heuristic algorithm

The Graph Isomorphism Problem (GIP) is an open problem because of its computational complexity. No polynomial-time deterministic algorithm has been proposed yet, and heuristic and meta-heuristic approaches have been the only ways to solve it. Because its belonging to the NP-complete problem has not yet been proven, it is considered an NP problem. This paper introduces a simple but efficient polynomial algorithm, both in terms of computational complexity and memory complexity, to determine the isomorphism of connected unlabeled graphs. The proposed algorithm introduces two functions that compute the features for all vertices and edges. The outputs of the function provide canonical labeling to the given graphs, and a comparison of these labels specifies the graph isomorphism of the given graphs. The experimental results show that the proposed algorithm correctly detects the isomorphism of the graphs in more than 99% of cases. The algorithm requires Ο(n^3) time where n is the number of vertices of the given graphs.

Loading and haulage operation in open pit mines is the last stage of the mining process. truck- shovel system, due to its many advantages  including high flexibility, is preferred for this operation. Due to high operating costs, proper fleet management and optimization can significantly affect the project economics. Truck allocation and dispatching issue is a very complex problem, especially in large mines with numerous loading and dumping points. Because of the problem size and complexity, employing mathematical methods is not justified due to very high solution time which leads to employing super computers. To overcome the aforesaid shortcoming, heuristic algorithms can be applied. In this paper, in MATLAB environment, a heuristic algorithm was developed to solve allocation and dispatching problem of transportation fleet of a real mine. According to the obtained results, a running time of 39 seconds was computed for the heuristic algorithm. Finally, the same problem was solved with an available mathematical model with a running time of 24 hours which shows the superiority of the proposed algorithm over the mathematical modeling.

Establishing the structure and expansion of sustainable closed-loop supply chains is critical to meeting environmental, economic, and social standards to strengthen their position in competitive markets. This study aims to decide on operational and tactical levels to configure the Stable Closed Chain Supply Chain Network (SCLSC) to maximize Net Present Value (NPV) and seek to minimize carbon emissions while maintaining environmentally friendly policies and considering inflation.

This paper considers a solid Fuzzy Robust Optimization (FRO) approach to deal with stable, closed-loop supply chain uncertainties. Also, due to the complexity of the model and its multi-objective, a new combined method of Heuristic algorithm (HA) and Multi-Choice Goal Programming with Utility Function (MCGP-UF) is used. The proposed Mixed Integer Linear Programming (MILP) model is applied in the electronics industry.

The proposed model is evaluated in several experiments and discussed in different scenarios to confirm the efficiency and validity of the proposed model and method. The results were compared with the two factors of optimal gap and solution time, which showed the proper performance of the proposed method. Then, the tactical results and model strategy were presented for a case study in which the optimal flow between facilities, selection of suitable suppliers, selection of transportation type, and opening of facilities were presented. The findings showed that in different scenarios, the effective improvement of the obtained solutions by reducing the solution time by twenty percent could address large-scale problems.

Originality/Value:

 By considering a new combined method of heuristic algorithm and multi-choice ideal programming with a utility function, this paper is done to solve the problem of designing a stable closed-loop supply chain network under uncertainty.

In this article, we intend to address the issue of routing of flying objects such as drones, missiles, etc., using the proposed innovative algorithm. For this purpose, an innovative algorithm has been presented on a precise line that provides the best path without hitting obstacles to guide a flying object to intercept and reach the target. The environmental conditions are assumed in such a way that a flying object has no prior knowledge of the environment in which it is located, and it learns about its surroundings through the sensors embedded in it, which have a limited exploration area. Existing obstacles can be considered fixed or moving, and their movements are also unknown to the flying object, and they can also be of different geometric shapes. Finally, the flying object must reach a fixed target by which it can be reached. Also, the effectiveness of the proposed algorithm will be measured in the case that the flying object must avoid and pass through a security or forbidden space with a certain confidence interval.

Comminution is the most energy intensive operation which constitutes the major portion of operating and capital costs of the mineral processing plants.  Working at the maximum operating capacity of comminution equipment plays a significant role in the efficiency of the circuit.  Also, due to the effect of crusher efficiency on the downstream circuit performance, optimization of the crushing circuits has received considerable attention.  In this research, the effect of feed chute design on tertiary cone crusher performance at the Sarcheshmeh copper complex was studied.  A close monitoring of the performance crusher revealed that main problems were high fluctuations of power draw and uneven and high-rate wear of crusher liners.  Such pitfalls were clear evidences of an improper feeding arrangement into the crusher.  Accordingly, various feed chute designs were employed in the simulations by an in-house developed DEM software called KMPCDEM© to find more uniform feed distribution on the distribution plate of the crusher.  Results showed that by changing the shape of feed chute from cubic to cylindrical, decreasing its surface area from 0.34 to 0.24 m2 and increasing the cylinder length above and below the feed chute plate from 0 to 45 cm and from 53 to 95 cm, respectively, uniform feed distribution was obtained.  After installing the new feed chute design in the plant, a detail monitoring over a period of 15 months showed a reduction of the standard deviation of crusher power draw from 13 to 3 kW.  A better crusher control caused choke feeding.  Therefore, 36% increase in the crusher throughput and finer and narrower product size distribution occurred.  Furthermore, the life of crusher liners increased from 8 months to 15 months on account of more uniform and lower rate of wear on mantle and liners.

With the advent of Internet of Things (IoT) applications, the number of processing requests has dramatically increased. In order to response to these requests, the Fog-Cloud environment has recently been introduced as a hybrid computing system. Although, the Fog-Cloud is a very promising environment for processing IoT requests, it faces many challenges. In this regard, task scheduling problem is one of the key challenges which has a significant impact on the efficiency and overall system cost. Motivated by this, in this paper, we first present a multi-objective optimization model including makespan, energy consumption and processing cost for scheduling tasks in an integrated Fog-Cloud environment. Then we propose a heuristic algorithm to efficiently solve the model. Simulation results demonstrate that our proposed algorithm significantly reduces all the aforementioned metrics and can achieve a good tradeoff between them. Specifically, the proposed algorithm improves the objective function around 98%, 43% and 32% in comparison with the random, genetic and the power of two choices algorithms, respectively.

By increasing the use of container transportation, one of the existing problems is the constant capacity of container terminals due to problems, such as lengthy construction process, lack of budget and space to build new locations, as well as lack of manpower. Also, this constant capacity leads to problems such as reduced trade relations, increased maintenance and warehousing costs, increased transportation costs, and increased loading and unloading times, as well as container allocation problems. To solve this problem without increasing the area of the terminal, this paper present a mathematical model to allocate containers that can be used not only to solve this problem, but also in other cases such as transportation and shipping used. Due to the size of problems used in this research, a heuristic algorithm, namely LOGIC algorithm is used. According to studies, carried out in the literature, this algorithm has not been used in relevant problems so far. Also, due to the development of the LOGIC algorithm in this paper, it can be used for other large-scale optimization problems. The development of the proposed algorithm can be improved to solve the layout problem of maritime containers with other real constraints.

Service vessels in the offshore oil industry have a noticeable logistics role in protection and continuity of quality and quantity of oil production. Offshore oil production takes place on oil wellhead platforms. In order to maintain oil production in offshore areas, using supportive vessels and mobile wellhead vessels, the National Iranian Oil Company periodically provides public services and well services for equipment located on oil wellhead platforms. However, in the meantime, mobile wellhead servants themselves need to receive service from supportive vessels in specific periods and, also, specific time windows. In fact, mobile wellhead servants have a dual role. On the one hand, they have a role to play in providing well services for oil wellhead platforms and, on the other hand, they have the role of receiving public services from supportive vessels. Service vessels are few in number compared to service requirements; however, they have a high shipping cost instead. Therefore, on the one side, using them without an appropriate plan leads to significant lost opportunity cost of oil production due to service shortages and, on the other hand, imposes high shipping costs. In order to determine the periodic routing of service vessels, a mixed-integer programming model is proposed with the aim of minimizing the cost of shipping and the lack of services. Given that the mathematical model is Np-hard, a heuristic algorithm based on practical conditions of the problem is introduced to solve the problem, and its performance is evaluated using real-life instances related to different oilfields located on the Iranian side in the Persian Gulf. Numerical results indicate the algorithm's speed in achieving appropriate solutions in a very short amount of time compared to existing algorithms. In fact, implementing the heuristic algorithm leads us to creating very good solutions in the primary iterations of running the heuristic algorithm and improving them in the next iterations.