On a perturbed analogue of the minimization method with the order of convergence 1+√2

The use of the perturbation operator to construct new modifications of Newton's method for solving minimization problems, in particular the Ulm method of split differences, Steffensen's method, is considered. and as a result of its work we obtain a sequence of points that converge to the solution point.

An Analysis of a KNN Perturbation Operator: An Application to the Binarization of Continuous Metaheuristics

The optimization methods and, in particular, metaheuristics must be constantly improved to reduce execution times, improve the results, and thus be able to address broader instances. In particular, addressing combinatorial optimization problems is critical in the areas of operational research and engineering. In this work, a perturbation operator is proposed which uses the k-nearest neighbors technique, and this is studied with the aim of improving the diversification and intensification properties of metaheuristic algorithms in their binary version. Random operators are designed to study the contribution of the perturbation operator. To verify the proposal, large instances of the well-known set covering problem are studied. Box plots, convergence charts, and the Wilcoxon statistical test are used to determine the operator contribution. Furthermore, a comparison is made using metaheuristic techniques that use general binarization mechanisms such as transfer functions or db-scan as binarization methods. The results obtained indicate that the KNN perturbation operator improves significantly the results.

Materialized View Selection Using Self-Adaptive Perturbation Operator-Based Particle Swarm Optimization

A data warehouse is a central repository of time-variant and non-volatile data integrated from disparate data sources with the purpose of transforming data to information to support data analysis. Decision support applications access data warehouses to derive information using online analytical processing. The response time of analytical queries against speedily growing size of the data warehouse is substantially large. View materialization is an effective approach to decrease the response time for analytical queries and expedite the decision-making process in relational implementations of data warehouses. Selecting a suitable subset of views that deceases the response time of analytical queries and also fit within available storage space for materialization is a crucial research concern in the context of a data warehouse design. This problem, referred to as view selection, is shown to be NP-Hard. Swarm intelligence have been widely and successfully used to solve such problems. In this paper, a discrete variant of particle swarm optimization algorithm, i.e. self-adaptive perturbation operator based particle swarm optimization (SPOPSO), has been adapted to solve the view selection problem. Accordingly, SPOPSO-based view selection algorithm (SPOPSOVSA) is proposed. SPOPSOVSA selects the Top-K views in a multidimensional lattice framework. Further, the proposed algorithm is shown to perform better than the view selection algorithm HRUA.

An Enhanced Two-Level Metaheuristic Algorithm with Adaptive Hybrid Neighborhood Structures for the Job-Shop Scheduling Problem

For solving the job-shop scheduling problem (JSP), this paper proposes a novel two-level metaheuristic algorithm, where its upper-level algorithm controls the input parameters of its lower-level algorithm. The lower-level algorithm is a local search algorithm searching for an optimal JSP solution within a hybrid neighborhood structure. To generate each neighbor solution, the lower-level algorithm randomly uses one of two neighbor operators by a given probability. The upper-level algorithm is a population-based search algorithm developed for controlling the five input parameters of the lower-level algorithm, i.e., a perturbation operator, a scheduling direction, an ordered pair of two neighbor operators, a probability of selecting a neighbor operator, and a start solution-representing permutation. Many operators are proposed in this paper as options for the perturbation and neighbor operators. Under the control of the upper-level algorithm, the lower-level algorithm can be evolved in its input-parameter values and neighborhood structure. Moreover, with the perturbation operator and the start solution-representing permutation controlled, the two-level metaheuristic algorithm performs like a multistart iterated local search algorithm. The experiment’s results indicated that the two-level metaheuristic algorithm outperformed its previous variant and the two other high-performing algorithms in terms of solution quality.

Effective Algorithms for Scheduling Workflow Tasks on Mobile Clouds

In mobile cloud computing, the computing resources of mobile devices can be integrated to execute complicated applications, in order to tackle the problem of insufficient resources of mobile devices. Such applications are, in general, characterized as workflows. Scheduling workflow tasks on a mobile cloud system consisting of heterogeneous mobile devices is a NP-hard problem. In this paper, intelligent algorithms, e.g., particle swarm optimization (PSO) and simulated annealing (SA), are widely used to solve this problem. However, both PSO and SA suffer from the limitation of easily being trapped into local optima. Since these methods rely on their evolutionary mechanisms to explore new solutions in solution space, the search procedure converges once getting stuck in local optima. To address this limitation, in this paper, we propose two effective metaheuristic algorithms that incorporate the iterated local search (ILS) strategy into PSO and SA algorithms, respectively. In case that the intelligent algorithm converges to a local optimum, the proposed algorithms use a perturbation operator to explore new solutions and use the newly explored solutions to start a new round of evolution in the solution space. This procedure is iterated until no better solutions can be explored. Experimental results show that by incorporating the ILS strategy, our proposed algorithms outperform PSO and SA in reducing workflow makespans. In addition, the perturbation operator is beneficial for improving the effectiveness of scheduling algorithms in exploring high-quality scheduling solutions.

Logistics Distribution Route Optimization Based on Chaotic Cuckoo Algorithm

In order to efficiently solve the routing optimization problem of logistics distribution vehicle, a new chaotic cuckoo optimization algorithm have been put forward, first, the algorithm is used for seeking optimization, chaotic perturbation operator is added in the parasitic nest position in the iteration, thereby the population diversity is expanded and the algorithm accuracy is improved. The simulation experiment is carried out for this algorithm; the result shows that the algorithm is to seek the optimal solution, the average solution, and find the optimal solution frequency and time, which all has obvious effects.

Approximating solutions of generalized pseudocontractive variational inequalities by admissible perturbation type iterative methods

In this paper we give the solvability class of generalized strongly nonlinear variational inequalities modified by the use of the new concept of admissible perturbation operator on nonempty closed convex sets in Hilbert spaces.

Generalized Solution of the Photon Transport Problem

The purpose of this paper is to show the existence of a generalized solution of the photon transport problem. By means of the theory of equicontinuous C0-semigroup on a sequentially complete locally convex topological vector space we show that the perturbed abstract Cauchy problem has a unique solution when the perturbation operator and the forcing term function satisfy certain conditions. A consequence of the abstract result is that it can be directly applied to obtain a generalized solution of the photon transport problem.