Neutrosophic Triangular Fuzzy Travelling Salesman Problem Based on Dhouib-Matrix-TSP1 Heuristic

In this paper, the Travelling Salesman Problem is considered in neutrosophic environment which is more realistic in real-world industries. In fact, the distances between cities in the Travelling Salesman Problem are presented as neutrosophic triangular fuzzy number. This problem is solved in two steps: At first, the Yager’s ranking function is applied to convert the neutrosophic triangular fuzzy number to neutrosophic number then to generate the crisp number. At second, the heuristic Dhouib-Matrix-TSP1 is used to solve this problem. A numerical test example on neutrosophic triangular fuzzy environment shows that, by the use of Dhouib-Matrix-TSP1 heuristic, the optimal or a near optimal solution as well as the crisp and fuzzy total cost can be reached

Dhouib-Matrix-TSP1 Method to Optimize Octagonal Fuzzy Travelling Salesman Problem Using α-Cut Technique

This paper proposes the optimization of the fuzzy travel salesman problem by using the α-Cut technique as a ranking function and the Dhouib-Matrix-TSP1 as an approximation method. This method is enhanced by the standard deviation metric and obtains a minimal tour in fuzzy environment where all parameters are octagonal fuzzy numbers. Fuzzy numbers are converted into a crisp number thanks to the ranking function α-Cut. The proposed approach in details is discussed and illustrated by a numerical example. This method helps in designing successfully the tour to a salesman on navigation through the distance matrix so that it minimizes the total fuzzy distance

DTW-Global Constraint Learning Using Tabu Search Algorithm

AbstractMany methods have been proposed to measure the similarity between time series data sets, each with advantages and weaknesses. It is to choose the most appropriate similarity measure depending on the intended application domain and data considered. The performance of machine learning algorithms depends on the metric used to compare two objects. For time series, Dynamic Time Warping (DTW) is the most appropriate distance measure used. Many variants of DTW intended to accelerate the calculation of this distance are proposed. The distance learning is a subject already well studied. Indeed Data Mining tools, such as the algorithm of k-Means clustering, and K-Nearest Neighbor classification, require the use of a similarity/distance measure. This measure must be adapted to the application domain. For this reason, it is important to have and develop effective methods of computation and algorithms that can be applied to a large data set integrating the constraints of the specific field of study. In this paper a new hybrid approach to learn a global constraint of DTW distance is proposed. This approach is based on Large Margin Nearest Neighbors classification and Tabu Search algorithm. Experiments show the effectiveness of this approach to improve time series classification results

Improving the ISO 9000 Factual Approach Principle through Metaheuristic

In this paper, the efficiency of the factual approach principle to decision making is improved by the mean of an Artificial Bees Colony metaheuristic. This principle is one of the eight basic principles in which the quality management system of the ISO 9000 series is based. This metaheuristic is adapted to solve the Flow-Shop Scheduling Problems with Makespan criterion, and the result proves the efficiency of the factual approach to decision making. Keywords: data analysis, factual approach to decision making, quality management system, metaheuristic, production schedulin

Shortest path planning via the rapid Dhouib-Matrix-SPP (DM-SPP) method for the autonomous mobile robot

Planning the shortest path for an autonomous mobile robot is a challenging problem. It consists in designing for the robot the optimal path to join the ending location from a starting position with avoiding the obstacle spaces. In this paper, the innovative greedy Dhouib-Matrix-SPP (DM-SPP) method is proposed to address this problem in a static environment with a grid model representation. At first, the grid model is codified as a graph using the eight movement directions where the maximal time complexity of DM-SPP for this problem is O(9*n) with n is the number of nodes in the graph. Then, DM-SPP uses this graph to rapidly search for the shortest path between the initial and the goal nodes. Hence, DM-SPP is developed with Python language and the planning path is illustrated using the Matplotlib library. Finally, experiments on eleven grid models with comparison on twelve metaheuristics (such as Particle Swarm Optimization integrated with Gray Wolf Optimization, Ant Colony Optimization combined with A* method and other metaheuristics) are studied and the results demonstrated the rapidity and the effectiveness of DM-SPP in designing the shortest path for the autonomous mobile robot. Clearly, DM-SPP improves massively the running time and the quality compared to all the other techniques and it can be concluded that DM-SPP is the fastest artificial intelligence method for the Mobile Robot Path Planning Problem

Innovative method to solve the minimum spanning tree problem: The Dhouib-Matrix-MSTP (DM-MSTP)

