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1

A Mathematical Model for the Vehicles Routing Problem with Multiple Depots, Considering the Possibility of Return Using the Tabu Search Algorithm

Ahmed Alim Al Ayub, Singhal Saurabh, Prakaash A. S., Dayupay Johnry, Rahadi Irwan, Marhoon Haydar Abdulameer, Iswanto A. Heri, Abbas Saja Fadhil, Aravindhan Surendar

Foundations of Computing and Decision Sciences

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2022

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Vol. 47, No. 4

359--370

EN

The current study examines an essential type of vehicle routing problem (VRP). This type is one where customers are served by limited-capacity vehicles from multiple depots and is known as Multi-Depot Capacitated Vehicle Routing Problem (MDCVRP). The novelty of this study is that in the present case, cars, after Leaving the Depot, can go back to any other depot. Those issues seem to occur in most real-world issues where information, messages, or news are sent electronically from somewhere. The purpose of the problem is to minimize the costs associated with routing. Regarding the literature on such issues, it has been proven in previous studies and research that these problems are among the hard-NP problems, and to solve them using the metaheuristic method, the exact methods justify it. After changing the basic model, this study developed a Tabu Search (TS) algorithm. The study results demonstrate that if the equipment can return to any depot, the cost is significantly reduced in contrast to the case where equipment is forced to return to their depot.

2

A logistic optimization for the vehicle routing problem through a case study in the food industry

Akpinar Muhammet Enes

LogForum

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2021

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Vol. 17, no. 3

387--397

EN

Background: In this study, the food delivery problem faced by a food company is discussed. There are seven different regions where the company serves food and a certain number of customers in each region. The time of requesting food for each customer varies according to the shift situation. This type of problem is referred to as a vehicle routing problem with time windows in the literature and the main aim of the study is to minimize the total travel distance of the vehicles. The second aim is to determine which vehicle will follow which route in the region by using the least amount of vehicle according to the desired mealtime. Methods: In this study, genetic algorithm methodology is used for the solution of the problem. Metaheuristic algorithms are used for problems that contain multiple combinations and cannot be solved in a reasonable time. Thus in this study, a solution to this problem in a reasonable time is obtained by using the genetic algorithm method. The advantage of this method is to find the most appropriate solution by trying possible solutions with a certain number of populations. Results: Different population sizes are considered in the study. 1000 iterations are made for each population. According to the genetic algorithm results, the best result is obtained in the lowest population size. The total distance has been shortened by about 14% with this method. Besides, the number of vehicles in each region and which vehicle will serve to whom has also been determined. This study, which is a real-life application, has provided serious profitability to the food company even from this region alone. Besides, there have been improvements at different rates in each of the seven regions. Customers' ability to receive service at any time has maximized customer satisfaction and increased the ability to work in the long term. Conclusions: The method and results used in the study were positive for the food company. However, the metaheuristic algorithm used in this study does not guarantee an optimal result. Therefore, mathematical models or simulation models can be considered in terms of future studies. Besides, in addition to the time windows problem, the pickup problem can also be taken into account and different solution proposals can be developed.

3

Metaheuristic approach to optimal power flow using mixed integer distributed ant colony optimization

Suresh Vishnu, Janik Przemyslaw, Jasinski Michal

Archives of Electrical Engineering

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2020

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Vol. 69, nr 2

335--348

EN

This paper presents the application of an improved ant colony optimization algorithm called mixed integer distributed ant colony optimization to optimize the power flow solution in power grids. The results provided indicate an improvement in the reduction of operational costs in comparison with other optimization algorithms used in optimal power flow studies. The application was realized to optimize power flow in the IEEE 30 and the IEEE 57 bus test cases with the objective of operational cost minimization. The optimal power flow problem described is a non-linear, non-convex, complex and heavily constrained problem.

4

Routing of Vehicles from Depot in Two-Level Supply Chain with a Meta-Heuristic Algorithm

Hosseini Zahra Sadat, Kamali Iman

Advances in Science and Technology. Research Journal

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2019

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Vol. 13, no 2

38--45

EN

The present study aimed at routing vehicles from a depot in two-level supply chain with a meta-heuristic algorithm. This study is an analytical type of research. The issue of routing which includes time, travel duration dependent on the day, has first been introduced by Mandraki and Duskin. They proposed the issue of time-dependent Travelling Salesman Problem (TSP), such that their simplified issue was a VRP issue and service should be provided to all customers, and each customer should only be visited by one vehicle. Mathematical modeling was used as a research tool, and in the examined problem, there are a number of demand points with simultaneous delivery and return. This demand should pass the depot which should be selected from among candid points, and it should be determined that the construction of depot in each of these locations has a specific fixed cost. In order to send service from depot to the demand points, vehicles with special carrying capacity, fixed using costs, and overhead carrying costs. Given that solving the problem is time-consuming, the MOPSO meta-heuristic algorithm was used in order to solve the problem. The obtained results were fully presented, and in different repetitions it was observed that the second vehicle has the highest load carrying.

5

Heuristic algorithms for joint optimization of unicast and anycast traffic in elastic optical network-based large-scale computing systems

Markowski M.

International Journal of Applied Mathematics and Computer Science

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2017

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Vol. 27, no. 3

605--622

EN

In recent years elastic optical networks have been perceived as a prospective choice for future optical networks due to better adjustment and utilization of optical resources than is the case with traditional wavelength division multiplexing networks. In the paper we investigate the elastic architecture as the communication network for distributed data centers. We address the problems of optimization of routing and spectrum assignment for large-scale computing systems based on an elastic optical architecture; particularly, we concentrate on anycast user to data center traffic optimization. We assume that computational resources of data centers are limited. For this offline problems we formulate the integer linear programming model and propose a few heuristics, including a meta-heuristic algorithm based on a tabu search method. We report computational results, presenting the quality of approximate solutions and efficiency of the proposed heuristics, and we also analyze and compare some data center allocation scenarios.

6

Balance of cost, time, and quality related to construction projects regarding the reinforced concrete of underground structures using a meta-heuristic algorithm

Hosseini S. A., Akbarpour A., Ahmadi H., Aminnejad B.

Archives of Civil Engineering

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2017

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Vol. 63, nr 4

103--121

EN

Underground spaces having features such as stability, resistance, and being undetected can play a key role in reducing vulnerability by relocating infrastructures and manpower. In recent years, the competitive business environment and limited resources have mostly focused on the importance of project management in order to achieve its objectives. In this research, in order to find the best balance among cost, time, and quality related to construction projects using reinforced concrete in underground structures, a multi-objective mathematical model is proposed. Several executive approaches have been considered for project activities and these approaches are analyzed via several factors. It is assumed that cost, time, and quality of activities in every defined approach can vary between compact and normal values, and the goal is to find the best execution for activities, achieving minimum cost and the maximum quality for the project. To solve the proposed multi-objective model, the genetic algorithm NSGA-II is used.

PL

Pomysł stworzenia bezpiecznej przestrzeni ma na celu zmniejszenie lub wyeliminowanie skutków zniszczenia i promieniowania, ze względu na bombardowanie klasyczne lub jądrowe i inne ataki. W przypadku ataków lotniczych zwykle używa się bomb z ogromnym potencjałem wybuchu i siłą niszczycielską, a zatem zderzenie tych bomb z celami powstaje bardzo wysoki poziom energii kinetycznej. Ta energia kinetyczna rozchodzi się jako ciśnienie i ciepło w środowisku, co może zakłócić i zniszczyć cel. Czasem ochrona przed bombardowaniami w budynkach i obiektach jest zapewniona przez modernizację zapobiegającą bezpośredniemu uderzeniu. Odbywa się to w przypadku ważnych miejsc, takich jak stanowiska dowodzenia i kluczowe elementy infrastruktury. Jednakże, w innych przypadkach, jest to nieuzasadnione z ekonomicznego punktu widzenia, dlatego też zamiast tego często wykorzystuje się podziemne lub częściowo podziemne bezpieczne przestrzenie (Movahedinia [5]). Zarządzanie projektem to zorganizowany system służący do zarządzania zasobami, dzięki czemu projekt może być ukończony zgodnie z określoną wizją w zakresie jakości, czasu i kosztu (Burke [7]). Projekty budowlane, podobnie jak inne działania i projekty, posiadają swoje własne ograniczenia. W odniesieniu do zarządzania projektem, są to tradycyjnie ograniczenia zakresu, czasu i kosztu. Te trzy czynniki są również określane jako trójkąt zarządzania projektem, w którym każde ograniczenie określa jedną stronę trójkąta. Podobnie jak w geometrii, jeśli jedna strona ulegnie zmianie, inne strony również się zmieniają; w zarządzaniu projektem, zmiany jednego czynnika wpływają również na inne czynniki. Trójkąt zarządzania projektem można również stosować w relacjach czasu, kosztu i jakości (Clements i Gido [8]). Oznacza to, że każdy projekt posiada trzy ograniczenia, którymi są czas, koszt i zakres. Ogólnie rzecz biorąc, kwestia równoważenia kosztu, czasu i jakości jednocześnie stara się uwzględnić trzy ważne czynniki w zarządzaniu projektem. Łatwo zrozumieć, że kwestia ta ma charakter wieloczynnościowy i może być przedstawiana w postaci modeli o wielu celach (Shuquan i Kongguo [11]). Struktura takiego modelu zawiera wiele opcji dla każdego działania, a model próbuje wybrać te z minimalnym koszem i czasem oraz najwyższą maksymalną jakością, lecz w tym przypadku mamy do czynienia z równoważeniem selekcji, ponieważ wysoka jakość i szybkość mają swoją cenę, a wykonanie kosztownego projektu może nie być możliwe. Badanie to ma na celu modelowanie problemu równoważenia kosztu, czasu i jakości w formie problemu o wielu celach, a następnie jego rozwiązanie za pomocą meta-heurystycznych algorytmów.

