ارزيابي و مقايسه الگوريتم هاي بهينه سازي فرا ابتكاري در مكان يابي تسهيلات مطالعه موردي: بانك ها

The assessment and comparison algorithms for optimization of the facility location Case Study: Banks

مسأله مكان يابي بانك‌ ها به فاكتورهاي زيادي نياز داشته و جزء مسايل NP-HARD طبقه‌بندي مي‌ شود. استفاده از روش‌ هاي فراابتكاري براي حل مسايل NP-HARD عليرغم تقريبي بودن، مناسب‌ ترين راه حل به نظر مي‌ رسد. در اين تحقيق از روش‌ هاي بهينه‌ سازي گرگ خاكستري، علف‌ هاي هرز، ژنتيك، اجتماع ذرات و الگوريتم فرهنگي در حل مسأله مكان يابي بانك‌ ها استفاده شده است. براي اين كار هدف به صورت جذب مشتري بيشتر و محدوديت در تعداد نفرات جذب شده به بانك جديدالتأسيس تعريف شد. روش‌ ها به طوري آماده شدند كه قابليت پيدا نمودن مكان بانك جديد با وجود بانك‌ هاي ديگر در منطقه را دارند و مكان بانك جديد بايد از بانك‌ هاي هم نوع خودش تا حد ممكن دورتر شده (هدف بازاريابي) و همچنين در مجموع كل مشتريان اين نوع بانك نبايستي از يك حدي كمتر شده و ميزان جذب مشتري شعبه جديدالتأسيس بانك از يك تعدادي كمتر نشود (محدوديت‌ها). بدين منظور قسمتي از كلان شهر تبريز جهت پياده‌ سازي انتخاب شد. به منظور ارزيابي كيفيت و دقت الگوريتم‌ها از تست تكرارپذيري و مقايسه اعداد همگرايي براي نتايج حاصل از اجراي هر الگوريتم روي داده‌ ها اجرا شد. همچنين نتايج الگوريتم‌ ها با آزمون آماري ويلكاكسون مورد ارزيابي قرار گرفت. نتايج حاصل از اين آزمون‌ ها عملكرد دقيق‌ تر، الگوريتم علف‌ هاي هرز نسبت به روش‌ هاي بهينه‌ سازي مذكور در مكان يابي بانك‌ ها را نشان مي‌ دهد.

Introduction Bank branches location-allocation problem belongs to NP-Hard problems which can be possibly solved only in exponential time by the increase in the number of banks and the large number of customers; especially when the location model includes various datasets, several objectives and constraints. As a consequent, we need to use heuristic methods to solve this type of problems. Also, since majority of data and analyses applied in the location-allocation problems are spatial; GIScience’s abilities should be employed beside optimization methods. Nowadays, to perform particular financial tasks bank customers often need to be present at their bank. For the sake of its customers, a bank should increase its branches in the city to attract more customers in the race with competing banks. However, establishing new branches is too expensive and banks prefer to carry out an optimal location finding procedure. Such procedures should consider many criteria and objectives including spatial data of customers, new and existing bank branches as well as level of attraction of banks –in the real-life. Customers often select a bank that is closer to them, has better services or financial records and also consider other human or physical factors. Hence, planning to increase the number of customers for a new branch of a bank considering spatial criteria and various other objectives appear necessary. Materials & Methods This paper determines the location of bank branches. Finding an optimum location of branches depends on many factors and these problems are known as NP-hard problems. Despite being approximate methods, meta-heuristic algorithms seem suitable tools for solving NP-hard problems. In this paper, Grey Wolf Optimizer (GWO), Genetic Algorithms (GA), Particle Swarm Optimization (PSO), Cultural Algorithms (CA) and Invasive Weed Optimization (IWO) are applied for finding the best location of bank branches. From marketing point of view, the aim is to attract more customers while the number of attracted persons to a new branch should be acceptable. The new methods have capability to find the optimum location of new branches. The location of a new branch should be as far away as possible from branches of the same bank. The other condition is that the total number of customers for the new branch should not be less than a specified number, while the new branch should not attract customers of old branches of the same bank more than a threshold. To fulfill this propose a part of the Tabriz city was selected for implementation. The assumptions for the defined problem can be expressed as the following statements: a)We consider four different banks (Melli, Mellat, Sepah and Meher) in our study area. b)Population density (of people over 15 years of age) is available at the building block level. c)Banks have infinite capacity for accepting customers. d)Each customer refers to only one bank. e)New bank branches should have maximum distance from branches of the same bank, so that; it attracts minimum number of customers from branches of the same bank. According to the above-mentioned assumptions, mathematical model of the function for optimization is as follows: objective: Maximizes the distance between newly established branch and other existing branches of the same bank. Constraint1: Not less likely to attract new customers to the bank established a certain extent. Constraint2: Other branches of the same bank customers not less so after the creation of a new bank branch. Results & Discussion To assess the accuracy of the algorithms in the problem, suggests, in this study, repeatability and convergence of the algorithm is used. The results from the convergence of the algorithms used in this study, 100 iteration, is provided. For comparison, the cost for the logarithmic axis is provided. The axis can be said that IWA algorithm has better convergence than the other four algorithms. The convergence of the algorithm optimization methods, PSO and GW are next in priority. The answer and the cost of repeated 5 times 50 algorithm implementation of this algorithm is compared. It also answers the PSO algorithm and GW are next in priority. It should be noted that the number of adjustable parameters optimization algorithm optimization method IWA far more than the PSO and GW. Conclusion Finally, to evaluate quality and accuracy of the algorithms, several iterations are performed. The results of statistical and final tests indicate that the accuracy and convergence speed of Invasive Weed Optimization are more than other Algorithms in finding optimal location of bank branches.