The artificial bee colony algorithm is a relatively new optimization technique. This paper presents an improved artificial bee colony (IABC) algorithm for global optimization. Inspired by ...differential evolution (DE) and introducing a parameter
M, we propose two improved solution search equations, namely “
ABC/best/1” and “
ABC/rand/1”. Then, in order to take advantage of them and avoid the shortages of them, we use a selective probability
p to control the frequency of introducing “
ABC/rand/1” and “
ABC/best/1” and get a new search mechanism. In addition, to enhance the global convergence speed, when producing the initial population, both the chaotic systems and the opposition-based learning method are employed. Experiments are conducted on a suite of unimodal/multimodal benchmark functions. The results demonstrate the good performance of the IABC algorithm in solving complex numerical optimization problems when compared with thirteen recent algorithms.
► “
ABC/best/1” and “
ABC/rand/1” are proposed. ► A new search mechanism is got by introducing a selective probability
p. ► Both opposition-based learning method and chaotic maps are employed. ► The experiment results demonstrate the good performance of the IABC algorithm.
The artificial bee colony (ABC) algorithm is a relatively new optimization technique which has been shown to be competitive to other population-based algorithms. However, there is still an ...insufficiency in the ABC algorithm regarding its solution search equation, which is good at exploration but poor at exploitation. Inspired by differential evolution (DE), we propose a modified ABC algorithm (denoted as ABC/best), which is based on that each bee searches only around the best solution of the previous iteration in order to improve the exploitation. In addition, to enhance the global convergence, when producing the initial population and scout bees, both chaotic systems and opposition-based learning method are employed. Experiments are conducted on a set of 26 benchmark functions. The results demonstrate good performance of ABC/best in solving complex numerical optimization problems when compared with two ABC based algorithms.
•Present a novel mechanism combining network reciprocity and indirect reciprocity.•The effects of initial reputation distribution and parameters are analyzed.•An interesting strategy updating rule ...based on reputation and payoff are introduced.•We find that large scale of reputation accumulation promotes cooperation.•Our conclusions universe for various network topologies.
Indirect reciprocity is a fascinating topic in the field of social cooperation. In this paper, we propose a novel updating strategy based on the critical reputation-aware calculation. The joint of reputation allows players to make decisions not only on current payoffs but also from a third party, which improves the status of cooperators in the prisoner's dilemma game and provides a possibility for surviving. Experiments show that the discrepancies in initial fitness caused by reputation will support cooperators in occupying a high proportion in communities. Interestingly, we find that the massive scale of reputation fluctuation helps to enhance the cooperative effect, and newly name this character as “quasi-time lag”. The simulations show that the promotion of our proposed mechanism is effective and robust on different network topologies. This work provides a new perspective for the study of the cooperative game.
This paper presents an extragradient-like method for solving a pseudomonotone equilibrium problem with a Lipschitz-type condition on Hadamard manifolds. The algorithm only needs to know the existence ...of the Lipschitz-type constants of the bifunction, and the stepsize of each iteration is determined by the adjacent iterations. Convergence of the algorithm is analyzed, and its application to variational inequalities is also provided. Finally, several experiments are made to verify the effectiveness of the algorithms.
Symbiotic organisms search (SOS) algorithm is a current popular stochastic optimization algorithm. It has been widely used to handle all kinds of optimization problems, whereas SOS has some ...disadvantages, such as over-exploration phenomenon and unbalance between exploration and exploitation. To improve the search capability of SOS, in this study, a novel improved SOS (GMSOS) with good point set and memory mechanism is presented. For enhancing the population diversity and the optimization ability of SOS algorithm, good point set instead of uniform distribution is utilized to produce the initial population, and memory mechanism is employed in three stages of SOS algorithm. In the mutualism stage and commensalism stage, history best organism in memory takes the place of the current best organism. In the parasitism stage, the new parasite vector based on history best organism is produced. These strategies help to effectively provide a better trade-off between exploration and exploitation in the search scope, and avoiding falling into local optima synchronously. The performance of the presented SOS is evaluated on 35 typical benchmark functions and 3 engineering design problems. The experimental results attest that the proposed algorithm is competitive as compared to other algorithms considered.
The Peaceman–Rachford splitting method (PRSM) is a preferred method for solving the two-block separable convex minimization problems with linear constraints at present. In this paper, we propose an ...inertial generalized proximal PRSM (abbreviated as IGPRSM) to improve computing efficiency, which unify the ideas of inertial proximal point and linearization technique. Both subproblems are linearized by positive semi-definite proximal matrices, and we explain why the matrix cannot be indefinite. The global convergence and the worst-case asymptotic iteration complexity are derived theoretically via the variational inequality framework. Numerical experiments on LASSO, total variation (TV) based denoising models and image decomposition problems are presented to show the effectiveness of the introduced method even compared with the state-of-the-art methods.
In this paper, we initially employ the disconjugacy theory to establish some sufficient conditions for the disconjugacy of
y
′
′
′
+
β
y
′
′
+
α
y
′
=
0
. We then utilize Elias’s spectrum theory to ...demonstrate the spectrum structure of the linear operator
y
′
′
′
+
β
y
′
′
+
α
y
′
coupled with the boundary conditions
y
(
0
)
=
y
(
1
)
=
y
′
(
1
)
=
0
. Ultimately, by utilizing the acquired results, we ascertain the existence of positive solutions for the corresponding nonlinear third-order problem with an indefinite weight, based on the principles of bifurcation theory and the Leray–Schauder fixed point theorem.
The symbiotic organisms search (SOS) algorithm is a current effective meta-heuristic algorithm, which is been applied to solve various types of optimization problems. However, the SOS can easily lead ...to overexploration in the parasitism phase, and it is difficult to balance between exploration and exploitation capabilities. In the present work, two extended versions of the SOS are proposed. Two different weight strategies (i.e., random-weight and adaptive-weight) are utilized to generate the weighted mutual vector, respectively. Meanwhile, the best organism is employed to produce the modified artificial parasite vector. The performance of the two improved algorithms is evaluated on 35 test functions. The results demonstrate that the proposed algorithms are able to provide very promising results. Furthermore, five real-world problems are solved by the two newly proposed methods. Experimental results demonstrate that the presented algorithms are more efficient than the compared algorithms. All the obtained results further indicate that the two proposed algorithms are competitive and provide better results when compared to a wide range of algorithms, including SOS and its five modified versions, as well as ten other meta-heuristic algorithms.
This paper studies rough sets from the operator-oriented view by matroidal approaches. We firstly investigate some kinds of closure operators and conclude that the Pawlak upper approximation operator ...is just a topological and matroidal closure operator. Then we characterize the Pawlak upper approximation operator in terms of the closure operator in Pawlak matroids, which are first defined in this paper, and are generalized to fundamental matroids when partitions are generalized to coverings. A new covering-based rough set model is then proposed based on fundamental matroids and properties of this model are studied. Lastly, we refer to the abstract approximation space, whose original definition is modified to get a one-to-one correspondence between closure systems (operators) and concrete models of abstract approximation spaces. We finally examine the relations of four kinds of abstract approximation spaces, which correspond exactly to the relations of closure systems.
In this paper, we propose a smoothing Levenberg-Marquardt method for the symmetric cone complementarity problem. Based on a smoothing function, we turn this problem into a system of nonlinear ...equations and then solve the equations by the method proposed. Under the condition of Lipschitz continuity of the Jacobian matrix and local error bound, the new method is proved to be globally convergent and locally superlinearly/quadratically convergent. Numerical experiments are also employed to show that the method is stable and efficient.
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