The Minimum Spanning Tree problem aims to create a subset of a graph where all the vertices are connected with the minimum edge weights and with no cycle. In this field, an innovative method entitled Dhouib-Matrix-MSTP (DM-MSTP) is designed in this research work with a time complexity independently of the number of edges O(n*log(n)) where n is the number of vertices. DM-MSTP is a constructive algorithm based on a matrix navigation with two new lists (Min-Columns and MST-Path) in order to organize the steering flow. DM-MSTP is composed of four simple steps where the first and the fourth steps are repeated only once, whereas the second and third are reiterated (n-1). For more clarification, a step-by-step application of the proposed method is presented in details. Besides, the performance of DM-MSTP is proved through different examples from the literature including a graph with negative weighted edges and complete graphs from TSP-LIB. Moreover, with a simple modification (Min by Max) the DM-MSTP is tested on the Maximum (Largest) Spanning Tree Problem. Also, DM-MSTP is applied on eight case studies and compared to six methods developed in the literature. All these experimental results in the above different environments show that DM-MSTP can rapidly plan the shortest spanning tree with a stable performance and convivial representation of the optimal tree. Hence, DM-MSTP is developed under Python programming language using Matplotlib and Numpy standard libraries

An optimal method for the Shortest Path Problem: The Dhouib-Matrix-SPP (DM-SPP)

This paper introduces an optimal method entitled Dhouib-Matrix-SPP (DM-SPP) in order to solve the Shortest Path Problem with a complexity time of On+mwhere n and m are respectively the number of vertices and edges. DM-SPP is a rapid method, it can reduce reasonably the research time and consequently the running time as well as the energy consumption. It is composed of five simple steps repeated in (n-1) iterations and for more clarification a guided step-by-step application of the novel method DM-SPP is presented. Moreover, several examples are solved wherein a fully complete and random distribute graphs are analyzed with the variation of the number of vertices from 20 to 6000 and the number of edges from 49 to 17097565. DM-SPP is coded under Python programming language and all experimental results demonstrate that DM-SPP can rapidly generate the optimal short path. Furthermore, by comparing the complexity time required by DM-SPP to the time prerequisite by Dijkstra algorithm, it can be concluded that DM-SPP and Dijkstra are concurrent for small instances and for larger instances DM-SPP can easily outperform Dijkstra and especially for the case of incomplete undirected graphs which are more realistic in the real-world viewing that all graphs are really not complete. The performance of DM-SPP is statistically confirmed with the Mann–Whitney U nonparametric test Further research trends will focus on the test of DM-SPP for the uncertain Shortest Path problem and the resolution of the autonomous mobile robot path planning problem

Unravelling the assignment problem under intuitionistic triangular fuzzy environment by the novel heuristic Dhouib-Matrix-AP1

The Assignment Problem (AP) can be stated as n activities to be assigned to n resources in such a way that the overall cost of assignment is minimized and each activity is assigned to one and only one resource. In real-life, the parameters of the AP are presented as uncertain numbers due to the lack of knowledge, experiences or any other (internal or external) factor. In this paper, the AP is considered under intuitionistic triangular fuzzy number and solved by the novel constructive heuristic Dhouib-Matrix-AP1 (DM-AP1) with a time complexity of O(n). Actually, this paper presents the first enhancement of the novel heuristic DM-AP1 to solve the AP under intuitionistic triangular fuzzy environment. DM-AP1 is composed of three simple steps: computing the total cost, selecting the highest value and finding the minimal element. These steps are repeated in n iterations with the use of a standard deviation statistical metric. Two case studies of AP under intuitionistic triangular fuzzy set are taken from the literature and a step-by-step application of the novel DM-AP1 heuristic is presented for more clarification

Increasing the Performance of Computer Numerical Control Machine via the Dhouib-Matrix-4 Metaheuristic

The Computer Numerical Control (CNC) machine represents a turning point in today's production which has high requirements for product accuracy. The CNC machine enables a high flexibility in work and time saving and also reduces the time required for product accuracy control. Moreover, the CNC machine are used for several activities, most often for turning, drilling and milling operations. Usually, the productivity of any CNC machine can be increased thanks to the minimization of the non-productive of tool movement. In this paper, the results of a new metaheuristic named Dhouib-Matrix-4 (DM4) with an application on the NP-hard problem based on the Travelling Salesman Problem are presented. DM4 is used for increasing the performance of the CNC Machine by optimizing a tool path length in the drilling process performed on the CNC milling machine. The proposed algorithm (DM4) achieves a solution closed to the optimum, compared with the results obtained with the Ant Colony Optimization algorithm and the results found with the manual programming in G code by using a control unit for the selected CNC milling machine

Decision-maker's preferences modelling in the engineering design through the interactive goal-programming

Engineering design problems are usually formulated as non-linear problems with integer, discrete or continuous variables. This paper presents a new interactive procedure to handle these kinds of problems. This procedure is based on the interactive goal programming model and the concept of satisfaction functions which are used to elucidate and integrate explicitly the decision-maker's preferences. A record-to-record travel (RRT) technique is adapted to solve this new interactive goal programming model. The proposed approach provides a satisfactory solution in the presence of conflicting objectives with a minimum distance from the fixed goals. Two engineering design problems are presented to illustrate the applicability and the performance of the proposed interactive technique.interactive goal programming; IGP; decision making; preference modelling; record-to-record travel; RRT; engineering design; decision maker preferences.