Existence results and optimal control for a class of quasi mixed equilibrium problems involving the (f, g, h)-quasimonotonicity

In this paper, by introducing a new concept of the (f, g, h)-quasimonotonicity and applying the maximal monotonicity of bifunctions and KKM technique, we show the existence results of solutions for quasi mixed equilibrium problems when the constraint set is compact, bounded and unbounded, respectively, which extends and improves several well-known results in many respects. Next, we also obtain a result of optimal control to a minimization problem. Our main results can be applied to the problems of evolution equations, differential inclusions and hemivariational inequalities

Existence of solutions for implicit obstacle problems of fractional laplacian type involving set-valued operators

The paper is devoted to a new kind of implicit obstacle problem given by a fractional Laplacian-type operator and a set-valued term, which is described by a generalized gradient. An existence theorem for the considered implicit obstacle problem is established, using a surjectivity theorem for set-valued mappings, Kluge’s fixed point principle and nonsmooth analysis

A vision-based optical character recognition system for real-time identification of tractors in a port container terminal

Automation has been seen as a promising solution to increase the productivity of modern sea port container terminals. The potential of increase in throughput, work efficiency and reduction of labor cost have lured stick holders to strive for the introduction of automation in the overall terminal operation. A specific container handling process that is readily amenable to automation is the deployment and control of gantry cranes in the container yard of a container terminal where typical operations of truck identification, loading and unloading containers, and job management are primarily performed manually in a typical terminal. To facilitate the overall automation of the gantry crane operation, we devised an approach for the real-time identification of tractors through the recognition of the corresponding number plates that are located on top of the tractor cabin. With this crucial piece of information, remote or automated yard operations can then be performed. A machine vision-based system is introduced whereby these number plates are read and identified in real-time while the tractors are operating in the terminal. In this paper, we present the design and implementation of the system and highlight the major difficulties encountered including the recognition of character information printed on the number plates due to poor image integrity. Working solutions are proposed to address these problems which are incorporated in the overall identification system.postprin

Optimal Control and Approximate controllability of fractional semilinear differential inclusion involving ψ\psi- Hilfer fractional derivatives

The current paper initially studies the optimal control of linear $\psi$-Hilfer fractional derivatives with state-dependent control constraints and optimal control for a particular type of cost functional. Then, we investigate the approximate controllability of the abstract fractional semilinear differential inclusion involving $\psi$-Hilfer fractional derivative in reflexive Banach spaces. It is known that the existence, uniqueness, optimal control, and approximate controllability of fractional differential equations or inclusions have been demonstrated for a similar type of fractional differential equations or inclusions with different fractional order derivative operators. Hence it has to research fractional differential equations with more general fractional operators which incorporate all the specific fractional derivative operators. This motivates us to consider the $\psi$-Hilfer fractional differential inclusion. We assume the compactness of the corresponding semigroup and the approximate controllability of the associated linear control system and define the control with the help of duality mapping. We observe that convexity is essential in determining the controllability property of semilinear differential inclusion. In the case of Hilbert spaces, there is no issue of convexity as the duality map becomes simply the identity map. In contrast to Hilbert spaces, if we consider reflexive Banach spaces, there is an issue of convexity due to the nonlinear nature of duality mapping. The novelty of this paper is that we overcome this convexity issue and establish our main result. Finally, we test our outcomes through an example.Comment: 39 page

Job shop scheduling with artificial immune systems

The job shop scheduling is complex due to the dynamic environment. When the information of the jobs and machines are pre-defined and no unexpected events occur, the job shop is static. However, the real scheduling environment is always dynamic due to the constantly changing information and different uncertainties. This study discusses this complex job shop scheduling environment, and applies the AIS theory and switching strategy that changes the sequencing approach to the dispatching approach by taking into account the system status to solve this problem. AIS is a biological inspired computational paradigm that simulates the mechanisms of the biological immune system. Therefore, AIS presents appealing features of immune system that make AIS unique from other evolutionary intelligent algorithm, such as self-learning, long-lasting memory, cross reactive response, discrimination of self from non-self, fault tolerance, and strong adaptability to the environment. These features of AIS are successfully used in this study to solve the job shop scheduling problem. When the job shop environment is static, sequencing approach based on the clonal selection theory and immune network theory of AIS is applied. This approach achieves great performance, especially for small size problems in terms of computation time. The feature of long-lasting memory is demonstrated to be able to accelerate the convergence rate of the algorithm and reduce the computation time. When some unexpected events occasionally arrive at the job shop and disrupt the static environment, an extended deterministic dendritic cell algorithm (DCA) based on the DCA theory of AIS is proposed to arrange the rescheduling process to balance the efficiency and stability of the system. When the disturbances continuously occur, such as the continuous jobs arrival, the sequencing approach is changed to the dispatching approach that involves the priority dispatching rules (PDRs). The immune network theory of AIS is applied to propose an idiotypic network model of PDRs to arrange the application of various dispatching rules. The experiments show that the proposed network model presents strong adaptability to the dynamic job shop scheduling environment.postprin

Advances in Optimization and Nonlinear Analysis

The present book focuses on that part of calculus of variations, optimization, nonlinear analysis and related applications which combines tools and methods from partial differential equations with geometrical techniques. More precisely, this work is devoted to nonlinear problems coming from different areas, with particular reference to those introducing new techniques capable of solving a wide range of problems. The book is a valuable guide for researchers, engineers and students in the field of mathematics, operations research, optimal control science, artificial intelligence, management science and economics

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal