A Survey of League Championship Algorithm: Prospects and Challenges <s> A Synopsis of LCA <s> We show that the problem of finding an optimal schedule for a set of jobs is NP-complete even in the following two restricted cases.o(1)All jobs require one time unit. (2)All jobs require one or two time units, and there are only two processor resolving (in the negative a conjecture of R. L. Graham, Proc. SJCC, 1972, pp. 205-218). As a consequence, the general preemptive scheduling problem is also NP-complete. These results are tantamount to showing that the scheduling problems mentioned are intractable. <s> BIB001 </s> A Survey of League Championship Algorithm: Prospects and Challenges <s> A Synopsis of LCA <s> Inspired by the competition of sport teams in a sport league, an algorithm is presented for optimizing nonlinear continuous functions. A number of individuals as sport teams compete in an artificial league for several weeks (iterations). Based on the league schedule in each week, teams play in pairs and the outcome is determined in terms of win or loss, given known the team’s playing strength (fitness value) resultant from a particular team formation (solution). In the recovery period, each team devises the required changes in the formation/playing style (a new solution) for the next week contest and the championship goes on for a number of seasons (stopping condition). Performance of the proposed algorithm is tested in comparison with that of particle swarm optimization algorithm (PSO) on finding the global minimum of a number of benchmarked functions. Results testify that the new algorithm performs well on all test problems, exceeding or matching the best performance obtained by PSO. This suggests that further developments and practical applications of the proposed algorithm would be worth investigating in the future. <s> BIB002 </s> A Survey of League Championship Algorithm: Prospects and Challenges <s> A Synopsis of LCA <s> The league championship algorithm (LCA) is a new algorithm originally proposed for unconstrained optimization which tries to metaphorically model a League championship environment wherein artificial teams play in an artificial league for several weeks (iterations). Given the league schedule, a number of individuals, as sport teams, play in pairs and their game outcome is determined given known the playing strength (fitness value) along with the team formation (solution). Modelling an artificial match analysis, each team devises the required changes in its formation (a new solution) for the next week contest and the championship goes for a number of seasons. In this paper, we adapt LCA for constrained optimization. In particular: (1) a feasibility criterion to bias the search toward feasible regions is included besides the objective value criterion; (2) generation of multiple offspring is allowed to increase the probability of an individual to generate a better solution; (3) a diversity mechanism is adopted, which allows infeasible solutions with a promising objective value precede the feasible solutions. Performance of LCA is compared with comparator algorithms on benchmark problems where the experimental results indicate that LCA is a very competitive algorithm. Performance of LCA is also evaluated on well-studied mechanical design problems and results are compared with the results of 21 constrained optimization algorithms. Computational results signify that with a smaller number of evaluations, LCA ensures finding the true optimum of these problems. These results encourage that further developments and applications of LCA would be worth investigating in the future studies. <s> BIB003 </s> A Survey of League Championship Algorithm: Prospects and Challenges <s> A Synopsis of LCA <s> is a lot of discussion in the literature on the advantages of one soft computing technique over the other. Number of new meta heuristic algorithms are made available for solving different optimization problems. But always there is some ambiguity in deciding which technique is better than the other to solve a specific optimization problem in a particular context. A new methodology has been proposed in this paper which provides some theoretical frame work to use multiple optimization techniques at the same time onto a single optimization problem. This new approach has been implemented to solve image enhancement problem in a fingerprint. First the methodology of this new approach has been described then the application of the proposed methodology is presented with some experimental results. <s> BIB004 </s> A Survey of League Championship Algorithm: Prospects and Challenges <s> A Synopsis of LCA <s> League Championship Algorithm (LCA) is a recently proposed stochastic population based algorithm for continuous global optimization which tries to mimic a championship environment wherein artificial teams play in an artificial league for several weeks (iterations). Given the league schedule in each week, a number of individuals as sport teams play in pairs and their game outcome is determined in terms of win or loss (or tie), given the playing strength (fitness value) along with the intended team formation/arrangement (solution) developed by each team. Modeling an artificial match analysis, each team devises the required changes in its formation (generation of a new solution) for the next week contest and the championship goes on for a number of seasons (stopping condition). An add-on module based on modeling the end season transfer of players is also developed to possibly speed up the global convergence of the algorithm. Extensive analysis to verify the rationale of the algorithm and suitability of the updating equations together with investigating the effect of different settings for the control parameters are carried out empirically on a large number of benchmark functions. Results indicate that LCA exhibits promising performance suggesting that its further developments and practical applications would be worth investigating in the future studies. <s> BIB005
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 BIB002 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 BIB003 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  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 BIB005 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  came up with a new approach for reliability optimization based on LCA, while Lenin, Reddy  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 BIB004 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  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 BIB001 . 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 .