A Novel Design of Morlet Wavelet to Solve the Dynamics of Nervous Stomach Nonlinear Model

The present study introduces a novel design of Morlet wavelet neural network (MWNN) models to solve a class of a nonlinear nervous stomach system represented with governing ODEs systems via three categories, tension, food and medicine, i.e., TFM model. The comprehensive detail of each category is designated together with the sleep factor, food rate, tension rate, medicine factor and death rate are also provided. The computational structure of MWNNs along with the global search ability of genetic algorithm (GA) and local search competence of active-set algorithms (ASAs), i.e., MWNN-GA-ASAs is applied to solve the TFM model. The optimization of an error function, for nonlinear TFM model and its related boundary conditions, is performed using the hybrid heuristics of GA-ASAs. The performance of the obtained outcomes through MWNN-GA-ASAs for solving the nonlinear TFM model is compared with the results of state of the article numerical computing paradigm via Adams methods to validate the precision of the MWNN-GA-ASAs. Moreover, statistical assessments studies for 50 independent trials with 10 neuron-based networks further authenticate the efficacy, reliability and consistent convergence of the proposed MWNN-GA-ASAs.

Evolutionary heuristic with Gudermannian neural networks for the nonlinear singular models of third kind

The presented research work articulates a new design of heuristic computing platform with artificial intelligence algorithm by exploitation of modeling with feed-forward Gudermannian neural networks (FFGNN) trained with global search viability of genetic algorithms (GA) hybrid with speedy local convergence ability of sequential quadratic programing (SQP) approach, i.e., FFGNN-GASQP for solving the singular nonlinear third order Emden-Fowler (SNEF) models. The proposed FFGNN-GASQP intelligent computing solver Gudermannian kernel unified in the hidden layer structure of FFGNN systems of differential operators based on the SNEF that are arbitrary connected to represent the error-based merit function. The optimization objective function is performed with hybrid heuristics of GASQP. Three problems of the third order SNEF are used to evaluate the correctness, robustness and effectiveness of the designed FFGNN-GASQP scheme. Statistical assessments of the performance of FFGNN-GASQP are used to validate the consistent accuracy, convergence and stability.

Evolutionary Integrated Heuristic with Gudermannian Neural Networks for Second Kind of Lane–Emden Nonlinear Singular Models

In this work, a new heuristic computing design is presented with an artificial intelligence approach to exploit the models with feed-forward (FF) Gudermannian neural networks (GNN) accomplished with global search capability of genetic algorithms (GA) combined with local convergence aptitude of active-set method (ASM), i.e., FF-GNN-GAASM to solve the second kind of Lane–Emden nonlinear singular models (LE-NSM). The proposed method based on the computing intelligent Gudermannian kernel is incorporated with the hidden layer configuration of FF-GNN models of differential operatives of the LE-NSM, which are arbitrarily associated with presenting an error-based objective function that is used to optimize by the hybrid heuristics of GAASM. Three LE-NSM-based examples are numerically solved to authenticate the effectiveness, accurateness, and efficiency of the suggested FF-GNN-GAASM. The reliability of the scheme via statistical valuations is verified in order to authenticate the stability, accuracy, and convergence.

Vehicle Routing Problem with Transshipment: Mathematical Model and Algorithm

This paper presents a new variant of vehicle routing problem with paired transshipment demands (VRPT) between retail stores (customers) in addition to the regular demand from depot to retail stores. The problem originates in a real distribution network of high-end retail department stores in Thailand. Transshipment demands arise for one-order-per-season expensive items, whose inventories at the depot may become shortage after the middle of a season, while they remain available at some retail stores. A transshipment demand is a request for items that need to be picked up from a specific store that has the items and delivered to the store that requests the items. The objective of solving the VRPT is to find delivery routes that can satisfy both regular demands and transshipment demands in the same routes without incurring too much additional transportation distance. A mixed integer linear programming model is formulated to represent the VRPT. Six small problem instances are used to test the model. A hybrid threshold accepting and neighborhood search heuristic is also developed to solve large problem instances of VRPT. The heuristic is further extended to include a forbidden list of transshipment demands that should not be included in the same routes. The purpose is to prevent incurring too much additional distance from satisfying transshipment demands. With the forbidden list, the problem becomes vehicle routing problem with optional transshipment demands (VRPOT). Computational testing shows promising results that indicate effectiveness of the proposed hybrid heuristics as well as the forbidden list.

Economical connections between several European countries based on TSP data

A fluent economical collaboration between countries is a major need. European flows of trade and people are supported by efficient connections between main localities from a geographic region, in many cases overriding national borders. This paper introduces three traveling salesmen problem instances based on freely available geographic coordinates of the main cities of France, Portugal and Spain. These instances are unified, generating other four larger instances: three with all pairs of countries and one instance with the settlements from all the three countries. The study includes an analysis of quality of solutions for a version of branch & cut algorithm and some hybrid heuristics including the Lin–Kernighan algorithm. $Bor\mathring{u}vka$, Quick$Bor\mathring{u}vka$ and Greedy algorithms are also used in the hybrid approaches in order to obtain a potential beneficent initial solution for the Lin–Kernighan algorithm. Concorde solver, nowadays state-of-the-art exact software, together with the already mentioned algorithms, is used to test and furthermore analyze the new TSP instances. Some results are represented using online services such as Google Maps, showing the potential integration of the Concorde’s optimum results into commercial routing applications. The very good results provided by the Lin–Kernighan method allow its usage for real medium-sized routing instances.