Nowadays, the speed at which municipalities provide urban services and collect urban waste play an important role in improving the efficiency of this organization, and therefore, the satisfaction of the citizens. In recent decades, due to the dominance of consumerism culture in Third World countries, especially Iran, we witness an increase in the urban waste each and every single day. In spite of the modernization of waste collection machines, the service delivery speed has been neglected although it has always had a significant impact on cost reduction and quality of service delivery. The city of Ardabil is no exception to this. It has four districts and 100 large and small neighborhoods in total that have always encountered the municipality with a major PROBLEM in terms of the rate at which urban wastes was collected and thus provided a beautiful outlook of the city. This article aims at adding the speed as a factor to the waste collection units by proposing the best route for the machines via TRAVELLING SALESMAN PROBLEM approach and Imperialist Competitive Algorithm in MATLAB environment. Using the appropriate programming and defining those 100 neighborhoods for the model, the most optimal routes for the municipality’, s service units are introduced provided that the service units pass each neighborhood once and at the end return to the starting point again. The results of the study showed that the algorithm used in this research for 100 neighborhoods in those four districts can provide the optimal solution with the repetition of 200 and respectively with the values of 99, 91, 93, and 97 and within the intervals of 30, 22, 30, and 24 seconds.

We extend our previous work on complexity indices for the TRAVELLING SALESMAN PROBLEM ((TSP)) using graph spectral techniques of data mining. A complexity index is an invariant of an instance I by which we can predict the execution time of an exact algorithm for (TSP) for I. We consider the symmetric TRAVELLING SALESMAN PROBLEM with instances I represented by complete weighted graphs G. Intuitively, the hardness of an instance G depends on the distribution of short edges within G.Therefore we consider some short edge subgraphs of G (minimal spanning tree and several others) as non-weighted graphs and several their invariants as potential complexity indices. Here spectral invariants (e.g. spectral radius of the adjacency matrix) play an important role. Spectral clustering algorithms are used including information obtained from the spectral gap in Laplacian spectra of short edge subgraphs.

In today’s competitive transportation systems, passengers search to find traveling agencies that are able to serve them efficiently considering both traveling time and transportation costs. In this paper, we present a new model for the traveling SALESMAN PROBLEM with multiple transporters ((TSP)MT). In the proposed model, which is more applicable than the traditional versions, each city has different transporting vehicles and the cost of travel through each city is dependent on the transporting vehicles type. The aim is to determine an optimal sequence of visited cities with minimum traveling times by available transporting vehicles within a limited budget. First, the mathematical model of (TSP)MT is presented. Next, since the PROBLEM is NP-hard, a new hybrid parallel simulated annealing algorithm with a new coding scheme is proposed. To analyze the performance of the proposed algorithm, 50 numerical examples with different budget types are examined and solved using the algorithm. The computational results of these comparisons show that the algorithm is an excellent approach in speed and solution quality.

The TRAVELLING SALESMAN PROBLEM is one of the fundamental operational research PROBLEMs where the objective is to generate the cheapest route for a SALESMAN starting from a given city, visiting all the other cities only once and finally returning to the starting city. In this paper, we study the TRAVELLING SALESMAN PROBLEM in uncertain environment. Particularly, the single valued triangular neutrosophic environment is considered viewing that it is more realistic and general in real-world industrial PROBLEMs. Each element in the distance matrix of the TRAVELLING SALESMAN PROBLEM is presented as a single valued triangular neutrosophic number. To solve this PROBLEM, we enhance our novel column-row heuristic Dhouib-Matrix-(TSP)1 by the means of the center of gravity ranking function and the standard deviation metric. In fact, the center of gravity ranking function is applied for defuzzification in order to convert the single valued triangular neutrosophic number to crisp number.A stepwise application of several numerical TRAVELLING SALESMAN PROBLEMs on the single valued triangular neutrosophic environment shows that the optimal or a near optimal solution can be easily reached thanks to the Dhouib-Matrix-(TSP)1 heuristic enriched with the center of gravity ranking function and the standard deviation metric.