A Survey of League Championship Algorithm: Prospects and Challenges

The League Championship Algorithm (LCA) is sport-inspired optimization algorithm that was introduced by Ali Husseinzadeh Kashan in the year 2009. It has since drawn enormous interest among the researchers because of its potential efficiency in solving many optimization problems and real-world applications. The LCA has also shown great potentials in solving non-deterministic polynomial time (NP-complete) problems. This survey presents a brief synopsis of the LCA literatures in peer-reviewed journals, conferences and book chapters. These research articles are then categorized according to indexing in the major academic databases (Web of Science, Scopus, IEEE Xplore and the Google Scholar). The analysis was also done to explore the prospects and the challenges of the algorithm and its acceptability among researchers. This systematic categorization can be used as a basis for future studies.


Introduction
League Championship Algorithm (LCA) is a population based algorithmic framework for global optimization over a continuous search space first proposed by Kashan 1 .It is a Swarm optimization algorithm [2][3][4][5] .A general characteristic between all population based optimization algorithms similar to the LCA is that they both try to improve a population of achievable solutions to potential areas of the search space when seeking the optimization.LCA is a newly proposed stochastic population based algorithm for continuous global optimization which tries to imitate a championship situation where synthetic football clubs participate in an artificial league for a number of weeks.This algorithm has been tested in many areas and performed creditably well as compared to other known optimization schemes or heuristics algorithms 6 .
Optimization algorithms are dynamic research areas with rapidly increasing literatures.It is a common knowledge among researchers that combinatorial optimization problems like the travelling salesman problem are non-deterministic polynomial times (NP-hard) problems 7,8 , which implies that there are no fast solutions or exact solutions for such problems.Some of the most effective solutions to NP-hard problems are to utilize heuristic or metaheuristic algorithms.Heuristic algorithms are to look for solutions using trial and error, while the metaheuristic algorithm can be seen as a higher-level algorithm that use information and selection of the solutions to guide optimization problems with the intention of finding the optimality, even though such optimality is not mostly attainable.But many discrete and continues optimization problems are NP-complete, optimal solution techniques which we can execute as a polynomial time is also not attainable with a very high probability.Therefore, these types of problems are tackled by the construction of heuristics, metaheuristics or approximation algorithms which run in polynomial time and are often the best known method to find efficient solutions 9,10 .
In recent times, many inspirational optimization algo rithms have gained large popularity among researchers in solving artificial intelligence, machine learning, computational intelligence, engineering applications, distributed computing (parallel, grid and cloud) and data mining.These includes; nature-inspired optimization algorithms 11 , bio-inspired optimization algorithms 12 , evolutionary algorithms 13 , physics-inspired optimization algorithms 14 , ecologically-inspired optimization algorithms 15 and now sports-inspired optimization algorithms 6 .The LCA is a sport-inspired optimization algorithm which is also a type of swarm algorithm.It has been used in several researches in comparison with other established techniques to evaluate its efficiency and in most cases the results obtained are quite remarkable.
The aim of this paper is to survey all available research articles on the League Championship Algorithm (LCA) and its applications.We also wish to highlight some potential application areas that are yet to be exploited and some challenges.Therefore, the paper is organised as follows: Section 2 presents the LCA as it appears in previous literatures.Section 3 reviews in brief, a synopsis of the LCA researches.Section 4 investigates the acceptability of the LCA algorithm within the academic community.Section 5 presents the future prospects of using the LCA and its applications in other research areas.Section 6 describes some of the challenges faced by the users of the LCA algorithms and section 7 is the conclusion of the survey.

League Championship Algorithm in Literatures
Since the introduction of LCA in the year 2009, different researchers tried to apply it in different areas of research to solve specific problems.This section discussed the chronological history of this sport inspired algorithm as the researches continue to appear in major academic indexing and abstracting databases.

LCA in Major Academic Databases
Four major academic databases were used in this survey (in no particular order) to check the presence of the papers published with the LCA optimization technique.This gives us more inside on how the research community is utilizing this algorithm by its present in the major academic databases for indexing and abstracting.The research databases used for this survey are; the ISI (Thomson Reuters) also called the Web of Science, the Scopus, the IEEE Xplore and the Google Scholar.Table 1 shows a record of research articles that used the LCA in the selected databases as at 31 st January, 2015.It also shows that the LCA have a very high presence in the Google Scholar academic database as at the period under review as almost all the LCA research papers are indexed in it.The Scopus academic database powered by the Elsevier has the second largest indexed documents of the LCA research articles.It contains some articles as at the period under review (17, 20, 24, 6, 18, 19, 1) etc.The IEEE Xplore database contains three research documents that implemented the LCA optimization technique (17,  19, 1).The Web of Science which is the most important scientific database contains about five documents (6,  18) etc. as at the time under review 24 .The fact that the LCA only made it to the Web of Science after just about four years shows that the algorithm is not get the desired attention that it deserved.

A Synopsis of LCA
The research papers presented in this synopsis are gathered through searches from the above mentioned academic indexing databases.These same papers are also available through http://drkashan.ir.It is also important to mention that, this survey only considers publications written in English, as we are aware that there are some LCA publications written in other languages especially Arabic.
From Figure 1, Kashan 16 presented a paper that proposed and introduced a new evolutionary algorithm called League Championship Algorithm (LCA) for global optimization, which mimics the sport league championships.It is a new algorithm for numerical function optimization.Kashan and Karimi 17 tasted the effectiveness of the proposed optimization algorithm by measuring the test functions from a recognized yardstick, usually adopted to authenticate new constraint-handling algorithms strategy.The outcome derived from the proposed technique are very competitive with regards to other well-known techniques that already exist for constrained optimization and testify that the new algorithm can be regarded as an capable technique for optimization in the presence of constraints.
Kashan 18 modified and adapted LCA for constrained optimization in mechanical engineering design.The algorithm was used for a practicability criterion to favour the search toward feasible regions is included in addition the objective value condition.It then generates many children which increase the possibility of an entity to generate a better result.A multiplicity system is also adopted, which permits infeasible solutions with a potential objective value to come head of the feasible solutions.The effectiveness of LCA system was measured up against other similar algorithms on benchmark problems where the experimental outcome indicates that LCA is a very viable algorithm.The effectiveness of the LCA system was also measured on well-known mechanical design problems and outcomes are evaluated with the outcomes of 21 other constrained optimization algorithm techniques.The outcome of this comparison shows that with a smaller number of evaluations, LCA guarantees discovering the true optimum of these problems.
Kashan, Karimiyan 19 modifies the LCA system to solve numerical function optimization through the artificial modelling of the "Between Two Halves Analysis".The research worker tried to enhance the basic algorithm by modelling a between two halves like analysis beside the post-match SWOT (strengths/weaknesses/opportunities/ threats) analysis to produce new outcomes.The result obtains from the modified algorithm was tested and compared with that of basic version and also the Particle Swarm Optimization Algorithm (PSO) on finding the global minimum of a number of benchmark functions.The outcome shows that the improved algorithm called RLCA, perform well in terms of both final solution quality and convergence speed.
Pourali and Aminnayeri 20 develops a new evolutionary LCA to tackle a new single machine scheduling nonlinear problem in Just-In-Time (JIT) system with batch delivery cost and different due dates.Regardless of its complexity, finding a solution to a non-convex function which reduces earliness and tardiness costs concurrently appears to be computing.The research presented a double combinatorial auction derived from allocation system which was also derived from the properties of cloud computing resources and inspired by the elasticity and efficiency of microeconomic methods.The feedback assessment derived from reputation system with reduced coefficient of time and the chain of command of clients that was introduced was implemented to steer clear of malicious actions.To ensure informed scientific conclusions, the researchers came up with a price decision system derived from a back propagation neural network.In the price decision system, the different parameters are considered, so the requesting price can adapt to the varying supply-demand relation in the system.In view of the fact that the winner determination is an NP-complete problem, LCA was utilized to attain optimal allocation with the optimization objectives as market surplus and total reputation.The research was concluded by conducting empirical studies to show the practicability and efficiency of the anticipated mechanism.
Edraki 25 presents a new approach for engineering design optimization of centrifuge pumps based on LCA.Also Kahledan 7 applied the League Championship Algorithm to solve the Travelling Salesman Problem.The travelling salesman problem (TSP) tries to optimize a list of cities and the distances between each pair of cities, and then find the shortest feasible route that visits each city exactly once and returns to the origin city.It is also an NP-hard problem in combinatorial optimization, which is vital in operations research and theoretical computer science.The result of the LCA shows that its very effective compared to other known methods.
Kashan 6 comes up with an improved version of the LCA detailing the workings and functionalities of the different add-on modules of the algorithm.This latest paper also details more about the iterations, fitness value, generation of new solutions and stopping conditions.Lastly, an analysis was carried out to validate the foundation of the algorithm and the appropriateness of the updating equations collectively with investigating the consequence of diverse settings for the control parameters are carried out empirically on several of benchmark functions.The outcome of the analysis shows that the LCA shows potential performance suggesting that its further developments and practical applications would be worth investigating in the future research and applications.
Sebastian and Isabel 26 presents an implementation of the LCA in a Job Shop scheduling in an industrial   very helpful and practical in industry.In order to find a solution to this composite problem, the research presented a mathematical model and then designed a new discrete nonlinear LCA algorithm that was very proficient and helpful in combinatorial problems, in terms of computational time or solution quality.Kejani 21 came up with a new approach for reliability optimization based on LCA, while Lenin, Reddy 22 came up with another adapted LCA for solving optimal multiobjective reactive power dispatch problem.Then a modal analysis was used for fixed voltage stability estimation.The optimization of voltage stability margin is taken as the goals.The research shows that the LCA produce very good results.Stephen and PVGD 23 presented a simple LCA in an effort to make optimization process free from ambiguities.The new method provided a number of theoretical frameworks to utilize multiple optimization techniques simultaneously in a single optimization problem.This optimization process was been implemented to provide solution to image enhancement problem in a fingerprint, with some experimental results to authenticate the validity of this new process.
Sun, Wang 24 presents an auction and LCA-based resource allocation mechanism for distributed cloud situation.The Job Shop is a production system problem of "n" machines and "m" jobs to be distributed among the machines; each job is to follow particular production line and also need to use all machines.The optimum scheduling method need to be found in order to minimizing the production time and the make span.The modified algorithm was evaluated using instances of tests taken from the previously proposed methods in the literatures.The results shows the LCA produced more accurate values as compared with the previous methods.
From the synopsis of LCA literatures presented above, it shows that the algorithm has the flexibility, capability and efficiency of being adapted or adopted to solve different types of problems in different non-deterministic polynomial time (NP-hard or NP-complete) situations.As all the previous researches also applied the scheme to solve the NP-complete problems 32 .The most distinguished attribute of NP-complete problems is that no quick answer to them is known and also no exact solution is known.NP-complete problems are often addressed by using heuristic methods, evolutionary algorithms, and approximation algorithms  .

