Chu-Beasley Genetic Algorithm Research Articles

A hybrid heuristic approach for the multi-objective multi depot vehicle routing problem

Efficiency in logistics is often affected by the fair distribution of the customers along the routes and the available depots for goods delivery. From this perspective, in this study, the Multi-depot Vehicle Routing Problem (MDVRP), by considering two objectives, is addressed. The two objectives in conflict for MDVRP are the distance traveled by vehicles and the standard deviation of the routes’ length. A significant standard deviation value provides a small distance traveled by vehicles, translated into unbalanced routes. We have used a weighted average objective function involving the two objectives. A Variable Neighborhood Search algorithm within a Chu-Beasley Genetic Algorithm has been proposed to solve the problem. For decision-making purposes, several values are chosen for the weight factors multiplying the terms at the objective function to build up a non-dominated front of solutions. The methodology is tested in large-size instances for the MDVRP, reporting noticeable results for managerial insights.

A new matheheuristic approach based on Chu-Beasley genetic approach for the multi-depot electric vehicle routing problem

Operations with Electric Vehicles (EVs) on logistic companies and power utilities are increasingly related due to the charging stations representing the point of standard coupling between transportation and power networks. From this perspective, the Multi-depot Electric Vehicle Routing Problem (MDEVRP) is addressed in this research, considering a novel hybrid matheheuristic approach combining exact approaches and a Chu-Beasley Genetic Algorithm. An existing conflict is shown in three objectives handled through the experimentations: routing cost, cost of charging stations, and increased cost due to energy losses. EVs driving range is chosen as the parameter to perform the sensitivity analysis of the proposed MDEVRP. A 25-customer transportation network conforms to a newly designed test instance for methodology validation, spatially combined with a 33 nodes power distribution system.

Implementation of a new matheuristic to solve the vehicle routing problem with simultaneous deliveries and pick-ups – VRPSPD

The objective of this article is to present a new methodology for solving the Homogeneous Vehicle Routing Problem with Simultaneous Pickups and Deliveries (VRPSPD). The methodology integrates a matheuristic using the Chu-Beasley genetic algorithm and mixed integer linear programming, based on the Branch-and-Bound procedure. The best configuration obtained from the genetic algorithm is improved through the use of constructive heuristic methods in determining sub-problems, which contribute to the creation of the initial population necessary in the stage of local improvement. The goal is to determine minimum-cost routes that satisfy the pick-up and delivery demands of a group of geographically dispersed customers, while considering the restrictions of the system and the number of vehicles required. The methodology is implemented in C++ and a solver CPLEX software is used to find the solution. Results from test instances in specialized literature demonstrate the efficiency of this new hybrid model, showing good results in short computation times. This article is based on the author's doctoral thesis in engineering and presents similar topics discussed in international congresses, which may explain the similarities in the consulted bibliographical references.

Chu and Beasley Genetic Algorithm to Solve the Transmission Network Expansion Planning Problem Considering Active Power Losses

Due to the accelerated growth of electricity demand, the scarcity of primary resources to produce electricity, and technological advances in recent years, electricity companies must face and solve these challenges in the best possible way, and for that, the Transmission Network Expansion Planning (TNEP) plays a crucial role, since the decisions taken in longterm planning determine the optimal form of expansion of the networks, to respond to these needs of electricity demands. On the other hand, there is also the tendency to leave the TNEP problem more efficient, robust, and closer to what happens in real electrical networks. For these reasons, this article proposes a methodology to solve the TNEP problem considering active power losses. The problem is formulated as a mixed-integer nonlinear programming (MINLP) problem. The Chu-Beasley Genetic Algorithm (CBGA) is used to transform the MINLP problem into a linear programming (LP) problem. Furthermore, the Villasana Garver constructive heuristic (VGCH) algorithm is used to make the investment proposals made by the AGCB feasible. To measure the efficiency and effectiveness of the proposed methodology several tests are performed on the 6- bus Garver system, the IEEE 24-bus test system, and the South Brazilian 46-bus test system