7

A metaheuristic for a numerical approximation to the mass transfer problem

Avendaño-Garrido M. L., Gabriel-Argüelles J. R., Quintana-Torres L., Mezura-Montes E.

International Journal of Applied Mathematics and Computer Science

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2016

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Vol. 26, no. 4

757--766

EN

This work presents an improvement of the approximation scheme for the Monge–Kantorovich (MK) mass transfer problem on compact spaces, which is studied by Gabriel et al. (2010), whose scheme discretizes the MK problem, reduced to solve a sequence of finite transport problems. The improvement presented in this work uses a metaheuristic algorithm inspired by scatter search in order to reduce the dimensionality of each transport problem. The new scheme solves a sequence of linear programming problems similar to the transport ones but with a lower dimension. The proposed metaheuristic is supported by a convergence theorem. Finally, examples with an exact solution are used to illustrate the performance of our proposal.

8

Algorytm metaheurystyczny dla problemu układania tras pojazdów

Jachimowski R.

Logistyka

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2014

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nr 6

4616-4624

PL

W artykule przedstawiono możliwość zastosowania algorytmu roju cząstek do rozwiązywania problemu układania tras pojazdów. Przedstawiony algorytm zaimplementowano w autorskiej aplikacji komputerowej i testowano na przykładzie wieloszczeblowego systemu dystrybucji.

EN

The paper presents the possibility of using the Particle Swarm Optimization algorithm for solving The Vehicle Routing Problem. Algorithm presented in the article was implemented in author’s computer application and tested on multi-level distribution systems.

9

Optymalizacja kosztów struktury systemu energetycznego przy założonej niezawodności określona metodą poszukiwania równowagi

Rami A., Zeblah A., Massim Y.

Przegląd Elektrotechniczny

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2009

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R. 85, nr 4

169-172

PL

W pracy zaprezentowano meta-heurystyczny algorytm poszukiwania równowagi zastosowany do rozwiązania problemu optymalizacji wielostanowego szeregowo-równoległego systemu zasilania energią. Założono że krzywa wahań obciążenia jest wokół wartości zerowej. Określono minimalne koszty inwestycyjne konfiguracji systemu do otrzymania satysfakcjonującej niezawodności. Rezultaty poszukiwania równowagi porównano z wynikami metody wykorzystującej algorytmy genetyczne.

EN

In this study, the meta-heuristic harmony search algorithm was introduced and applied to solve a redundant optimization problem presented by multi-state series-parallel systems. We supposed variation of the load cumulative demand curve null. The proposed meta-heuristic determines the minimal investment-costs system configuration to satisfy reliability constraints. A universal generating function technique is applied to evaluate system availability. The results obtained by HS are compared to those obtained by genetic algorithm.

10

Algorytmy metaheurystyczne dla problem harmonogramowania projektu z kamieniami milowymi

Klimek M., Łebkowski P.

Zeszyty Naukowe. Automatyka / Politechnika Śląska

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2008

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z. 150

63-72

PL

W artykule zaproponowano model matematyczny problemu harmonogramowania projektu z ograniczoną dostępnością zasobów RCPSP (ang. Resource-Constrained Project Scheduling Problem), który uwzględnia system kamieni milowych. Dla części zadań (związanych z kamieniami milowymi) określono nieprzekraczalne terminy ich zakończenia. Opracowano funkcję celu, która uwzględnia terminy realizacji wszystkich tych czynności. Dla zdefiniowanego problemu przetestowano skuteczność działania algorytmów) genetycznych i symulowanego wyżarzania.

EN

In article is proposed mathematical model for Resource-Constrained Project Scheduling Problem with milestones. For some activities (related to the milestones), unsurpassable term of completion is determinate. We have defined objective function, taking into consideration the observance of the times of completion of all these activities. For defined problem we have tested effectiveness of genetic and simulated annealing algorithms.