Comparative Solutions of Exact and Approximate Methods for Traveling Salesman Problem

Hay dos métodos principales de optimización: Exact y aproximate. Un método exacto bien conocido, algoritmo de rama y atado (B&B) y métodos aproximados, el algoritmo de optimización de la mosca de la fruta basada en la eliminación (EFOA) y el algoritmo de átomo artificial (A3) se utilizan para resolver el problema del vendedor ambulante (TSP). Para 56 destinos, se compararán los resultados de la distancia total, el tiempo de procesamiento y la desviación entre el método exacto y el aproximado donde se encuentre la distancia entre dos destinos es una distancia euclídea y este estudio muestra que la distancia de B&B es 270, la EFOA es 270 y A3 es 288,38, lo que se desvía un 6,81%. Para el aspecto de procesamiento de tiempo, B&B necesita 12,5 días para procesar, EFOA necesita 36,59 segundos, A3 necesita 35,34 segundos. Pero para 29 destinos, el método exacto es más poderoso que el método aproximado.There are two major optimization methods: Exact and Approximate methods. A well known exact method, Branch and Bound algorithm (B&B) and approximate methods, Elimination-based Fruit Fly Optimization Algorithm (EFOA) and Artificial Atom Algorithm (A3) are used for solving the Traveling Salesman Problem (TSP). For 56 destinations, the results of total distance, processing time, and the deviation between exact and approximate method will be compared where the distance between two destinations is a Euclidean distance and this study shows that the distance of B&B is 270 , EFOA is 270 and A3 is 288.38 which deviates 6.81%. For time processing aspect, B&B needs 12.5 days to process, EFOA needs 36.59 seconds, A3 needs 35.34 seconds. But for 29 destinations, exact method is more powerful than approximate method

Scientific research trends about metaheuristics in process optimization and case study using the desirability function

This study aimed to identify the research gaps in Metaheuristics, taking into account the publications entered in a database in 2015 and to present a case study of a company in the Sul Fluminense region using the Desirability function. To achieve this goal, applied research of exploratory nature and qualitative approach was carried out, as well as another of quantitative nature. As method and technical procedures were the bibliographical research, some literature review, and an adopted case study respectively. As a contribution of this research, the holistic view of opportunities to carry out new investigations on the theme in question is pointed out. It is noteworthy that the identified study gaps after the research were prioritized and discriminated, highlighting the importance of the viability of metaheuristic algorithms, as well as their benefits for process optimization

Discrete Flower Pollination Algorithm for solving the symmetric Traveling Salesman Problem

A dissertation submitted in fulfilment of the requirements for the degree of Masters of Science in Engineering (Electrical) to the Faculty of Engineering and the Built Environment, University of the Witwatersrand, Johannesburg, 2017The Travelling Salesman Problem (TSP) is an important NP-hard combinatorial optimisation problem that forms the foundation of many modern-day, practical problems such as logistics or network route planning. It is often used to benchmark discrete optimisation algorithms since it is a fundamental problem that has been widely researched. The Flower Pollination Algorithm (FPA) is a continuous optimisation algorithm that demonstrates promising results in comparison to other well-known algorithms. This research proposes the design, implementation and testing of two new algorithms based on the FPA for solving discrete optimisation problems, more specifically the TSP, namely the Discrete Flower Pollination Algorithm (DFPA) and the iterative Discrete Flower Pollination Algorithm (iDFPA). The iDFPA uses two proposed update methods, namely the Best Tour Update (BTU) and the Rejection Update (RU), to perform the iterative update process. The two algorithms are compared to the Ant Colony Optimisation’s (ACO) MAX−MIN Ant System (MMAS) as well as the Genetic Algorithm (GA) since they are well studied and developed. The DFPA and iDFPA results are significantly better than the GA and the iDFPA is able to outperform the ACO in all tested instances. The iDFPA with 300 iterations was able to achieve the optimal solution in the Berlin52 benchmark TSP problem as well as have improvements of up to 4.56% and 41.87% compared to the ACO and GA respectively. An analysis of how the RU and the annealing schedule used in the RU impacts on the overall results of the iDFPA is given. The RU analysis demonstrates how the annealing schedule can be manipulated to achieve certain results from the iDFPA such as faster convergence or better overall results. A parameter analysis is performed on both the DFPA and iDFPA for different TSP problem sizes and the suggested initial parameters for these algorithms are outlined.XL201

An Overview of Evolutionary Algorithms toward Spacecraft Attitude Control

Evolutionary algorithms can be used to solve interesting problems for aeronautical and astronautical applications, and it is a must to review the fundamentals of the most common evolutionary algorithms being used for those applications. Genetic algorithms, particle swarm optimization, firefly algorithm, ant colony optimization, artificial bee colony optimization, and the cuckoo search algorithm are presented and discussed with an emphasis on astronautical applications. In summary, the genetic algorithm and its variants can be used for a large parameter space but is more efficient in global optimization using a smaller chromosome size such that the number of parameters being optimized simultaneously is less than 1000. It is found that PID controller parameters, nonlinear parameter identification, and trajectory optimization are applications ripe for the genetic algorithm. Ant colony optimization and artificial bee colony optimization are optimization routines more suited for combinatorics, such as with trajectory optimization, path planning, scheduling, and spacecraft load bearing. Particle swarm optimization, firefly algorithm, and cuckoo search algorithms are best suited for large parameter spaces due to the decrease in computation need and function calls when compared to the genetic algorithm family of optimizers. Key areas of investigation for these social evolution algorithms are in spacecraft trajectory planning and in parameter identification

PID Tuning of Servo Motor Using Bat Algorithm

AbstractThe Proportional-Integral-Derivative (PID) controller uses three parameters to produce the desired output of a system. The desired system performances are in terms of overshoot, rise time, settling time and steady state error. This has brought about various methods to tune the controller to the desired response. Therefore, the presence of the bat algorithm as part of the system will reduce the time and cost of tuning these parameters and improve the overall system performance

Comparative analysis of evolutionary-based maximum power point tracking for partial shaded photovoltaic

The characteristics of the photovoltaic module are affected by the level of solar irradiation and the ambient temperature. These characteristics are depicted in a V-P curve. In the V-P curve, a line is drawn that shows the response of changes in output power to the level of solar irradiation and the response to changes in voltage to ambient temperature. Under partial shading conditions, photovoltaic (PV) modules experience non-uniform irradiation. This causes the V-P curve to have more than one maximum power point (MPP). The MPP with the highest value is called the global MPP, while the other MPP is the local MPP. The conventional MPP tracking technique cannot overcome this partial shading condition because it will be trapped in the local MPP. This article discusses the MPP tracking technique using an evolutionary algorithm (EA). The EAs analyzed in this article are genetic algorithm (GA), firefly algorithm (FA), and fruit fly optimization (FFO). The performance of MPP tracking is shown by comparing the value of the output power, accuracy, time, and tracking effectiveness. The performance analysis for the partial shading case was carried out on various populations and generations

Time-Optimal Trajectory Generation and Way-Point Sequencing for 5-Axis Laser Drilling

