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Conjugate gradient (CG) method is used to find the optimum solution for the large scale unconstrained optimization problems. Based on its simple algorithm, low memory requirement, and the speed of obtaining the solution, this method is widely used in many fields, such as engineering, computer science, and medical science. In this paper, we modified CG method to achieve the global convergence with various line searches. In addition, it passes the sufficient descent condition without any line search. The numerical computations under weak Wolfe-Powell line search shows that the efficiency of the new method is superior to other conventional methods. [ABSTRACT FROM AUTHOR]

Population initialization is a crucial task in population-based optimization methods, which can affect the convergence speed and also the quality of the final solutions. Generally, if no a priori information about the solutions is available, the initial population is often selected randomly using random numbers. This paper presents a new initialization method by applying the concept of adaptive randomness (AR) to distribute the individuals as spaced out as possible over the search space. To verify the performance of AR, a comprehensive set of 34 benchmark functions with a wide range of dimensions is utilized. Conducted experiments demonstrate that AR-based population initialization performs better than other population initialization methods such as random population initialization, opposition-based population initialization, and generalized opposition-based population initialization in the convergence speed and the quality of the final solutions. Further, the influences of the problem dimensionality, the new control parameter, and the number of trial individuals are also investigated. [ABSTRACT FROM AUTHOR]

The differential evolution algorithm (DE) is one of the most powerful stochastic real-parameter optimization algorithms. The theoretical studies on DE have gradually attracted the attention of more and more researchers. However, few theoretical researches have been done to deal with the convergence conditions for DE. In this paper, a sufficient condition and a corollary for the convergence of DE to the global optima are derived by using the infinite product. A DE algorithm framework satisfying the convergence conditions is then established. It is also proved that the two common mutation operators satisfy the algorithm framework. Numerical experiments are conducted on two parts. One aims to visualize the process that five convergent DE based on the classical DE algorithms escape from a local optimal set on two low dimensional functions. The other tests the performance of a modified DE algorithm inspired of the convergent algorithm framework on the benchmarks of the CEC2005. [ABSTRACT FROM AUTHOR]

To improve the performance of the krill herd (KH) algorithm, in this paper, a L'evy-flight krill herd (LKH) algorithm is proposed for solving optimization tasks within limited computing time. The improvement includes the addition of a new local L'evy-flight (LLF) operator during the process when updating krill in order to improve its efficiency and reliability coping with global numerical optimization problems. The LLF operator encourages the exploitation and makes the krill individuals search the space carefully at the end of the search. The elitism scheme is also applied to keep the best krill during the process when updating the krill. Fourteen standard benchmark functions are used to verify the effects of these improvements and it is illustrated that, in most cases, the performance of this novel metaheuristic LKH method is superior to, or at least highly competitive with, the standard KH and other population-based optimizationmethods. Especially, this newmethod can accelerate the global convergence speed to the true global optimum while preserving the main feature of the basic KH. [ABSTRACT FROM AUTHOR]

Artificial bee colony (ABC) is a new population-based stochastic algorithm which has shown good search abilities on many optimization problems. However, the original ABC shows slow convergence speed during the search process. In order to enhance the performance of ABC, this paper proposes a new artificial bee colony (NABC) algorithm, which modifies the search pattern of both employed and on looker bees. A solution pool is constructed by storing some best solutions of the current swarm. New candidate solutions are generated by searching the neighborhood of solutions randomly chosen from the solution pool. Experiments are conducted on a set of twelve benchmark functions. Simulation results show that our approach is significantly better or at least comparable to the original ABC and seven other stochastic algorithms. [ABSTRACT FROM AUTHOR]