Honey Bee Mating Optimization (HBMO) Algorithm: Propelled Behavior of Bees Mating for Solving Optimization Problems

1. Introduction

      A new optimization algorithm based on honey bee mating, first proposed by Afshar et al. (2007), has been used to solve difficult optimization problems such as optimal reservoir operation (Haddad et al, 2007) and clustering (Fathian et al. 2007) [1]. Honey Bee mating Optimization Algorithm (HBMO) under different context by various researchers and their merits and demerits are discussed. Specifically, the method is compared with limitations of swarm intelligence features in similar application. HBMO on load profile and elucidate the constraints and convergence properties of the algorithm and highlights its application in solving certain current issues by enhancing its approach with innovative changes that could be adopted within the context and requirement of the problem to be addressed. Honey-bee is among the most closely studied social insects [2]. Honey-bee mating may also be considered as a typical swarm-based approach to optimization, in which the search algorithm is inspired by the process of marriage in real honey-bee. Honey-bee has been used to model agent-based systems. In a recent work, Abbas developed an optimization algorithm based on the honey-bee marriage process. Honey-bee mating optimization (HBMO) algorithm for continuous optimization problems and its application to a single reservoir problem, considering reservoir releases as continuous variables. The honey-bee mating optimization (HBMO) algorithm has been previously adopted to solve mathematical and engineering problems and has proven to be efficient for searching optimal solutions in large-problem domains [3].

     The honey-bee mating optimization (HBMO) algorithm is a typical swarm-based approach to optimization, in which the search algorithm is inspired by the honey-bee mating process. Bozorg Haddad et al. demonstrated the efficiency and applicability of the HBMO algorithm by applying it to well-known mathematical optimization problems and compared the final solutions with those from analytical methods and genetic algorithm (GA). The performance of the HBMO algorithm was comparable with the results of well-developed GAs. The HBMO algorithm can find the known optimum rapidly. Thus, the HBMO algorithm appears to be a suitable approach for project management problems [4].

2. Process of Honey Bees

Fig1: Process of Honey Bees

      The honey-bee mating optimization algorithm was proposed to mimic the mating and breeding of the queen of a hive. Its computation starts with a mating flight process by using an annealing function to select good solutions and store in the spermatheca. The crossover operator is then adopted to generate new offspring (new solutions) along with the random-walk strategy or hill-climbing to mimic the brood-feeding process [5]. The feasibility of this approach has been verified with applications to several problems, yet its parameters are still difficult to determine appropriately, thereby motivating an improvement strategy, such as the inclusion of a plant growth simulation algorithm proposed in this study. The plant growth simulation algorithm was developed based on the characterization of the growth mechanism of plant phototropism, where a higher morphactin concentration corresponds to a larger probability of growing a new branch [6]. By establishing the root model, those possible solutions grown from this root would be evaluated. Only certain solutions satisfying the constraints along with their fitness are superior to those of the root model and are saved for the subsequent search. This way of intelligent growth was recognized to alleviate the computational burden since the additional work of external parameter settings can be largely saved, while the optimization performance of the proposed approach is upgraded in the meantime. In this paper, we will enhance the honey-bee mating optimization with this plant growth simulation algorithm. We will also test the proposed approach through a sample system and two real cases. For all types of faults to analyze, the aim of such a study is to find the most probable fault location that may consist of single phase to ground, double phase, double phase to ground, and three-phase fault. The results will be compared with several published techniques to analyze the robustness and computation efficiency of the method [7].

      A honey-bee colony typically consists of a queen, drones, workers, and broods. Only the queen is capable of laying eggs. The drones are sires in the honey-bee colony; they are haploid and act to amplify their mothers’ genome without altering its genetic composition. The broods arise from either fertilized or unfertilized eggs.

