

4. Complexity of matrix multiplication.

5. Discussion of the polynomial-time primality algorithms, and some historical survey of prior results.

6. Extensions to the Dijkstra algorithm3.

7. History of the origins and the theory of finite state machines.

8. Factorization + its application in Cryptography

9. Discrete Logarithm + its application in Cryptography

10. P, NP, and NP Complete

11. Chinese Remaindering + its application in Cryptrography

12. Greed Algorithm versus Dynamic Programming

## The Ant Colony Optimization Algorithm

Operation research and Computer science generally consists of the Ant Colony Optimization or the ACO, which is generally considered to be a probabilistic technique that is used in order to solve the problems related to computing. This this it can also be used for the purpose of finding the good paths by making use of the graphs. In this the artificial ants is multi-agent method that is generally inspired by the behaviours that the real ants are having (Mohan & Baskaran, 2012).

Communication based upon the usage of the pheromone by the biological ants is often considered to be a paradigm which is used predominantly. The artificial ants and the local search engines are combined so as to have a better method for different kind of optimization tasks that also involves the usage of some graphs as well.

Including of the burgeoning activity in this particular field has been associated with leading towards the conference which are entirely dedicated to the artificial ants as well as to other commercial applications by companies who are specialized in this field like the AntOptima. Ant Colony Optimization is also sometimes considered to be a class of optimization algorithm that has been modelled according to the actions conducted by the ant colony.

The artificial Ants are used for the purpose of locating the optimal solutions. This is done by moving throughout the entire parameter space by representing the solutions that are possible (Nishant et al., 2014). Like the real ants, the simulated ants are also associated with recording the positions and the quality of the solutions. This is done in order to make sure that the simulation iterations taking place later would help in the process of obtaining better solutions. Another variety of this approach includes the bees’ algorithm which operates in a similar fashion like that of another social insect known as the honey bee.

Discussion:

The Ant Colony Optimization is an algorithm that is generally considered to be a member of the swarm intelligence method which consists of some metaheuristic optimizations. This concept was initially proposed by Macro Dorigo in the year of 1992 and was associated with looking out for a path in the graph that is most optimal. This was done by depending upon the behaviour that the ants are having while looking out for a path that exists between the colony and the food source. This idea was further diversified so as to solve numerous numerical problems which initially lead to various type of problems (Mishra & Jaiswal, 2012). It can be stated that ACO is a model-based search which is also associated with sharing similarities with the estimation of the distribution algorithms.

## Ambient Networks of Intelligent Objects

Ambient Networks of Intelligent objects:

There exists the need of new concepts as the term intelligence is no longer centralized and is implemented across various type of objects, the Anthropocentric concepts is associated with leading towards an increased rate of IT system production of where it is seen that the control units, data processing and the forces responsible for calculating are present in centralized form. All this units which are centralized are associated with increasing their performance rate and this in turn can be compared with the capabilities that a human brain is having (Tawfeek et al., 2013).

The ultimate vision of the computers is the model of the brain. the ambient network of intelligent objects along with the new creation of new Information System that are of diffused nature and are dependent upon the nanotechnology and this is profoundly going to change the entire concept. Small devices that are generally compared with the insects are not associated with disposing high intelligence of their own and for this reason it can be stated that their intelligence is limited. For example it is not possible to combine the calculator of high performance with the power need to solve any type of mathematical related problems present in a biochip which is implemented inside a human body or are integrated with the intelligent tag that re-designed in order to track the commercial articles.

But whenever the objects gets connected with each other, then they are associated with disposing a form of intelligence (Jiang, Maskell, & Patra, 2013). It is possible to compare this intelligence with the colony of ants or bees so as to make those intelligence become superior in case of certain problems and this much superior than the reasoning conducted by the centralized system like a brain.

