This article addresses the implementation of the new generalized (G'∕G)-expansion method to the Caudrey–Dodd–Gibbon (CDG) equation and the Lax equation which are associated with the fifth-order KdV (fKdV) equation. The method works well to derive a variety of standard and functional closed-form wave solutions with distinct physical structures, such as, soliton, kink, periodic soliton, and bell-shaped soliton solutions. The solutions obtained using this method are useful and adequate than other methods. In order to understand the physical aspects and importance of the method, the attained solutions have been simulated graphically. The extracted results definitely establish that the new generalized(G'∕G)-expansion method is an effective mathematical tool to work out new solutions to different types of local nonlinear evolution equations emerging in applied science and engineering, but this method is not effective in solving nonlocal equations.
In this article, we form the exact wave solutions of the Jimbo-Miwa equation and the Calogero-Bogoyavlenskii-Schiff equation by applying the new generalized (G'/G)-expansion method. We explained the new generalized (G'/G)-expansion method to look for more general traveling wave solutions of the above mentioned equations. The traveling wave solutions attained by this method are in terms of hyperbolic, trigonometric and rational functions. The graphical representation of the obtained solutions is kink soliton, singular kink soliton, singular soliton and singular periodic solution. This method is very significant for extracting exact solutions of NLEEs which habitually occur in mathematical physics, engineering sciences and applied mathematics.
In this article, we establish the exact wave solutions of the Boussinesq equation and the (2 + 1)-dimensional extended shallow water wave equation by applying the new generalized (G'/G)-expansion method. When the condition of the fluid is such that the horizontal length scale is much greater than the vertical length scale, the shallow water equations are mostly suitable. In Ocean engineering, Boussinesq-type equations are commonly used in computer simulations for the model of water waves in shallow seas and harbors. We explained the new generalized (G'/G)-expansion method to seek further general traveling wave solutions of the above mentioned equations. The traveling wave solutions attained by this method are exposed in terms of hyperbolic, trigonometric and rational functions. The shape of the obtained solutions are bell shaped soliton, kink soliton, singular kink soliton, singular soliton, singular periodic solution and compaction. This method is very influential mathematical tool for extracting exact solutions of NLEEs which frequently arise in mathematical physics, engineering sciences and many scientific real world application fields.
The transportation problem is widely applied in the real world. This problem aims to minimize the total shipment cost from a number of sources to a number of destinations. This paper presents a new method named Dhouib-Matrix-TP1, which generates an initial basic feasible solution based on the standard deviation metric with a very reduced number of simple iterations. A comparative study is carried out in order to verify the performance of the proposed Dhouib-Matrix-TP1 heuristic.
In this article, we study an Inventory Routing Problem with deterministic customer demand in a two-tier supply chain. The supply chain network consists of a supplier using a single vehicle with a given capacity to deliver a single product type to multiple customers. We are interested in population-based algorithms to solve our problem. A Memetic Algorithm (MA) is developed based on the Genetic Algorithm (GA) and Variable Neighborhood Search methods. The proposed meta-heuristics are tested on small and large reference benchmarks. The results of the MA are compared to those of the classical GA and to the optimal solutions in the literature. The comparison shows the efficiency of using MA and its ability to generate high quality solutions in a reasonable computation time.
This mathematical model forms machine cells, optimises the costs of unassigned machines and components, and designs the shop floor cell layout to have minimal movement of materials. The complete similarity measure algorithm forms machine cells and part families in a refined form. Later, exceptional elements are eliminated in the optimisation model by using machine duplication and sub-contracting of parts. Then the shop floor layout is designed to have optimised material movements between and within cells. An evaluation of the cell formation algorithm’ performance is done on the benchmark problems of various batch sizes to reveal the process’s capability compared with other similar methods. The data of machining times are acquired and tabulated in a part incidence matrix, which is used as input for the algorithm. The results from the linear programming optimisation model are that costs are saved, machines are duplicated, parts are sub-contracted, and there are inter- and intra-cellular movements. Finally, the output of the inbound facility design is the floor layout, which has machine cell clusters within the optimised floor area.
This proposed work is used to optimize the costs of exceptional elements of machine cells for a variety of components in changing environments to have reduced material movements in cell layout. The exceptional ele¬ments are eliminated in the optimization model by doing machine duplication and part subcontract. Then the shop floor layout is designed to have optimized material movements between cells and within a cell. The result of a linear programming optimization model is cost savings, machines duplicated, parts subcon¬tracted, inter intracellular movements. Finally, the output of the inbound facility design is the floor layout which has machine cell clusters with optimized floor areas. The optimization model is provided with budg¬etary constraints for duplication and the economic tradeoff between machine duplication and part subcontract. Cell layout is prepared to reveal the saving in floor area and material movement lengths than in process layout with the help of distance matrix and dimensions of cells.
The high density of H-CRAN associated with frequent UE handover may degrade the throughput. The infrastructure equipment like RRHs and BBUs consumes more energy to reduce UE energy consumptions. In this paper, we propose a utility-based joint power control and resource allocation (UJPCRA) algorithm for heterogeneous cloud radio access network (H-CRAN). In this framework, the power consumption of baseband units (BBUs), remote radio heads (RRHs), and macrocell base station (MBS) are estimated by predicting their dynamic loads. The data rate achievable for UE associated with each RRH and MBS on resource block RBk is then estimated. The user wishing to connect to a RRH or MBS then checks the corresponding utility with minimum expected energy consumption and the maximum expected data rate. If any UE with high priority traffic connected to MBS could not achieve its desired data rate requirements, then it can cooperatively seek the assistance of any RRH for assigning the balance RBs. The throughput may be enhanced by the high density of H-CRAN and frequent UE handover. Inter- and intracell interference causes the H-CRAN macrocells’ improved data rate to diminish. To lower UE energy consumption, infrastructure devices like RRHs and BBUs need more energy. As a result, there is a trade-off between operators and UE energy conservation. It is possible to determine the power consumption of BBUs, RRHs, and MBS using predictions of their dynamic loads. The UE may then forecast the data rate for each RRH and MBS on the resource block. When a user wishes to connect to an RRH or MBS, they look at the utility with the highest expected data rate and the least predicted energy usage first. A UE with high priority traffic connected to the MBS can cooperatively ask any RRH for assistance in allocating the remaining RBs if it is unable to achieve its intended data rate needs. Experimental results have shown that the proposed JRAUA algorithm achieves higher throughput, resource utilization, and energy efficiency with reduced packet loss ratio, when compared to the existing techniques.