Search

l A non-convex fractional-order variational model is proposed to restore the image blurred by an unknown blur kernel. l Quaternion FTV with l p quasinorm constrained image and L 1 -norm constrained kernel are unified to a regularization framework. l The fractional-order total variation is extended to four-directional FTV including diagonal and back diagonal gradients. l An efficient algorithm based on the alternating direction method is proposed to address the non-convex optimization problem. This paper considers a variational model for single image blind restoration. By exploiting the fractional-order total variation (FTV) and L p quasinorm relaxation, a non-convex fractional-order variational model is proposed to restore the image blurred by an unknown blur kernel. A quaternion FTV model is first put forward to exploring more directional information of an image. The new model utilizes non-convex and non-smooth quaternion FTV with L p quasinorm to constrain the image and L 1 -norm to constrain the blur kernel, which are unified to a unified regularization framework. Further, an efficient algorithm is proposed to solve the non-convex problem via using the alternating direction minimization. The extensive experiments demonstrate the efficiency and viability of the proposed method and reveal superior performances in comparison with several existing methods. [ABSTRACT FROM AUTHOR]

• The different-level nonlinear system is first investigated. • The zeroing equivalency between different levels is proposed. • The new algorithm is proposed based on the equivalency and a discretization formula. • The problem is solved in a discrete-time manner with the future-instant solution predicted. • The problem of robotic system control with the end-effector orientation and fault tolerance considered simultaneously is solved. In this paper, we consider a special kind of time-dependent nonlinear system that includes different-level subsystems (i.e., a subsystem with respect to time-dependent solution and a subsystem with respect to its time derivative). To solve this kind of time-dependent nonlinear system, an equivalency between different-level subsystems is proposed and termed as zeroing equivalency based on the zeroing neural network method. This kind of time-dependent nonlinear system can be solved in a discrete-time manner with future-instant solution predicted at current instant based on the zeroing equivalency and a discretization formula. Prediction ability can perfectly meet the requirements of real-time computation, which is crucial in engineering fields. In addition, different-level algorithms are further employed to solve the problem of robotic system control considering additional restrictions. The position tracking control and end-effector orientation control are simultaneously achieved with even fault tolerance by utilizing the proposed algorithms. [ABSTRACT FROM AUTHOR]

This paper aims to bring in some notes and improvements for the paper (Kong et al., 2015). Firstly, we give some notes and suggestions on its assumption for numbers of dispensable parameter subsets in soft sets. This helps make the theories in Kong et al. (2015) much more logical clear and consistent. Then we propose a linear programming mathematical representation for normal parameter reduction problems of soft sets. This allows us to solve normal parameter reduction problems of soft sets with Lingo or MATLAB software. By the way, we point out that the answer of Example 6.1 in Kong et al. (2015) is not correct and figure out the right answer with our linear programming method. [ABSTRACT FROM AUTHOR]

This paper considers a group-shop scheduling problem (GSSP) with sequence-dependent set-up times (SDSTs) and transportation times. The GSSP provides a general formulation including the job-shop and the open-shop scheduling problems. The consideration of set-up and transportation times is among the most realistic assumptions made in the field of scheduling. In this paper, we study the GSSP with transportation and anticipatory SDSTs, where jobs are released at different times and there are several transporters to carry jobs. The objective is to find a job schedule that minimizes the makespan, that is, the time at which all jobs are completed and transported to the warehouse (or to the customer). The problem is formulated as a disjunctive programming problem and then prepared in a form of mixed integer linear programming (MILP). Due to the non-deterministic polynomial-time hardness (NP-hardness) of the GSSP, large instances cannot be optimally solved in a reasonable amount of time. Therefore, a genetic algorithm (GA) hybridized with an active schedule generator is proposed to tackle large-sized instances. Both Baldwinian and Lamarckian versions of the proposed hybrid algorithm are then implemented and evaluated through computational experiments. [ABSTRACT FROM AUTHOR]

This paper applies a new hybrid method by a combination of three population base algorithms such as Genetic Algorithm (GA), Particle Swarm Optimization (PSO) and Symbiotic Organisms Search (SOS). The proposed method has been inspired from natural selection process and it completes this process in GA by using the PSO and SOS. It tends to minimize the execution time and in addition to reduce the complexity. Symbiotic organisms search is a robust and powerful metaheuristic algorithm which has attracted increasing attention in recent decades. There are three alternative phases in the proposed algorithm: GA, which develops and selects best population for the next phases, PSO, which gets experiences for each appropriate solution and updates them as well and SOS, which benefits from previous phases and performs symbiotic interaction update phases in the real-world population. The proposed algorithm was tested on the set of best known unimodal and multimodal benchmark functions in various dimensions. It has further been evaluated in, the experiment on the clustering of benchmark datasets. The obtained results from basic and non-parametric statistical tests confirmed that this hybrid method dominates in terms of convergence, execution time, success rate. It optimizes the high dimensional and complex functions Rosenbrock and Griewank up to 10 − 330 accuracy in less than 3 s, out-performing other known algorithms. It had also applied clustering datasets with minimum intra-cluster distance and error rate. [ABSTRACT FROM AUTHOR]

Parameter reduction in soft set is a combinatorial problem. In the past, the problem of normal parameter reduction in soft set is usually be solved by deleting dispensable parameters, that is, by the trial and error method to search the dispensable parameters. This manual method usually need much time to reduce unnecessary parameters, and the method is more suitable for small data. For the large data, however, it is impossible for people to reduce parameters in soft set. In this paper, the particle swarm optimization is applied to reduce parameters in soft set. Firstly, a definition is introduced to define the dispensable core, and some cases about the dispensable core are discussed. Then the normal parameter reduction model is built and the particle swarm optimization algorithm is employed to reduce the parameters. Experiments have shown that the method is feasible and fast. [ABSTRACT FROM AUTHOR]

The problem of finding the un-deformed configuration of an elastic body, when the deformed configuration and the loads are known, occurs in many engineering applications. Standard solution methods for such problems include conservation laws based on Eshelby’s energy–momentum tensor and re-parameterization of the standard equilibrium equations. In this paper we present a different method for solving such problems, based on a re-parameterization of the nodal forces using the Total Lagrangian formulation. The obtained nonlinear system of equations describing equilibrium can be solved using either Newton–Raphson or an explicit dynamic relaxation algorithm. The solution method requires only minor modifications to similar algorithms designed for forward motion calculations. Several examples involving large deformations and different boundary conditions and loads are presented. [ABSTRACT FROM AUTHOR]

Recently, two new algorithms have been proposed to solve a fully fuzzy linear programming (FFLP) problem by Lotfi et al. [F.H. Lotfi, T. Allahviranloo, M.A. Jondabeha, L. Alizadeh, Solving a fully fuzzy linear programming using lexicography method and fuzzy approximate solution, Appl. Math. Model. 33 (2009) 3151–3156] and Kumar et al. [A. Kumar, J. Kaur, P. Singh, A new method for solving fully fuzzy linear programming problems, Appl. Math. Model. 33 (2011) 817–823]. In this paper, based on a new lexicographic ordering on triangular fuzzy numbers, a novel algorithm is proposed to solve the FFLP problem by converting it to its equivalent a multi-objective linear programming (MOLP) problem and then it is solved by the lexicographic method. By a theorem, it is shown that the lexicographic optimal solution of MOLP problem can be considered as an optimal solution of the FFLP problem. Then, a simple example and two real problems, as two case studies, will be used to illustrate our algorithm and compare it with the existing methods. [ABSTRACT FROM AUTHOR]

Second-order cone optimization (denoted by SOCO) is a class of convex optimization problems and it contains the linear optimization problem, convex quadratic optimization problem and quadratically constrained convex quadratic optimization problem as special cases. In this paper, we propose a new smoothing Newton method for solving the SOCO based on a non-symmetrically perturbed smoothing Fischer–Burmeister function. At each iteration, a system of linear equations is solved only approximately by using the inexact Newton method. It is shown that any accumulation point of the iteration sequence generated by the proposed algorithm is a solution of the SOCO. Furthermore, we prove that the generated sequence is bounded and hence it has at least one accumulation point. Under the assumption of nonsingularity, we establish the local quadratic convergence of the proposed algorithm without strict complementarity condition. Numerical experiments indicate that our method is effective. [ABSTRACT FROM AUTHOR]