There exists several examples of how the minuscule organisms of the world follow simple rules and form the collective intelligence in the macroscopic level. This is the model which is dependent upon the co-operation of the independent units by making use of simple as well as unpredictable behaviours. They are associated with moving all around so as to carry out certain tasks and they have a very little information for doing this (Ting & Chen, 2013). They are having the capability of getting adapted to the changes taking place in the environment along with having an enormous amount of strength so as to deal with various complex situations. This type of flexibility is very much beneficial for the mobile networks of various objects that are being developed in a perpetual way.

## Artificial Pheromone System

Artificial Pheromone System:

Pheromone-based Communication is considered to be the way which is most effective for creating a good quality communication. This type of communication is used on a wide basis. The pheromone-based communication is generally implemented by various means that includes the chemical or physical ways. But despite of this the implementation were not capable of duplicating all the features of the pheromones that are present.

Convergence of the ACO:

There exists some version of the ACO where it is possible to prove that they are convergent in nature.in the year of 2000 the first evidence of convergence ant colony algorithm was provided which was followed by the graph-based ant system algorithm and the algorithms for the ACS and the NMAS. Estimations regarding the theoretical speed of convergence I difficult like most of the Metaheuristics. Zlochin and his colleagues in the year of 2004 were associated with showing the COA-type algorithm which can be assimilated with the techniques related to stochastic gradient descent present in the cross-entropy and also made the estimations regarding the distributed algorithms, the performance analysis of the continuous ant colony algorithm depending upon the various parameters is associated with suggesting the sensitivity of convergence on the parameter tuning (Putha, Quadrifoglio, & Zechman, 2012).

Selection of Edge:

Ant is generally considered to be a simple computational agent of the ant colony optimization algorithm. This is associated with constructing a solution in an iterative way for the problems. This type of intermediate solutions are generally considered to be the solution states. Whenever an iteration is taking place in the algorithm each ant from the x state to the y state which is correspondent with the other intermediate solutions (Lopez-Ibanez & Stutzle, 2012).

For this reason each of the ant or k computes a set or A^{}_{k}(x) of the feasible expansion to a current state present in each of the iteration and moves to one of the these. For the ant K the probability P^{k}_{xy} of moving from the x state to the y state is entirely dependent upon the combination of two of the values that is the attractiveness ?_{xy} of the move as they are computed by some of the heuristic indicating the “a prior” desirability of that particular move and the trail level or the T_{xy }of the move which indicated how proficient it was in the past so as make a particular move.

The trail level is associated with representing a later indication of the moves that are desiered. Updating of the trail is usually done whenever all the ants have completed their solutions, by increasing the trail levels or decreasing the trail levels in correspondence to their move which were part of the solution that were good or bad (Mahi, Baykan, & Kodaz, 2015).

## Applications of ACO

In general the movement of the kth ant from x state to y states is having the probability provided below:

Pheromone update:

The equation that is used for updating the trail is shown below and this can be determined once all the ants have completed their solution:In this the T_{xy} is considered to be the amount of pheromone which has been deposited for the state transmission xy, ? is the pheromone evaporation coefficient.

Application of ACO:

The ant colony optimization algorithm is used so as to apply many problems related to combinatorial optimization which ranges from the quadratic assignment to protein folding or routing vehicles (DeléVacq et al., 2013). Along with this there exists an advantage over the simulated annealing as well as the genetic algorithm approaches regarding similar problems whenever there is a dynamic change in the graph (Lin et al., 2012). It is possible to run the ACO continuously and is also having the capability of getting adopted to the real time environment. This is very important in the network routing and the transport systems as well (Tabakhi, Moradi, & Akhlaghian, 2014).

At the initial stage the ACO was applied in the domain of NP-hard combinatorial optimization problems. It is surprizing that the major section of the ACO research is still being conducted in this area. Besides this another major application which is included in the history of ACO is routing in telecommunication networks. One of the successful example of ACO algorithm in this domain includes the AntNet.