3. Honey Bees Mating Optimization Algorithm (HBMO)

    Honey Bee Mating Optimization Algorithm (HBMO) is a search based optimization algorithm that mimics the mating behavior of Honey bee. In this method, Distributed Generators and loads that do not have constant output are considered as the state variables, in which the differences between measured and calculated values are assumed as the objective function. Honey bees are considered to perform one of the most complex communication tasks, in the animal world [8]. Indeed concepts of memory attention, recognition, understanding, interpretation, agreement, decision making, and knowledge as well questions about cognition and awareness have appeared regularly in honey bee literature. Bees are used to share info about location and nature of the resources. Honey bee mating algorithm can be considered as a general method based on insect behavior for optimization which, the search algorithm inspired from mating process in real bees life. Honey bee behavior is an interaction among genetic potential, physiologic and ecologic environment of hive social conditions and the hybrid of mentioned cases. A honey bee hive including: a queen with long life for laying eggs, about 10000 to 60000 worker bee, and up to hundreds of drone (according to the season). Queens have the main roll to generate some honey bee species, and laying eggs [9]. Drones are the hive father. They are mono-sexual and intensify the mother genes without changing in their genetic combination. Worker bees do laying eggs and mother-craft. Queen bee would feed by “royal jelly” that is a milky white jelly. Worker bees hide the dietary substances and consume it for the queen. This kind of feeding makes the queen larger than the others. The queen lives “between” 5-6 year, while the worker bees live about 6 months.

     Mating flight starts with a special dance by queen. Drones follow the queen and mate with her in the air. In a usual mating flight, she mates with about 7 to 20 drones. Sperms would collect in spermatheca and store there in any mating operation. Drones will die after mating, but their sperm would store in spermatheca. It means that queen will mate for several times and with several drones, but drones are able to mate for only one time. This kind of mating will make exclusive bees mating in comparison with the other insects. At the beginning of mating flight, queen’s energy is determined and at the end of any iteration – when queen return to the hive – her energy may reduce [10]. If her spermatheca has got full or her energy has reduced to zero, the queen would return to the hive. Any worker as an investigative function, promote the generation or take care a set of broods. At the beginning of a mating flight, drones are generated randomly and the queen selects a drone using the probabilistic rule [11].

Fig2: Honey Bee Mating Optimization Algorithm

3.1. Steps for HBMO Algorithm

  • Mating process
  • Crossover Operator
  • Mutation process

3.1.1. Mating Process

      Mating flight starts with a danced performed by the queen who then starts a mating flight during which the drones follow the queen and mate with her in the air. A drone mates with a queen probabilistically according to queen’s speed & fitness of the queen and drone [12]. Sperm of the drones will be deposited in the queen’s spermatheca to form the genetic pool of potential broods to be produced by the queen. The mating process which is based on crossover and mutation operation [13].

3.1.2. Crossover Operator

      The Second stage of evolutionary process starts after the genetic was filled with chromosomes and consists in breeding eggs with genetic information from spermatheca modified queen bee evolution model by using the weighted crossover operator and applied the algorithm for the tuning of input and output scaling factors [14]. Karci (2004) proposed a crossover operator type inspired by the sexual intercourses of honey bees. The operator selects a queen bee as a parent of crossover by the best fitness, worst fitness and sequentially. A novel crossover operator type inspired by the sexual intercourses of honeybees. The method selects a specific chromosome in present population as queen bee. While the selected queen bee is one parent of crossover, all the remaining chromosomes have the chance to the next parent for crossover each generation once.

  • In the first method, the chromosome with the best fitness score this queen honey bee and it is a fixed parent for cross over in current generation.
  • The second method handles the chromosome with the worst fitness score.
  • Finally, queen bee is changed sequentially in each generation.

3.1.3. Mutation Process

     Final stage of evolution process consists in raising the broods generated during the second stage, and creating a new generation of bee based on mutation process [15].

   Thus, an HBMO algorithm maybe constructed with the following five main stages:

  • The HBMO algorithm starts with the mating flight, where a queen (best solution) selects drones probabilistically to form the spermatheca. A drone then selected from the list randomly for the creation of broods. Creation of new broods by crossover the drone‘s genotypes with the queens.
  • Use of workers (heuristics) to conduct local search on broods (trial solutions).
  • Adaptation of worker‘s fitness, based on the amount of improvement achieved on broods.
  • Replacement of weaker queens by fitter broods.
  • Honey bee algorithm proposing is composed by three main a citrates.
  • Exploration recruitment.
  • Harvest.

3.2. Flow Chart of HBMO Algorithm

Fig3: Flowchart of HBMO Algorithm

3.3. HBMO process

                Natural Honey Bee            Artificial  Honey Bee
Mating, Breeding
Best Solution
Incumbent solution
New trial solution
Heuristic Search

4. Mathematical Methods of Honey Bee Mating Optimization (HBMO) Algorithm

     The mathematical methods of Honey Bee Mating Optimization (HBMO) Algorithm is given, Results from the GA and HBMO algorithm converge well with minor improvement in the HBMO solution [16].