Laser drilling provides a highly productive method for producing arrays of holes on planar and freeform shaped components. Industrial applications include fuel injection nozzles, printed circuit boards (PCB’s), inkjet printer heads, pinholes and slits for scientific instrumentation, high-resolution circuitry, sensors, fiber-optic interconnects, medical devices, and gas turbine combustion chamber panels. This thesis deals with time-optimal trajectory planning for two mainstream laser drilling methods: on-the-fly drilling and percussion drilling, which are used in the aerospace industry. The research has been conducted in collaboration with the Canadian aero-engine producer, Pratt & Whitney Canada (P&WC). The algorithms developed have been tested in a target application involving the laser drilling of cooling hole arrays on gas turbine engine combustion chamber panels. On-the-fly drilling is an operation in which each hole receives one low powered shot at a time while the workpiece is in motion, and the beam focal point is continuously proceeding to the next hole location. The positioning sequence repeats itself until all holes are gradually opened up in small increments. Each hole location has ample time to cool down before the next shot is received. Thus, this process can yield favorable material properties in terms of preserving the desired crystal structure, and also hole quality in terms of dimensional (size) and form (shape) accuracy, due to the reduction of local thermal loading. However, there is no existing trajectory planner, in industry, or in literature, capable of generating time-optimized positioning trajectories for on-the-fly laser drilling. This thesis studies this problem and presents a new algorithm, capable of handling 5 degree-of-freedom (axis) positioning capability. The ability to generate spline-based smooth trajectories is integrated within a Traveling Salesman Problem (TSP) type sequencing algorithm. The sequencing algorithm optimizes both the order of the waypoints (i.e., hole locations) and also the timing levels in between, which affect the temporal (time-dependent) nature of the motions commanded to the laser drilling machine’s actuators. Furthermore, the duration between consecutive holes has to be an integer multiple of the laser pulsing period, considering a machine configuration in which the laser is firing at a constant frequency, and unused pulses are diverted away using a quick shutter. It is shown that the proposed algorithm is capable of generating 17-25% reduction in the beam positioning time spent during a manufacturing cycle, compared to some of the contemporary practices in industry. 17% reduction in the vibrations induced onto the laser optics is also observed, which helps prevent downtime due to the optics hardware gradually losing alignment. The second type of laser drilling operation for which optimized 5-axis trajectory planning has been developed is percussion drilling. In this process, a series of pulses are sent to each hole while the part is stationary. Once the hole is completely opened up, then positioning to the next hole proceeds. While percussion drilling is less advantageous in terms of local thermal loading and achievable part quality, it is used extensively in industry; due to its simplicity of automation compared to on-the-fly drilling. Thus, a TSP-style trajectory planning algorithm has also been developed for percussion laser drilling. The novelty, in this case, is concurrent planning of 5-axis time-optimal point-to-point movements within the sequencing algorithm, and direct minimization of the total travel time, rather than just distance (in two Cartesian axes); as is the method for which significant portion of TSP solvers and trajectory planners in literature have been developed. Compared to currently applied methods at P&WC, 32-36% reduction in the beam positioning time has been achieved. Also, 39-45% reduction in the peak magnitude of vibration has been realized. Limited benchmarking with state-of-the-art TSP solvers from combinatorial mathematics, considering only 2-axis Euclidean distance as the objective function, indicate that the proposed sequencing algorithm for percussion drilling is sub-optimal by 9-12%. Thus, it can still use further improvement in future research. Nevertheless, the two trajectory planners that have been developed in this thesis for on-the-fly drilling and percussion drilling have experimentally demonstrated very promising improvements in terms of motion time and smoothness. As more advanced Computer Numerical Control (CNC) systems and laser control electronics with deterministic execution and rapid synchronization capability become available, such algorithms are expected to facilitate significant production gains in laser drilling processes used in different industries

Spontaneous Fruit Fly Optimisation for truss weight minimisation:Performance evaluation based on the no free lunch theorem

Over the past decade, several researchers have presented various optimisation algorithms for use in truss design. The no free lunch theorem implies that no optimisation algorithm fits all problems; therefore, the interest is not only in the accuracy and convergence rate of the algorithm but also the tuning effort and population size required for achieving the optimal result. The latter is particularly crucial for computationally intensive or high-dimensional problems. Contrast-based Fruit-fly Optimisation Algorithm (c-FOA) proposed by Kanarachos et al. in 2017 is based on the efficiency of fruit flies in food foraging by olfaction and visual contrast. The proposed Spontaneous Fruit Fly Optimisation (s-FOA) enhances c-FOA and addresses the difficulty in solving nonlinear optimisation algorithms by presenting standard parameters and lean population size for use on all optimisation problems. Six benchmark problems were studied to assess the performance of s-FOA. A comparison of the results obtained from documented literature and other investigated techniques demonstrates the competence and robustness of the algorithm in truss optimisation.Comment: Presented at the International conference for sustainable materials, energy and technologies, 201