Optimal Placement and Sizing of D-STATCOM in Radial and Meshed Distribution Networks Using a Discrete-Continuous Version of the Genetic Algorithm

In this paper, we propose a new discrete-continuous codification of the Chu–Beasley genetic algorithm to address the optimal placement and sizing problem of the distribution static compensators (D-STATCOM) in electrical distribution grids. The discrete part of the codification determines the nodes where D-STATCOM will be installed. The continuous part of the codification regulates their sizes. The objective function considered in this study is the minimization of the annual operative costs regarding energy losses and installation investments in D-STATCOM. This objective function is subject to the classical power balance constraints and devices’ capabilities. The proposed discrete-continuous version of the genetic algorithm solves the mixed-integer non-linear programming model that the classical power balance generates. Numerical validations in the 33 test feeder with radial and meshed configurations show that the proposed approach effectively minimizes the annual operating costs of the grid. In addition, the GAMS software compares the results of the proposed optimization method, which allows demonstrating its efficiency and robustness.

Accurate and Efficient Derivative-Free Three-Phase Power Flow Method for Unbalanced Distribution Networks

The power flow problem in three-phase unbalanced distribution networks is addressed in this research using a derivative-free numerical method based on the upper-triangular matrix. The upper-triangular matrix is obtained from the topological connection among nodes of the network (i.e., through a graph-based method). The main advantage of the proposed three-phase power flow method is the possibility of working with single-, two-, and three-phase loads, including Δ- and Y-connections. The Banach fixed-point theorem for loads with Y-connection helps ensure the convergence of the upper-triangular power flow method based an impedance-like equivalent matrix. Numerical results in three-phase systems with 8, 25, and 37 nodes demonstrate the effectiveness and computational efficiency of the proposed three-phase power flow formulation compared to the classical three-phase backward/forward method and the implementation of the power flow problem in the DigSILENT software. Comparisons with the backward/forward method demonstrate that the proposed approach is 47.01%, 47.98%, and 36.96% faster in terms of processing times by employing the same number of iterations as when evaluated in the 8-, 25-, and 37-bus systems, respectively. An application of the Chu-Beasley genetic algorithm using a leader–follower optimization approach is applied to the phase-balancing problem utilizing the proposed power flow in the follower stage. Numerical results present optimal solutions with processing times lower than 5 s, which confirms its applicability in large-scale optimization problems employing embedding master–slave optimization structures.

Hybrid Optimization Strategy for Optimal Location and Sizing of DG in Distribution Networks

Objective: In this paper, is present a hybrid optimization methodology for the optimal location and sizing of distributed generators (DGs) in electrical distribution networks. We propose a mixed-integer nonlinear problem (MINLP) model for the mathematical formulation, whose objective function is the minimization of power losses due to the Joule effect in conductors. The constraints we considered include active and reactive power balance, voltage regulation, percentage of penetration of DGs into the distribution network, and total DGs allowed in such network.
 Methodology: To solve the MINLP model, we employed a master–slave strategy that uses the Chu-Beasley genetic algorithm (CBGA) and the optimal power flow (OPF) model as the master and slave algorithms, respectively. This hybrid technique helps to reduce the complexity of the MINLP model by eliminating binary variables through the master algorithm and then solving the resulting Nonlinear problem (NLP), which corresponds to the OPF model, using a classical interior-point method available in MATLAB’s fmincon toolbox.
 Results: We tested the efficiency and robustness of the proposed methodology in 33- and 69-node radial distribution networks. The results show its high performance in terms of power loss reduction and final sizing of DGs
 Conclusions: The results obtained in the test systems under analysis reveal that there is a direct and proportional relationship between technical losses, the percentage of distributed generation penetration, and the number of generators available.

Vortex search and Chu-Beasley genetic algorithms for optimal location and sizing of distributed generators in distribution networks: A novel hybrid approach

In this study, we analyzed the optimal location and sizing of distributed generators (DGs) in radial distributed networks using a hybrid master-slave metaheuristic technique. The master stage corresponds to the selection of suitable points for the locations of the DGs, whereas the slave stage is the optimal dimensioning problem. The Chu-Beasley genetic algorithm (CBGA) is employed to solve the master stage, and the optimal power flow (OPF) method via the vortex search algorithm (VSA) is employed to solve the slave stage. The OPF solution from the VSA technique uses a successive approximation power flow to determine the voltage profiles and power losses by guaranteeing the energy balance in all the nodes of the network. The conventional and widely used 33- and 69-node test feeders are used to validate the hybrid CBGA-VSA for analyzing the optimal location and sizing of the DGs in the distribution networks using MATLAB software. The numerical results demonstrate the efficiency of the proposed optimization method in terms of power loss reduction as compared with the results available in the literature. An additional 24-h dimensioning analysis is included for demonstrating the efficiency and applicability of the proposed methodology for daily operations with renewable generation.

Impact of optimal location and sizing of distributed generation and automatic reclosers in distribution systems

In this paper, a cascade methodology of two stages to solve the problem of the optimal location and sizing of distributed generators (DG), and determining an adequate protection scheme to improve reliability indices and reduce the non-supplied energy level (NSEL) is proposed. In stage 1, the optimal location of DG is determined by using a mathematical model, in which the objective function is composed by a linear combination between reduction of power losses and investment cost. To solve this problem, three sensitivity indices to determine a candidate set of nodes to install DG and three types of technologies are considered. A hybrid methodology based on Chu-Beasley genetic algorithm and particle swarm optimisation is used as a solution technique. In stage 2, normally closed and normally open reclosers are located; the concept of operational areas is analysed and a multi-objective problem is formulated, where the investment costs minimisation is the first objective function and NSEL minimisation is the second objective function. To solve this stage, the NSGA II algorithm is employed. A 102-node test feeder was used in order to prove the efficiency of the methodology proposed.

Maintenance of generation units coordinated with annual hydrothermal scheduling using a hybrid technique

This paper presents a hybrid technique for solving the generation maintenance scheduling coordinated with middle term hydrothermal dispatch based on the Chu-Beasley genetic algorithm and linear programming. It takes into consideration the non-linearity derived from the cost of the fuel for thermal power plants. The output of the genetic algorithm is a proposal for the start week of the generation maintenance plan that minimises the hydrothermal dispatch cost. This work has two main contributions: on one hand proposing a solution that integrates hydrothermal dispatch and maintenance scheduling in a single model, therefore a new mathematical model and, on the other hand the proposed solution applies a specialised genetic algorithm that has not been applied before to solve this problem. The test system to validate the methodology is composed of three hydro plants and two thermal plants split into 22 generation units, considering three types of preventive maintenance, in a planning term of one year (52 weeks). This methodology combines an exact technique and a specialised genetic algorithm, which favours convergence.

Coordinated tuning of the parameters of PI, PSS and POD controllers using a Specialized Chu–Beasley's Genetic Algorithm

This paper presents a Specialized Chu–Beasley's Genetic Algorithm (SCBGA) to perform coordinated tuning of the parameters of proportional-integral and supplementary damping controllers (power system stabilizers and interline power flow controller-power oscillation damping) in multi-machine electric power systems. The objective is to insert additional damping to low frequency electromechanical oscillations. The current sensitivity model was used to represent the system, therefore all of its devices and components were modeled by current injection. A novel current injection model for the interline power flow controller is presented and a static analysis is considered to validate it. The New England test system – consisting of 10 generators, 39 buses, and 46 transmission lines, divided into two areas with both local and inter-area oscillation modes – was used for the simulations. The SCBGA was compared to other five algorithms: a Random Search, a Local Search, a Simulated Annealing, a Genetic Algorithm, and a Particle Swarm Optimization method, in terms of performance for the tuning of the parameters of the controllers. The results demonstrated that the SCBGA was more efficient than these other techniques. In addition, the obtained solutions proved to be robust when variation of the loads was considered.