5. Applications of HBMO Algorithm

  • Clustering [17]
  • Electricity generator
  • Economic dispatch
  • Image thresholding [18]
  • Traveling salesman problem
  • Feature selection problem [19]
Fig4: Applications of HBMO Algorithm

6. Advantages of HBMO Algorithm

  • The main disadvantage of the HBMO algorithm is the fact that it may miss the optimum, not strong enough to maximize the exploitation capacity and provide a near optimum solution in a limited runtime period [20].
  • Adaptability: HBMO algorithm respond better to rapidly changing environments, with their capabilities to adapt in a flexible manner [21].
  • Robustness: HBMO algorithm has the highest fault-tolerance capability and system keeps away from the risk of failure at most of the crucial circumstances [22].
  • Scalability: HBMO algorithms are highly scalable; their remarkable capacities are generally maintained when using applied to larger groups.
  • Integral Simplicity: HBMO algorithms are fairly simple to perform the functions with sufficient potential emerge as a sophisticated algorithm without losing the integral functions of the system [23].
  • Feedback control processes, artificial neurons, the DNA molecule description and similar genomics matters, studies of the behavior of natural immunological systems, and more, represent some of the very successful domains of this kind in a variety of real world applications [24].


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[8] Haddad, O., Afshar, A. and Mariño, M. (2006). Honey-Bees Mating Optimization (HBMO) Algorithm: A New Heuristic Approach for Water Resources Optimization. Water Resources Management, 20(5), pp.661-680.

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[12] Horng, M. and Jiang, T. (2011). Image vector quantization algorithm via honey bee mating optimization. Expert Systems with Applications, 38(3), pp.1382-1392.

[13] Ghasemi, A. (2013). A fuzzified multi objective Interactive Honey Bee Mating Optimization for Environmental/Economic Power Dispatch with valve point effect. International Journal of Electrical Power & Energy Systems, 49, pp.308-321.

[14] Marinaki, M., Marinakis, Y. and Zopounidis, C. (2010). Honey Bees Mating Optimization algorithm for financial classification problems. Applied Soft Computing, 10(3), pp.806-812.

[15] Shyh-Jier Huang, Xian-Zong Liu, Wei-Fu Su and Ting-Chia Ou (2013). Application of Enhanced Honey-Bee Mating Optimization Algorithm to Fault Section Estimation in Power Systems. IEEE Transactions on Power Delivery, 28(3), pp.1944-1951.

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[17] Niknam, T. (2008). Application of honey-bee mating optimization on state estimation of a power distribution system including distributed generators. Journal of Zhejiang University-SCIENCE A, 9(12), pp.1753-1764.

[18] Wen, X., Li, X., Gao, L. and Sang, H. (2012). Honey bees mating optimization algorithm for process planning problem. Journal of Intelligent Manufacturing, 25(3), pp.459-472.

[19] Sadjadi, S. and Soltani, R. (2012). Alternative design redundancy allocation using an efficient heuristic and a honey bee mating algorithm. Expert Systems with Applications, 39(1), pp.990-999.

[20] C. Yang and Q. Liu, “Algorithm of Marriage in Honey Bees Optimization Coperate with Linear Method”, Advanced Materials Research, vol. 871, pp. 330-337, 2013. Available: 10.4028/www.scientific.net/amr.871.330.

[21] Ming-Huwi Horng a,, Ren-Jean Liou b, Jun Wua ,”Parametric active contour model by using the honey bee mating optimization”. Expert Systems with Applications 37 (2010) 7015–7025.

[22] Qin-Ma Kanga,b,∗, Hong Heb, Hui-Min Songc, Rong Denga “Task allocation for maximizing reliability of distributed computing systems using honeybee mating optimization”. The Journal of Systems and Software 83 (2010) 2165–2174.

[23] Yannis Marinakis, Magdalene Marinaki, and Nikolaos Matsatsinis,”A Hybrid Clustering Algorithm Based on Honey Bees Mating Optimization and Greedy Randomized Adaptive Search Procedure”, Technical University of Crete, 73100.

[24] Seyed Jafar Sadjadi, Roya Soltani,”Alternative design redundancy allocation using an efficient heuristic and a honey bee mating algorithm”. Expert Systems with Applications 39 (2012) 990–999.

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