Hybrid Algorithm for Solving the Quadratic Assignment Problem

The Quadratic Assignment Problem (QAP) is a combinatorial optimization problem; it belongs to the class of NP-hard problems. This problem is applied in various fields such as hospital layout, scheduling parallel production lines and analyzing chemical reactions for organic compounds. In this paper we propose an application of Golden Ball algorithm mixed with Simulated Annealing (GBSA) to solve QAP. This algorithm is based on different concepts of football. The simulated annealing search can be blocked in a local optimum due to the unacceptable movements; our proposed strategy guides the simulated annealing search to escape from the local optima and to explore in an efficient way the search space. To validate the proposed approach, numerous simulations were conducted on 64 instances of QAPLIB to compare GBSA with existing algorithms in the literature of QAP. The obtained numerical results show that the GBSA produces optimal solutions in reasonable time; it has the better computational time. This work demonstrates that our proposed adaptation is effective in solving the quadratic assignment problem

An improved discrete bat algorithm for symmetric and asymmetric traveling salesman problems

Bat algorithm is a population metaheuristic proposed in 2010 which is based on the echolocation or bio-sonar characteristics of microbats. Since its first implementation, the bat algorithm has been used in a wide range of fields. In this paper, we present a discrete version of the bat algorithm to solve the well-known symmetric and asymmetric traveling salesman problems. In addition, we propose an improvement in the basic structure of the classic bat algorithm. To prove that our proposal is a promising approximation method, we have compared its performance in 37 instances with the results obtained by five different techniques: evolutionary simulated annealing, genetic algorithm, an island based distributed genetic algorithm, a discrete firefly algorithm and an imperialist competitive algorithm. In order to obtain fair and rigorous comparisons, we have conducted three different statistical tests along the paper: the Student's $t$-test, the Holm's test, and the Friedman test. We have also compared the convergence behaviour shown by our proposal with the ones shown by the evolutionary simulated annealing, and the discrete firefly algorithm. The experimentation carried out in this study has shown that the presented improved bat algorithm outperforms significantly all the other alternatives in most of the cases

An improved discrete bat algorithm for symmetric and asymmetric traveling salesman problems

Bat algorithm is a population metaheuristic proposed in 2010 which is based on the echolocation or bio-sonar characteristics of microbats. Since its first implementation, the bat algorithm has been used in a wide range of fields. In this paper, we present a discrete version of the bat algorithm to solve the well-known symmetric and asymmetric traveling salesman problems. In addition, we propose an improvement in the basic structure of the classic bat algorithm. To prove that our proposal is a promising approximation method, we have compared its performance in 37 instances with the results obtained by five different techniques: evolutionary simulated annealing, genetic algorithm, an island based distributed genetic algorithm, a discrete firefly algorithm and an imperialist competitive algorithm. In order to obtain fair and rigorous comparisons, we have conducted three different statistical tests along the paper: the Student's $t$-test, the Holm's test, and the Friedman test. We have also compared the convergence behaviour shown by our proposal with the ones shown by the evolutionary simulated annealing, and the discrete firefly algorithm. The experimentation carried out in this study has shown that the presented improved bat algorithm outperforms significantly all the other alternatives in most of the cases

Golden Ball Algorithm for solving Flow Shop Scheduling Problem

The Flow Shop Scheduling Problem (FSSP) is notoriously NP-hard combinatorial optimization problem. The goal is to find a schedule that minimizes the makespan. This paper proposes an adaptation of a new approach called Golden Ball Algorithm (GBA). The proposed algorithm has been never tested with FSSP; it’s based on soccer concept to obtain the optimal solution. Numerical results are presented for 22 instances of OR- Library. The computational results indicate that this approach is practical for small OR-Library instances

Efficient routing of snow removal vehicles

This research addresses the problem of finding a minimum cost set of routes for vehicles in a road network subject to some constraints. Extensions, such as multiple service requirements, and mixed networks have been considered. Variations of this problem exist in many practical applications such as snow removal, refuse collection, mail delivery, etc. An exact algorithm was developed using integer programming to solve small size problems. Since the problem is NP-hard, a heuristic algorithm needs to be developed. An algorithm was developed based on the Greedy Randomized Adaptive Search Procedure (GRASP) heuristic, in which each replication consists of applying a construction heuristic to find feasible and good quality solutions, followed by a local search heuristic. A simulated annealing heuristic was developed to improve the solutions obtained from the construction heuristic. The best overall solution was selected from the results of several replications. The heuristic was tested on four sets of problem instances (total of 115 instances) obtained from the literature. The simulated annealing heuristic was able to achieve average improvements of up to 26.36% over the construction results on these problem instances. The results obtained with the developed heuristic were compared to the results obtained with recent heuristics developed by other authors. The developed heuristic improved the best-known solution found by other authors on 18 of the 115 instances and matched the results on 89 of those instances. It worked specially better with larger problems. The average deviations to known lower bounds for all four datasets were found to range between 0.21 and 2.61%

The Plug-In Hybrid Electric Vehicle Routing Problem with Time Windows

There is an increasing interest in sustainability and a growing debate about environmental policy measures aiming at the reduction of green house gas emissions across di erent economic sectors worldwide. The transportation sector is one major greenhouse gas emitter which is heavily regulated to reduce its dependance on oil. These regulations along with the growing customer awareness about global warming has led vehicle manufacturers to seek di erent technologies to improve vehicle e ciencies and reduce the green house gases emissions while at the same time meeting customer's expectation of mobility and exibility. Plug-in hybrid electric vehicles (PHEV) is one major promising solution for a smooth transition from oil dependent transportation sector to a clean electric based sector while not compromising the mobility and exibility of the drivers. In the medium term, plug-in hybrid electric vehicles (PHEV) can lead to signi cant reductions in transportation emissions. These vehicles are equipped with a larger battery than regular hybrid electric vehicles which can be recharged from the grid. For short trips, the PHEV can depend solely on the electric engine while for longer journeys the alternative fuel can assist the electric engine to achieve extended ranges. This is bene cial when the use pattern is mixed such that and short long distances needs to be covered. The plug-in hybrid electric vehicles are well-suited for logistics since they can avoid the possible disruption caused by charge depletion in case of all-electric vehicles with tight time schedules. The use of electricity and fuel gives rise to a new variant of the classical vehicle routing with time windows which we call the plug-in hybrid electric vehicle routing problem with time windows (PHEVRPTW). The objective of the PHEVRPTW is to minimize the routing costs of a eet of PHEVs by minimizing the time they run on gasoline while meeting the demand during the available time windows. As a result, the driver of the PHEV has two decisions to make at each node: (1) recharge the vehicle battery to achieve a longer range using electricity, or (2) continue to the next open time window with the option of using the alternative fuel. In this thesis, we present a mathematical formulation for the plug-in hybrid-electric vehicle routing problem with time windows. We solve this problem using a Lagrangian relaxation and we propose a new tabu search algorithm. We also present the rst results for the full adapted Solomon instances

Hybridization of modified sine cosine algorithm with tabu search for solving quadratic assignment problem

Sine Cosine Algorithm (SCA) is a population-based metaheuristic method that widely used to solve various optimization problem due to its ability in stabilizing between exploration and exploitation. However, SCA is rarely used to solve discrete optimization problem such as Quadratic Assignment Problem (QAP) due to the nature of its solution which produce continuous values and makes it challenging in solving discrete optimization problem. The SCA is also found to be trapped in local optima since its lacking in memorizing the moves. Besides, local search strategy is required in attaining superior results and it is usually designed based on the problem under study. Hence, this study aims to develop a hybrid modified SCA with Tabu Search (MSCA-TS) model to solve QAP. In QAP, a set of facilities is assigned to a set of locations to form a one-to-one assignment with minimum assignment cost. Firstly, the modified SCA (MSCA) model with cost-based local search strategy is developed. Then, the MSCA is hybridized with TS to prohibit revisiting the previous solutions. Finally, both designated models (MSCA and MSCA-TS) were tested on 60 QAP instances from QAPLIB. A sensitivity analysis is also performed to identify suitable parameter settings for both models. Comparison of results shows that MSCA-TS performs better than MSCA. The percentage of error and standard deviation for MSCA-TS are lower than the MSCA which are 2.4574 and 0.2968 respectively. The computational results also shows that the MSCA-TS is an effective and superior method in solving QAP when compared to the best-known solutions presented in the literature. The developed models may assist decision makers in searching the most suitable assignment for facilities and locations while minimizing cost

Traveling Salesman Problem

This book is a collection of current research in the application of evolutionary algorithms and other optimal algorithms to solving the TSP problem. It brings together researchers with applications in Artificial Immune Systems, Genetic Algorithms, Neural Networks and Differential Evolution Algorithm. Hybrid systems, like Fuzzy Maps, Chaotic Maps and Parallelized TSP are also presented. Most importantly, this book presents both theoretical as well as practical applications of TSP, which will be a vital tool for researchers and graduate entry students in the field of applied Mathematics, Computing Science and Engineering

Traveling Salesman Problem

The idea behind TSP was conceived by Austrian mathematician Karl Menger in mid 1930s who invited the research community to consider a problem from the everyday life from a mathematical point of view. A traveling salesman has to visit exactly once each one of a list of m cities and then return to the home city. He knows the cost of traveling from any city i to any other city j. Thus, which is the tour of least possible cost the salesman can take? In this book the problem of finding algorithmic technique leading to good/optimal solutions for TSP (or for some other strictly related problems) is considered. TSP is a very attractive problem for the research community because it arises as a natural subproblem in many applications concerning the every day life. Indeed, each application, in which an optimal ordering of a number of items has to be chosen in a way that the total cost of a solution is determined by adding up the costs arising from two successively items, can be modelled as a TSP instance. Thus, studying TSP can never be considered as an abstract research with no real importance

Development of some local search methods for solving the vehicle routing problem

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