The Patch-Levy-Based Bees Algorithm Applied to Dynamic Optimization Problems

Many real-world optimization problems are actually of dynamic nature. These problems change over time in terms of the objective function, decision variables, constraints, and so forth. Therefore, it is very important to study the performance of a metaheuristic algorithm in dynamic environments to assess the robustness of the algorithm to deal with real-word problems. In addition, it is important to adapt the existing metaheuristic algorithms to perform well in dynamic environments. This paper investigates a recently proposed version of Bees Algorithm, which is called Patch-Levy-based Bees Algorithm (PLBA), on solving dynamic problems, and adapts it to deal with such problems. The performance of the PLBA is compared with other BA versions and other state-of-the-art algorithms on a set of dynamic multimodal benchmark problems of different degrees of difficulties. The results of the experiments show that PLBA achieves better results than the other BA variants. The obtained results also indicate that PLBA significantly outperforms some of the other state-of-the-art algorithms and is competitive with others

Multilevel Thresholding of Brain Tumor MRI Images: Patch-Levy Bees Algorithm versus Harmony Search Algorithm

Image segmentation of brain magnetic resonance imaging (MRI) plays a crucial role among radiologists in terms of diagnosing brain disease. Parts of the brain such as white matter, gray matter and cerebrospinal fluids (CFS), have to be clearly determined by the radiologist during the process of brain abnormalities detection. Manual segmentation is grueling and may be prone to error, which can in turn affect the result of the diagnosis. Nature-inspired metaheuristic algorithms such as Harmony Search (HS), which was successfully applied in multilevel thresholding for brain tumor segmentation instead of the Patch-Levy Bees algorithm (PLBA). Even though the PLBA is one powerful multilevel thresholding, it has not been applied to brain tumor segmentation. This paper focuses on a comparative study of the PLBA and HS for brain tumor segmentation. The test dataset consisting of nine images was collected from the Tuanku Muhriz UKM Hospital (HCTM). As for the result, it shows that the PLBA has significantly outperformed HS. The performance of both algorithms is evaluated in terms of solution quality and stability

Supply chain network design using an enhanced hybrid swarm-based optimization algorithm

This is the final version. Available from IGI Global via the DOI in this record. Supply chain network design is one of the most important strategic issues in operations management. The main objective in designing a supply chain is to keep the cost as low as possible. However, the modelling of a supply chain requires more than single-objective such as lead-time minimization, service level maximization, and environmental impact maximization among others. Usually these objectives may cause conflicts such as increasing the service level usually causes a growth in costs. Therefore, the aim should be to find trade-off solutions to satisfy the conflicting objectives. The aim of this chapter is to propose a new method based on a hybrid version of the Bees Algorithm with Slope Angle Computation and Hill Climbing Algorithm to solve a multi-objective supply chain network design problem. A real case from the literature has been selected and solved in order to show the potentiality of the proposed method in solving a large scale combinatorial problem

Diversifying search in bee algorithms for numerical optimisation

© Springer Nature Switzerland AG 2018. Swarm intelligence offers useful instruments for developing collective behaviours to solve complex, ill-structured and large-scale problems. Efficiency in collective behaviours depends on how to harmonise the individual contributions so that a complementary collective effort can be achieved to offer a useful solution. The harmonisation helps blend diversification and intensification suitably towards efficient collective behaviours. In this study, two renown honeybees-inspired algorithms were analysed with respect to the balance of diversification and intensification and a hybrid algorithm is proposed to improve the efficiency accordingly. The proposed hybrid algorithm was tested with solving well-known highly dimensional numerical optimisation (benchmark) problems. Consequently, the proposed hybrid algorithm has demonstrated outperforming the two original bee algorithms in solving hard numerical optimisation benchmarks

Cosine Harmony Search (CHS) for Static Optimization

Harmony Search (HS) is a behaviour imitation of a musician looking for the balance harmony. HS suffers to find the best parameter tuning especially for Pitch Adjustment Rate (PAR). PAR plays a crucial role in selecting historical solution and adjusting it using Bandwidth (BW) value. However, PAR in HS requires to be initialized with a constant value at the beginning step. On top of that, it also causes delay in convergence speed due to disproportion of global and local search capabilities. Even though, some HS variants claimed to overcome that shortcoming by introducing the self-modification of pitch adjustment rate, some of their justification were imprecise and required deeper and extensive experiments. Local Opposition-Based Learning Self-Adaptation Global Harmony Search (LHS) implements a heuristic factor, η for self-modification of PAR. It (η) manages the probability for selecting the adaptive step either as global or worst. If the value of η is large, the opportunity to select the global adaptive step is high, so the algorithm will further exploit for better harmony value. Otherwise, if η is small, the worst adaptive step is prone to be selected, therefore the algorithm will close to the global best solution. In this paper, regarding to the HS problem, we introduce a Cosine Harmony Search (CHS) by incorporating embedment of cosine and additional strategy rule with self-modification of pitch tuning to enlarge the exploitation capability of solution space. The additional strategy employs the η inspired by LHS and contains the cosine parameter. We test our proposed CHS on twelve standard static benchmark functions and compare it with basic HS and five state-of-the-art HS variants. Our proposed method and these state-of-the-art algorithms executed using 30 and 50 dimensions. The numerical results demonstrated that the CHS has outperformed with other state-of-the-art in accuracy and convergence speed evaluations

Enhancing the bees algorithm using the traplining metaphor

This work aims to improve the performance of the Bees Algorithm (BA), particularly in terms of simplicity, accuracy, and convergence. Three improvements were made in this study as a result of bees’ traplining behaviour. The first improvement was the parameter reduction of the Bees Algorithm. This strategy recruits and assigns worker bees to exploit and explore all patches. Both searching processes are assigned using the Triangular Distribution Random Number Generator. The most promising patches have more workers and are subject to more exploitation than the less productive patches. This technique reduced the original parameters into two parameters. The results show that the Bi-BA is just as efficient as the basic BA, although it has fewer parameters. Following that, another improvement was proposed to increase the diversification performance of the Combinatorial Bees Algorithm (CBA). The technique employs a novel constructive heuristic that considers the distance and the turning angle of the bees’ flight. When foraging for honey, bees generally avoid making a sharp turn. By including this turning angle as the second consideration, it can control CBA’s initial solution diversity. Third, the CBA is strengthened to enable an intensification strategy that avoids falling into a local optima trap. The approach is based on the behaviour of bees when confronted with threats. They will keep away from re-visiting those flowers during the next bout for reasons like predators, rivals, or honey run out. The approach will remove temporarily threatened flowers from the whole tour, eliminating the sharp turn, and reintroduces them again to the habitual tour’s nearest edge. The technique could effectively achieve an equilibrium between exploration and exploitation mechanisms. The results show that the strategy is very competitive compared to other population-based nature-inspired algorithms. Finally, the enhanced Bees Algorithms are demonstrated on two real-world engineering problems, namely, Printed Circuit Board insertion sequencing and vehicles routing problem

Enhancement of bees algorithm for global optimisation

This research focuses on the improvement of the Bees Algorithm, a swarm-based nature-inspired optimisation algorithm that mimics the foraging behaviour of honeybees. The algorithm consists of exploitation and exploration, the two key elements of optimisation techniques that help to find the global optimum in optimisation problems. This thesis presents three new approaches to the Bees Algorithm in a pursuit to improve its convergence speed and accuracy. The first proposed algorithm focuses on intensifying the local search area by incorporating Hooke and Jeeves’ method in its exploitation mechanism. This direct search method contains a pattern move that works well in the new variant named “Bees Algorithm with Hooke and Jeeves” (BA-HJ). The second proposed algorithm replaces the randomly generated recruited bees deployment method with chaotic sequences using a well-known logistic map. This new variant called “Bees Algorithm with Chaos” (ChaosBA) was intended to use the characteristic of chaotic sequences to escape from local optima and at the same time maintain the diversity of the population. The third improvement uses the information of the current best solutions to create new candidate solutions probabilistically using the Estimation Distribution Algorithm (EDA) approach. This new version is called Bees Algorithm with Estimation Distribution (BAED). Simulation results show that these proposed algorithms perform better than the standard BA, SPSO2011 and qABC in terms of convergence for the majority of the tested benchmark functions. The BA-HJ outperformed the standard BA in thirteen out of fifteen benchmark functions and is more effective in eleven out of fifteen benchmark functions when compared to SPSO2011 and qABC. In the case of the ChaosBA, the algorithm outperformed the standard BA in twelve out of fifteen benchmark functions and significantly better in eleven out of fifteen test functions compared to qABC and SPSO2011. BAED discovered the optimal solution with the least number of evaluations in fourteen out of fifteen cases compared to the standard BA, and eleven out of fifteen functions compared to SPSO2011 and qABC. Furthermore, the results on a set of constrained mechanical design problems also show that the performance of the proposed algorithms is comparable to those of the standard BA and other swarm-based algorithms from the literature

Animal distributions and movement behaviors in relation to resource dynamics

Animal movements, whether spatially constrained or spread across broad spatial scales, are often motivated by a need for resources. This thesis seeks to explore the role spatial and temporal resource dynamics may play in animal movements and population distributions. The first chapter synthesizes existing research of animal movements and builds a conceptual framework that integrates individual-level movement behaviors. It distinguishes among (1) non-oriented movements in response to proximate stimuli, (2) oriented movements utilizing perceptual cues of distant targets, and (3) memory mechanisms that assume prior knowledge of a target's location. I outline how species' use of these mechanisms should depend on resource dynamics and lead to population-level patterns, such as sedentary ranges, migration between disjunct and predictable seasonal resource areas, or nomadism when resource distributions are unpredictable in both space and time. The second chapter examines resource dynamics in an empirical setting, which, especially in ecosystems where changes may happen rapidly across broad spatial scales, is challenging because field measurements may be logistically infeasible. I use satellite imagery of vegetation productivity to track habitat dynamics for Mongolian gazelles in the eastern steppes of Mongolia. I show that spatiotemporal variation of gazelle habitats is extremely high, which may force gazelles to range over vast areas in search of food. This has important conservation implications because single protected areas may not provide sufficient gazelle habitats at all times and landscape level management plans are needed. In the third chapter I develop a theoretical simulation model, that implements and combines the three different classes of movement behaviors (non-oriented, oriented, memory) and explores their efficiency under different scenarios of resource dynamics. Adapting techniques from artificial evolution and intelligence, I show how individuals evolve to rely heavily on memory if their landscape dynamics are predictable. In contrast, non-oriented movement evolves predominately in situations where landscape dynamics are unpredictable. Oriented movement proves important at smaller scales, when movement targets are distributed within perceptual ranges. Future studies may transfer this theoretical model into empirical settings and use actual dynamic habitat models like that developed in chapter two, to reveal the underlying movement behaviors of real animals

Improvements on the bees algorithm for continuous optimisation problems

This work focuses on the improvements of the Bees Algorithm in order to enhance the algorithm’s performance especially in terms of convergence rate. For the first enhancement, a pseudo-gradient Bees Algorithm (PG-BA) compares the fitness as well as the position of previous and current bees so that the best bees in each patch are appropriately guided towards a better search direction after each consecutive cycle. This method eliminates the need to differentiate the objective function which is unlike the typical gradient search method. The improved algorithm is subjected to several numerical benchmark test functions as well as the training of neural network. The results from the experiments are then compared to the standard variant of the Bees Algorithm and other swarm intelligence procedures. The data analysis generally confirmed that the PG-BA is effective at speeding up the convergence time to optimum. Next, an approach to avoid the formation of overlapping patches is proposed. The Patch Overlap Avoidance Bees Algorithm (POA-BA) is designed to avoid redundancy in search area especially if the site is deemed unprofitable. This method is quite similar to Tabu Search (TS) with the POA-BA forbids the exact exploitation of previously visited solutions along with their corresponding neighbourhood. Patches are not allowed to intersect not just in the next generation but also in the current cycle. This reduces the number of patches materialise in the same peak (maximisation) or valley (minimisation) which ensures a thorough search of the problem landscape as bees are distributed around the scaled down area. The same benchmark problems as PG-BA were applied against this modified strategy to a reasonable success. Finally, the Bees Algorithm is revised to have the capability of locating all of the global optimum as well as the substantial local peaks in a single run. These multi-solutions of comparable fitness offers some alternatives for the decision makers to choose from. The patches are formed only if the bees are the fittest from different peaks by using a hill-valley mechanism in this so called Extended Bees Algorithm (EBA). This permits the maintenance of diversified solutions throughout the search process in addition to minimising the chances of getting trap. This version is proven beneficial when tested with numerous multimodal optimisation problems