IK-FA, a new heuristic inverse kinematics solver using firefly algorithm

In this paper, a heuristic method based on Firefly Algorithm is proposed for inverse kinematics problems in articulated robotics. The proposal is called, IK-FA. Solving inverse kinematics, IK, consists in finding a set of joint-positions allowing a specific point of the system to achieve a target position. In IK-FA, the Fireflies positions are assumed to be a possible solution for joints elementary motions. For a robotic system with a known forward kinematic model, IK-Fireflies, is used to generate iteratively a set of joint motions, then the forward kinematic model of the system is used to compute the relative Cartesian positions of a specific end-segment, and to compare it to the needed target position. This is a heuristic approach for solving inverse kinematics without computing the inverse model. IK-FA tends to minimize the distance to a target position, the fitness function could be established as the distance between the obtained forward positions and the desired one, it is subject to minimization. In this paper IK-FA is tested over a 3 links articulated planar system, the evaluation is based on statistical analysis of the convergence and the solution quality for 100 tests. The impact of key FA parameters is also investigated with a focus on the impact of the number of fireflies, the impact of the maximum iteration number and also the impact of (a, ß, ¿, d) parameters. For a given set of valuable parameters, the heuristic converges to a static fitness value within a fix maximum number of iterations. IK-FA has a fair convergence time, for the tested configuration, the average was about 2.3394 × 10-3 seconds with a position error fitness around 3.116 × 10-8 for 100 tests. The algorithm showed also evidence of robustness over the target position, since for all conducted tests with a random target position IK-FA achieved a solution with a position error lower or equal to 5.4722 × 10-9.Peer ReviewedPostprint (author's final draft

Optimizing Firefly Algorithm for Directional Overcurrent Relay Coordination: A case study on the Impact of Parameter Settings

This paper investigates the application of the Firefly Algorithm for solving the coordination problem in the IEEE 3-bus network. It analyzes the impact of key parameters, including the number of generations, population size, absorption coefficient (γ), and randomization parameter (α), on the algorithms performance. Through extensive experimentation, the study demonstrates the impact on solution quality, feasibility, computational requirements, and efficiency. Results indicate that increasing the number of generations improves solution quality, but benefits diminish beyond a certain point. Feasibility improves with higher generations, but a balance between solution quality and feasibility becomes apparent at very high generations. Objective function evaluations and computation time increase linearly with generations. Larger population sizes yield better solution quality and feasibility, but a balance is observed at very high population sizes. Objective function evaluations and computation time scale proportionally with population size. The randomization parameter has a modest influence on performance, with no significant changes observed. However, extreme values impact solution quality, feasibility, and computation time. The absorption coefficient significantly affects convergence and solution quality. Lower values expedite convergence but may lead to suboptimal solutions, while higher values enhance exploration at the cost of increased computational effort. This study provides a comprehensive understanding of parameter selection and optimization in the Firefly Algorithm for solving the coordination problem of the IEEE 3-bus network, offering valuable guidance for future research in enhancing performance through parameter refinement and adaptive techniques

Makespan minimizing on multiple travel salesman problem with a learning effect of visiting time

-The multiple traveling salesman problem (MTSP) involves the assignment and sequencing procedure simultaneously. The assignment of a set of nodes to each visitors and determining the sequence of visiting of nodes for each visitor. Since specific range of process is needed to be carried out in nodes in commercial environment, several factors associated with routing problem are required to be taken into account. This research considers visitors’ skill and category of customers which can affect visiting time of visitors in nodes. With regard to learning-by-doing, visiting time in nodes can be reduced. And different class of customers which are determined based on their potential purchasing of power specifies that required time for nodes can be vary. So, a novel optimization model is presented to formulate MTSP, which attempts to ascertain the optimum routes for salesmen by minimizing the makespan to ensure the balance of workload of visitors. Since this problem is an NP-hard problem, for overcoming the restriction of exact methods for solving practical large-scale instances within acceptable computational times. So, Artificial Immune System (AIS) and the Firefly (FA) metaheuristic algorithm are implemented in this paper and algorithms parameters are calibrated by applying Taguchi technique. The solution methodology is assessed by an array of numerical examples and the overall performances of these metaheuristic methods are evaluated by analyzing their results with the optimum solutions to suggested problems. The results of statistical analysis by considering 95% confidence interval for calculating average relative percentage of deviation (ARPD) reveal that the solutions of proposed AIS algorithm has less variation and Its’ confidence interval of closer than to zero with no overlapping with that of FA. Although both proposed meta-heuristics are effective and efficient in solving small-scale problems, in medium and large scales problems, AIS had a better performance in a shorter average time. Finally, the applicability of the suggested pattern is implemented in a case study in a specific company, namely Kalleh