Acceptability of LCA
In this section, we investigated how acceptable the LCA algorithm was over the years within the research community.By making simple search in some of the major academic databases revealed that the number of research documents (both research articles and documents citing LCA articles) that cited the terms "League Championship Algorithm" and "Champions League Algorithm" are increasing yearly.Below we presented the outcome of such investigation in the Google Scholar, Scopus, IEEE Xplore and also in the Web of Science.The Google Scholar is a very robust open access academic database.It keeps record of many scientific publications ranging from research articles, books, journals and conferences.These records are normally obtained from different sources.It is also a very reliable search engine that keeps records of citations, h-index and i10-index.
The Scopus academic database is one of the most reliable scientific research databases.But, unlike the Google Scholar it is not an open access, as researchers needs to subscribe to get access to the facilities.It is a very versatile indexing facility with the capabilities of graphical analysis of articles and cited documents.The IEEE Xplore is also an academic database that hosts millions of academic researches worldwide.It is known for archiving most science and technology journals, conferences and transactions.
Web of Science is also called the ISI or the web of knowledge.It is an online subscription-based scientific citation indexing service controlled by Thomson Reuters that presents a detailed citation search and impact factor of academic journals.It gives access to multiple databases that reference cross-disciplinary research, which allows for in-depth exploration of specialized sub-fields within an academic or scientific discipline.
If you consider that the year 2015 is just one month old as at the time of this research.Figure 2 shows that the number of documents that contains the terms "League Championship Algorithm" or "Champions League Algorithm" in the Google Scholar database is increasing yearly.This implies that, the prospect of the LCA algorithm amongst the research community is high and the algorithm is also gaining more acceptances.This means that the LCA is an effective scheme for solving NP-complete problems.The LCA also got a very important citation through the Google Scholar from the yearly soft computing Clever Algorithm book called Innovative Computational Intelligence 36 .This shows that, the LCA was well received within the research community.
Figure 2 also shows that similarly the number of documents that contains the terms "League Championship Algorithm" or "Champions League Algorithm" in the Scopus database is also increasing yearly.This implies that, the prospect of the LCA algorithm amongst the research community is high and the algorithm is also gaining more acceptances.This means that, the LCA is an effective scheme for solving NP-complete problems.Similar to the investigation in the Google Scholar, the result shows that the algorithm was fairly utilized in many areas of scientific research.
The graph above also shows that both IEEE Xplore and the Web of Science recorded both citations and archived documents containing the terms "League Championship Algorithm" or "Champions League Algorithm".Even though the number of documents in these databases is not much, but it shows great promises of growing over time.This implies that, the algorithm under review is well accepted by the academic communities.