The ACO algorithm was firstly used with the name ant system which was mainly associated with solving the various problems that were faced by the travelling salesman (Cecilia et al., 2013). The main goal of using this system was to locate the path that is shortest for completed the round-trip which would initially result in linking of numerous cities. The over-all form of this algorithm is simple and besides this it is seen that they are dependent upon a set of ants where the individual ants are capable of making one round trip along the cities. By following some rules the ant are associated with moving from a particular city to another city and the rules includes the following:

- The ant must visit each city exactly once.
- There is less chance of choosing a distinct city
- The edge would be chosen depending upon the intensity of the pheromone trail laid out at the edges of two cities.
- After completion of the journey the ants are associated with depositing more phenomenon on all the edges it has gone across in case if the journey is to short.
- Once the iteration is completed the trail of the pheromones evaporates.

Problems faced by ACO

Scheduling problems faced by ACO

Some of the scheduling problems faced by the ACO have been listed below:

- Job-Shop scheduling problem
- Open-Shop scheduling problem

- Permutation flow shop problem (PFSP)
- Resource-constrained project scheduling problem (RCPSP)
- Single machine total weighted tardiness problem (SMTWTP) (Chen & Zhang, 2013)
- Single machine total tardiness problem (SMTTP)
- Multistage flowshop scheduling problem (MFSP) with sequence dependent setup/changeover times
- Group-shop scheduling problem (GSP)
- Single-machine total tardiness problem with sequence dependent setup times (SMTTPDST)

Vehicles routing problems:

Some of the vehicle routing problems faced by ACO are listed below:

- Period vehicle routing problem (PVRP)
- Multi-depot vehicle routing problem (MDVRP)
- Vehicle routing problem with time windows and multiple service workers (VRPTWMS)
- Vehicle routing problem with pick-up and delivery (VRPPD)Stochastic vehicle routing problem (SVRP)
- Capacitated vehicle routing problem (CVRP)
- Split delivery vehicle routing problem (SDVRP)
- Time dependent vehicle routing problem with time windows (TDVRPTW)
- Vehicle routing problem with time windows (VRPTW)

## Conclusion

Assignment problem

Some of the assignment problems faced by the ACO are listed below:

- Frequency assignment problem (FAP)
- Quadratic assignment problem (QAP)
- Redundancy allocation problem (RAP)
- Generalized assignment problem (GAP)

Set problem

Some of the set problems faced by ACO are listed below:

- Maximum independent set problem (MIS) Partition problem (SPP)
- Multiple knapsack problem (MKP)
- Set cover problem (SCP)
- Arc-weighted l-cardinality tree problem (AWlCTP)
- Weight constrained graph tree partition problem (WCGTPP)
- Optimization of the Antennas and synthesis:

The different form of antennas are optimized by making use of the ACO or the ant colony optimization. For example the antennas based upon the RFID tags makes use of the ACO.

Methods related to ACO:

**Genetic algorithms (GA):**This is associated with maintenance of a pool of solutions instead of just one solution. This process which involves finding of the superior solution is generally a mimic of the evolution with the solutions that are being combined or mutated one so as to alter the pool of solutions along with discarding the inferior quality solutions (Kabir, Shahjahan, & Murase, 2012).**An estimation of distribution algorithm (EDA):**this is generally considered to be an evolutionary algorithm that is associated with substituting the traditional reproduction operators by making use of the operators that are guided by the models. This type of models are learned from the population and this is generally done by employment of the machine learning techniques (Liu, Yi, & Ni, 2013). This usages initially results in representation of the probabilistic graphical models, which can be used so as to obtain new solutions from guided-crossover.**Simulated annealing (SA):**This is generally considered to be a related global optimization technique which is associated with traversing the space of search. This is generally done by generation of the neighbouring solutions. The behaviour which is superior is always excepted whereas the acceptability of the inferior neighbour is done probabilistically and is dependent on the difference existing in the quality and the temperature (Jovanovic & Tuba, 2013). Modification of the temperature parameter is done in order to obtain the progress of the algorithm needed which would be helping in altering the nature of the search.**Reactive search optimization:**This optimization technique is associated with focusing upon the combination of machine learning with the optimization. This is generally done by addition of an internal feedback loop. Addition is mainly done so as to obtain a free parameter of an algorithm by self-tuning (Mavrovouniotis & Yang, 2013).**Tabu search (TS):**This is the type of search that is considered to have similar characteristics like that of the simulated annealing. In this the traversing of the solution space is done by testing of the mutations that the individual solutions are having. Whereas the simulated annealing is associated with generating only a single mutated solution, and the tabu search is associated with generating numerous solutions of mutated nature. This initially tends towards the solution which is of lowest fitness amongst those solutions which has already been generated. For the purpose of preventing the cycling and for encouraging a greater movement through the solution space there is a need of maintaining a tabu list which consists of partial or a complete solutions (Ho et al., 2012). This is initially updated when the solution gets traversed through the solution space.**Artificial immune system (AIS):**This are the algorithms which are generally modelled upon the vertebrate immune systems.**Particle swarm optimization (PSO):**This is generally considered to be a swarm intelligence method.**Intelligent water drops (IWD):**This is a swarm-based optimization algorithm that is dependent upon the natural water drops which are flowing in the rivers.**Gravitational search algorithm (GSA):**This is also considered to be another swarm intelligence method (Marzband et al., 2016).**Ant colony clustering method (ACCM):**This is a method which is responsible for making use of clustering approach, which is associated with extending the ACO.**Stochastic diffusion search (SDS):**this is an agent-dependent probabilistic global search and optimization technique which is suitable for tackling the various difficulties, where it is seen that the objectives function are having the probability of getting decomposed and transform into a multiple independent partial-functions.

Conclusion:

Reliable Ant Colony Optimization along with the State Transition Ant Rule (ACOSTAR) is associated with offering a better solution so as to tackle the computational problem that are related to the aggregation of data in the wireless sensor network (WSN). Clustering which is dependent upon the ACO is based upon the density of the pheromone and the movements of the lively pheromone. The dependency act as one of the key movements of the sensed nodes.

By making use of the ACO with STAR helps in steady achievement of the global optimal solution which is generally done by the effective forwarding of data packets that are sensed in the WSN. Usage of the ACO-STAR, makes the delivery of the data much faster which initially helps in minimization of the delay measurements. The results that are generally obtained during the process of simulation is associated with showing the best quality characterization and this is done by better management of the computational problems which are complex in nature.

Usage of the novel special routing algorithms in order to forward the data from the source to the destination would be very beneficial. This novel approach is associated with tackling of the problems related to the structure of the topology, routing of the data and loss of tolerance, which is generally occurring due to the comprising of different optimization techniques.

Which is initially associated with reducing the cost of the message along with getting a better tolerance against the failure and loss. In addition to this the execution of these techniques necessarily needs rethinking about some of these technique. This needs to be done so as to expose more accuracy to the variations in the network. Besides this the various exterior aspects effects of the ACO-STAR and FACOC approaches includes mobility of the nodes, difficulties and many more issues.

References:

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Chen, W. N., & Zhang, J. (2013). Ant colony optimization for software project scheduling and staffing with an event-based scheduler. IEEE Transactions on Software Engineering, 39(1), 1-17.

DeléVacq, A., Delisle, P., Gravel, M., & Krajecki, M. (2013). Parallel ant colony optimization on graphics processing units. Journal of Parallel and Distributed Computing, 73(1), 52-61.

Ho, J. H., Shih, H. C., Liao, B. Y., & Chu, S. C. (2012). A ladder diffusion algorithm using ant colony optimization for wireless sensor networks. Information Sciences, 192, 204-212.

Jiang, L. L., Maskell, D. L., & Patra, J. C. (2013). A novel ant colony optimization-based maximum power point tracking for photovoltaic systems under partially shaded conditions. Energy and Buildings, 58, 227-236.

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Marzband, M., Yousefnejad, E., Sumper, A., & Domínguez-García, J. L. (2016). Real time experimental implementation of optimum energy management system in standalone microgrid by using multi-layer ant colony optimization. International Journal of Electrical Power & Energy Systems, 75, 265-274.

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