Application of Firefly Algorithm and Its Parameter Setting for Job Shop Scheduling

AbstractJob shop scheduling problem (JSSP) is one of the most famous scheduling problems, most of which are categorisedinto Non-deterministic Polynomial (NP) hard problem. The objectives of this paper are to i) present the application of a recent developed metaheuristic called Firefly Algorithm (FA) for solving JSSP; ii) investigate the parameter setting of the proposed algorithm; and iii) compare the FA performance using various parameter settings. The computational experiment was designed and conducted using five benchmarking JSSP datasets from a classical OR-Library. The analysis of the experimental results on the FA performance comparison between with and without using optimised parameter settings was carried out. The FA with appropriate parameters setting that got from the experiment analysis produced the best-so-far schedule better than the FA withoutadopting parameter settings

Nature-inspired Methods for Stochastic, Robust and Dynamic Optimization

Nature-inspired algorithms have a great popularity in the current scientific community, being the focused scope of many research contributions in the literature year by year. The rationale behind the acquired momentum by this broad family of methods lies on their outstanding performance evinced in hundreds of research fields and problem instances. This book gravitates on the development of nature-inspired methods and their application to stochastic, dynamic and robust optimization. Topics covered by this book include the design and development of evolutionary algorithms, bio-inspired metaheuristics, or memetic methods, with empirical, innovative findings when used in different subfields of mathematical optimization, such as stochastic, dynamic, multimodal and robust optimization, as well as noisy optimization and dynamic and constraint satisfaction problems

A survey of swarm intelligence for dynamic optimization: algorithms and applications

Swarm intelligence (SI) algorithms, including ant colony optimization, particle swarm optimization, bee-inspired algorithms, bacterial foraging optimization, firefly algorithms, fish swarm optimization and many more, have been proven to be good methods to address difficult optimization problems under stationary environments. Most SI algorithms have been developed to address stationary optimization problems and hence, they can converge on the (near-) optimum solution efficiently. However, many real-world problems have a dynamic environment that changes over time. For such dynamic optimization problems (DOPs), it is difficult for a conventional SI algorithm to track the changing optimum once the algorithm has converged on a solution. In the last two decades, there has been a growing interest of addressing DOPs using SI algorithms due to their adaptation capabilities. This paper presents a broad review on SI dynamic optimization (SIDO) focused on several classes of problems, such as discrete, continuous, constrained, multi-objective and classification problems, and real-world applications. In addition, this paper focuses on the enhancement strategies integrated in SI algorithms to address dynamic changes, the performance measurements and benchmark generators used in SIDO. Finally, some considerations about future directions in the subject are given

Enhanced Cuckoo Search Algorithm for Virtual Machine Placement in Cloud Data Centers

In order to enhance resource utilisation and power efficiency in cloud data centres it is important to perform Virtual Machine (VM) placement in an optimal manner. VM placement uses the method of mapping virtual machines to physical machines (PM). Cloud computing researchers have recently introduced various meta-heuristic algorithms for VM placement considering the optimised energy consumption. However, these algorithms do not meet the optimal energy consumption requirements. This paper proposes an Enhanced Cuckoo Search (ECS) algorithm to address the issues with VM placement focusing on the energy consumption. The performance of the proposed algorithm is evaluated using three different workloads in CloudSim tool. The evaluation process includes comparison of the proposed algorithm against the existing Genetic Algorithm (GA), Optimised Firefly Search (OFS) algorithm, and Ant Colony (AC) algorithm. The comparision results illustrate that the proposed ECS algorithm consumes less energy than the participant algorithms while maintaining a steady performance for SLA and VM migration. The ECS algorithm consumes around 25% less energy than GA, 27% less than OFS, and 26% less than AC

Energy-Efficient Virtual Machine Placement using Enhanced Firefly Algorithm

The consolidation of the virtual machines (VMs) helps to optimise the usage of resources and hence reduces the energy consumption in a cloud data centre. VM placement plays an important part in the consolidation of the VMs. The researchers have developed various algorithms for VM placement considering the optimised energy consumption. However, these algorithms lack the use of exploitation mechanism efficiently. This paper addresses VM placement issues by proposing two meta-heuristic algorithms namely, the enhanced modified firefly algorithm (MFF) and the hierarchical cluster based modified firefly algorithm (HCMFF), presenting the comparative analysis relating to energy optimisation. The comparisons are made against the existing honeybee (HB) algorithm, honeybee cluster based technique (HCT) and the energy consumption results of all the participating algorithms confirm that the proposed HCMFF is more efficient than the other algorithms. The simulation study shows that HCMFF consumes 12% less energy than honeybee algorithm, 6% less than HCT algorithm and 2% less than original firefly. The usage of the appropriate algorithm can help in efficient usage of energy in cloud computing