Expansion of Transmission Networks Considering Large Wind Power Penetration and Demand Uncertainty

This paper presents an algorithm for solving the Transmission Expansion Planning (TEP) problem when large scale wind generation is considered. Variability of wind speed and demand uncertainty are also taken into account. The formulation includes the DC model of the network, and the obtained expansion plans minimize the investment, the load shedding, and also the wind generation curtailment. The Chu-Beasley Genetic Algorithm (CBGA) is used for finding feasible optimal expansion plans. Uncertainties are included by scenario reduction to obtain robust expansion plans capable of meeting the uncertainty set. The approach allows finding robust expansion plans to cope with the uncertainties in load forecasting and also to take advantage of wind generation. The proposed algorithm is validated on the 6-bus Garver system, IEEE 24-bus RTS test system and the real life South-Brazilian 46-bus system. Comparison with other methods is carried out to demonstrate the performance of the proposed approach.

Enhanced multiobjective algorithm for transmission expansion planning consideringN − 1 security criterion

Summary Power system deregulation and the high penetration of renewable energies have introduced new challenges for the transmission expansion planning (TEP), which is a high complex mixed-integer non-linear problem. The search space and the computational effort increase if these constraints are included; therefore, efficient methods for solving the problem are needed. This paper presents an enhanced NSGA-II multiobjective algorithm for solving the security-constrained TEP problem, taking into account the N − 1 security criterion. This new methodology takes advantage of the NSGA-II crowded distance features and the Chu–Beasley genetic algorithm. The performance of the proposed algorithm is validated using three test systems. A set of optimal non-dominated solutions for each test system is thoroughly analyzed from the power systems and computational standpoint. The analysis of the obtained results and the comparison with others from the specialized literature show the robustness and the advantages of using this algorithm. Copyright © 2014 John Wiley & Sons, Ltd.

Planeamiento de la transmisión considerando seguridad e incertidumbre en la demanda empleando programación no lineal y técnicas evolutivas

En este trabajo se presenta una metodología de solución para el problema de Planeamiento de la Expansión de Redes de Transmisión de Energía Eléctrica considerando contingencias simples (N-1) e incertidumbre en la demanda futura. Para resolver el problema se utiliza un Algoritmo Genético Especializado de Chu & Beasley (AGCH) para realizar las propuestas de inversión cuyos flujos de carga son resueltos mediante Programación Lineal con un Método de Punto Interior de Alto Orden o Método Predictor Corrector (MPC). Adicionalmente, es implementada una inicialización de la población mediante un Método de Punto Interior No Lineal. La metodología propuesta es validada utilizando tres sistemas de prueba de la literatura especializada: el sistema del Sur Brasilero de 46 barras, el sistema IEEE de 24 barras y el sistema Garver de 6 nodos.

Optimal placement of faulted circuit indicators in power distribution systems

AbstractPower distribution utilities often use impedance-based methods for locating faults along their feeders. For feeders with laterals, these techniques may identify different possible locations for the same fault. This leads to higher costs and longer restoration time. In order to improve impedance-based methods, faulted-circuit indicators (FCI) can be allocated along the feeder to reduce, or even eliminate, the uncertainty about the fault location. This paper proposes a technique for optimally allocating a given number of FCIs along distribution feeders using the Chu–Beasley genetic algorithm to solve the optimization problem. The proposed objective functions measure the number of locations that are suspected to be the actual fault location or the distance among them. Additionally, it is possible to consider the presence of priority areas. We present results for the IEEE 34-bus system and for a 475-bus actual system. The results show the effectiveness of the proposed technique in improving impedance-based fault location methods.