Firefly algorithm is a nature-inspired metaheuristic algorithm inspired by the flashing behavior of fireflies. It is originally proposed for continuous problems. However, due to its effectiveness and success in solving continuous problems, different studies are conducted in modifying the algorithm to suit discrete problems. Many engineering as well as optimization problems from other disciplines involve discrete variables. Recent reviews on the application and modifications of firefly algorithm mainly focus on continuous problems. This paper is devoted to the detailed review of the modifications done on firefly algorithm in order to solve optimization problems with discrete variables. Hence, advances on the application of firefly algorithm for optimization problems with binary, integer as well as mixed variables will be discussed. Possible future works will also be highlighted.

Firefly algorithm for discrete optimization problems: A survey

Firefly algorithm is one of the well-known swarm-based algorithms which gained popularity within a short time and has different applications. It is easy to understand and implement. The existing studies show that it is prone to premature convergence and suggest the relaxation of having constant parameters. To boost the performance of the algorithm, different modifications are done by several researchers. In this chapter, we will review these modifications done on the standard firefly algorithm based on parameter modification, modified search strategy and change the solution space to make the search easy using different probability distributions. The modifications are done for continuous as well as non-continuous problems. Different studies including hybridization of firefly algorithm with other algorithms, extended firefly algorithm for multiobjective as well as multilevel optimization problems, for dynamic problems, constraint handling and convergence study will also be briefly reviewed. A simulationbased comparison will also be provided to analyse the performance of the standard as well as the modified versions of the algorithm.

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A Review and Comparative Study of Firefly Algorithm and its Modified Versions

Transportation problems, which concerned in finding the minimum cost of transporting a single commodity from a given number of sources to a given number of destinations, are an integral part of the industrial system that has been around for a long time. The number of potential losses caused by transportation problems has made many parties take initiatives and efforts to solve those problems, usually by designing an optimal distribution model. The current study employs two methods named North West Corner (NWC) and Stepping Stone (SS) method in order to find distribution model with the most optimal costs for common good products. Through this research, the NWC method is utilized to generate initial model or solution, while the SS method is used afterward to find the optimal solution. According to it scheme, the result shows that through the NWC method there was cost reduction of $ 8,301, while the distribution model obtained from the Stepping Stone method resulted in a significant cost increased of $ 307,369. Thus, it can be concluded that the use of single method, namely NWC method, in this study provides much better results than using the combined NWC and Stepping Stone method.

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The optimization of distribution and transportation costs for common good products

Most world class universities are like small cities because of their sizes and compositions. They therefore face urban transportation problems due to increase in human activities. This paper looks at minimizing the time spent to move from one point to another in Covenant University. Covenant University is a potential world class university whose fast growth in the past twelve years can lead to transportation problems in the future if the transportation system is not properly planned. Transportation problem is one of the major areas of application of linear programming. Google map was used to calculate the distance and time it takes to move from one point to the other in the University. Three transportation methods: Northwest corner method, least cost method and Vogel Approximation method were used to find the initial feasible solution, while MODI method was used to find the optimal solution. The optimal solution shows that the movement of people and goods can be enhanced in Covenant University if time spent to move from one point to another is reduced. Reduction in the time spent reduces stress and results in having more time to attend to more pressing issues.

Enhancing the Movement of People and Goods in A Potential World Class University using Transportation Model

A systematic and organized overview of various existing transportation problems and their extensions developed by different researchers is offered in the review article. The article has gone through different research papers and books available in Google scholar, Sciencedirect, Z-library Asia, Springer.com, Research-gate, shodhganga, and many other E-learning platforms. The main purpose of the review paper is to recapitulate the existing form of various types of transportation problems and their systematic developments for the guidance of future researchers to help them classify the varieties of problems to be solved and select the criteria to be optimized.

A Comprehensive Literature Review on Transportation Problems

Transportation problem is considered a vitally important aspect that has been studied in a wide range of operations including research domains. As such, it has been used in simulation of several real life problems. Thus, optimizing transportation problem of variables has remarkably been significant to various disciplines. In this paper, three variables will be optimized to reduce transportation cost using four methods which will include: Northwest corner method, least cost method, Vogel method and modi method. This will mainly aim at finding the best and cheapest route on how supply will be used to satisfy demand at specific points. This will imply that, a variable cost of shipping products from suppliers to demand points will be considered.

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Rekha Vivek Joshi

Papers

Optimization Techniques for Transportation Problems of Three Variables