The Prospects of LCA Optimization
The league championship algorithm is still an evolving soft computing algorithm that is gradually gaining relevance every passing day within the research community.The prospect of using the LCA in other application areas is very high.The performance of the scheme in previous literatures implies that the algorithm can also be widely applied in other similar research areas, especially for solving NP-hard problems.Table 2 presented some applications that are yet to be explored with some associated research problems.
From Table 2, it shows that the LCA as an affective algorithm used in previous researches to tackle NP-complete problems can as well effective in a wide range of research domains.This includes but not limited to; data mining, big data, mobile computing, sensor networks, engineering design, distributed systems, graph colouring, machine learning, timetable, subset problem, etc.The research issue in the different domains also differs greatly, ranges from resource allocation, search techniques, energy conservation, routing issues, assignment problem to mention but a few.

The Challenges of LCA Optimization
Even though the league championship optimization algorithm has made great progresses in recent years, there are some essential and attractive challenges that needs to be probing further.Some of these problems are listed below.

Generalization
Generalization is a very important feature of any optimization algorithm and this also includes the LCA.
Evaluating the LCA's generalization can be a complex task because of the diverse implementations.The complexity is correlated to that of evaluating the generalization ability of LCA system in general.It is not unusual to come Table 2. Future Application Areas across researches that only relay a algorithm developed at a certain number of generations.But it is not normally clear, if such an algorithm is the outcome of a single run or the mean of many runs.More so, in some cases it is not very clear how to choose when to discontinue getting a good system.It is also uncertain how fit the LCA might generalize to diverse situations in these cases 83 .Most of the related LCA literatures show that some enhancements need to be done to suite a particular situation.Different problems have different conditions and parameters, and therefore may need different approach to solve.This problem of generalization is not particular to the LCA as most optimization and heuristic algorithms also suffered from this issue.In essence, more comprehensive studies of generalization and standardization in LCA will greatly improve it applicability in other areas.

Robustness
Robustness is an important feature for the reliability of any optimization scheme.In case of failures in an optimization scheme, the failure detection algorithm should instantaneously identify the error and starts a reprogramming that correct the process.In the LCA, such a scheme is not clearly spelt out, and therefore failure and reliability that can leads to robustness is an open issue till now.However, the robustness of LCA scheme may be accomplished through many methods of failure identification and restore, and the robustness of LCA quality should be further scrutinized in future researches.

Hybridization
Hybridization is acknowledged these days to be an important part of optimization algorithms.Most of the established heuristics and optimization schemes especially in computation intelligence (CI) include components and ideas derived from other optimization schemes.Even though, the LCA also derived some of its features from other swam algorithms, hybridization with other optimization algorithms (both heuristics and CI) need to be explore the more to increase its versatility and utility.However, these hybridizations most at times reach their limits when either large-scale problem instances with massive search spaces or highly constrained problems for which it is complex to get feasible solutions are considered 84 .Therefore, researchers are encouraged to investigate the integration of more classical CI, heuristics and operation research (OR) techniques into the LCA scheme.But, one reason why the LCA algorithm is especially suited for hybridization is its constructive nature.

Conclusion
In this survey paper, we gave a briefed description of the origins of the LCA algorithm.Then, we outlined the synopsis of some of the existing theoretical and experimental results in LCA literature.We provided a survey on a very interesting recent research direction as the prospects of future LCAs.The acceptability of this sportinspired technique was investigated using some of the major academic databases.The paper also pointed out some of the challenges of the algorithm which includes; generalization, robustness and the hybridization of LCA algorithms with more classical CI, heuristics and operations research schemes.In conclusion, haven studied the LCA and most researches that have in one way or the other used the algorithm to solve problems in similar application areas, and based on the chronological literatures detailed in this paper, it shows that the LCA is a global optimization algorithm that performed superbly and efficiently in solving many NP-hard problems and this research direction offers many possibilities for valuable future research.

Table 1 .
LCA in Major Academic Indexed Databases