Bang-Big Crunch Optimization Research Articles

A Hybrid Big Bang–Big Crunch optimization algorithm for solving the different economic load dispatch problems

In this paper, we applied a Hybrid Big Bang–Big Crunch optimization technique for solving the different types of economic load dispatch (ELD) problems in power systems. Many nonlinear characteristics of the generator, such as ramp rate limits, prohibited operating zone, and non-smooth cost functions are considered using the proposed method in practical generator operation. The proposed method is tested on three different systems (six-unit system considering losses, 15 units: ED considering transmission loss, large system: 40 generating units with valve-point loading effects). Furthermore, results are compared with other optimization approaches proposed in the recent literature, showing the feasibility of this technique to highly nonlinear and different ELD problem.

Fuzzy 2-partition entropy threshold selection based on Big Bang–Big Crunch Optimization algorithm

The fuzzy 2-partition entropy approach has been widely used to select threshold value for image segmenting. This approach used two parameterized fuzzy membership functions to form a fuzzy 2-partition of the image. The optimal threshold is selected by searching an optimal combination of parameters of the membership functions such that the entropy of fuzzy 2-partition is maximized. In this paper, a new fuzzy 2-partition entropy thresholding approach based on the technology of the Big Bang–Big Crunch Optimization (BBBCO) is proposed. The new proposed thresholding approach is called the BBBCO-based fuzzy 2-partition entropy thresholding algorithm. BBBCO is used to search an optimal combination of parameters of the membership functions for maximizing the entropy of fuzzy 2-partition. BBBCO is inspired by the theory of the evolution of the universe; namely the Big Bang and Big Crunch Theory. The proposed algorithm is tested on a number of standard test images. For comparison, three different algorithms included Genetic Algorithm (GA)-based, Biogeography-based Optimization (BBO)-based and recursive approaches are also implemented. From experimental results, it is observed that the performance of the proposed algorithm is more effective than GA-based, BBO-based and recursion-based approaches.

A new hybrid algorithm for simultaneous size and semi-rigid connection type optimization of steel frames

A hybrid algorithm based on Harmony Search (HS) and Big Bang-Big Crunch (BB-BC) optimization methods is proposed for optimal design of semi-rigid steel frames. The algorithm selects suitable sections for beams and columns and assigns suitable semi-rigid connection types for beam-to-column connections, such that the total member plus connection cost of the frame, is minimized. Stress and displacement constraints of AISC-LRFD code together with the size constraints are imposed on the frame in the design procedure. The nonlinear moment-rotation behavior of connections and P-Δ effects of beam-column members are taken into account in the non-linear structural analysis. Three benchmark steel frames are designed and the results are compared with those of standard BB-BC and of other studies. The comparisons demonstrate that proposed algorithm performs better than standard BB-BC and HS methods in all examples and that the total cost of a frame can be reduced through suitable selection of its beam-to-column connection types.

An Optimal Robust Tuning Method for First Order plus Dead Time Systems with Parameter Uncertainty

This paper presents a simple PI tuning method for first order plus dead time (FOPDT) systems. Firstly, stabilizing PI parameters region is found for these kinds of systems. Then, optimal point of this region is selected using the Big Bang Big Crunch optimization algorithm and this work is extended to FOPDT systems that contain parameter uncertainty. After the optimizations done for a wide range of systems, an optimal and robust PI tuning method is proposed with a curve fitting of the obtained optimization data. Lastly, the proposed method is compared with other PI tuning methods for their performance and robustness.

Preventive and corrective control applications in power systems via Big Bang–Big Crunch optimization

Abstract This paper proposes a new method of optimization, the Big Bang–Big Crunch (BB–BC) method, for the optimization of preventive and corrective control actions to enhance the dynamic security of a power system against transient instabilities. The control actions, generation rescheduling and load shedding, are considered as constrained optimization problems with static and dynamic security constraints. These optimization problems are solved through the BB–BC method to minimize some operational costs related to the control actions. To reduce the size of the search spaces and the computational burden, decision trees and correlation coefficients are used as feature selection tools, which determine the most effective generators and loads for shaping the system’s transient stability. The proposed method is applied to a test system and compared with genetic algorithms, particle swarm optimization, differential evolution and active set method. The BB–BC method is promising since it gives comparable results with the other population based optimization methods.

Big Bang–Big Crunch optimization based interval type-2 fuzzy PID cascade controller design strategy

Fuzzy logic control is a recognized approach for handling the faced uncertainties within control applications. However, type-1 fuzzy controllers using crisp type-1 fuzzy sets might not be able to fully handle the high levels of uncertainties and nonlinear dynamics associated with real world control applications. On the other hand, interval type-2 fuzzy controllers using Interval Type-2 Fuzzy Sets (IT2-FSs) might be able to handle such uncertainties to produce a better control performance. However, the systematic design of interval type-2 fuzzy controllers is still a challenging problem due to the difficulty in determining the parameters of the IT2-FSs. In this paper, we will present the novel application of Big Bang–Big Crunch optimization (BB–BC) approach to optimize the antecedent membership parameters of Interval Type-2 Fuzzy PID (IT2-FPID) controllers in a cascade control structure. Since the IT2-FPID control structure involves more design parameters compared to its type-1 counterpart, it is beneficial to employ the BB–BC method which has a low computational cost and a high convergence speed. The presented BB–BC based optimized IT2-FPID cascade structure will be compared with its Type-1 Fuzzy PID (T1-FPID) and conventional PID controller counterparts which were also optimized with the BB–BC optimization. In addition, the proposed IT2-FPID structure will be compared with a self-tuning T1-FPID control structure. We will then present the novel application of the cascade control architecture to solve the path tracking control problem of mobile robots which inherits large amounts of uncertainties caused by the internal dynamics and/or feedback sensors of the controlled system. Several experiments were performed in simulation and in real world using the PIONEER 3-DX mobile robot which will act as a platform to evaluate the proposed control systems in this paper. The results illustrated that the IT2-FPID structure enhanced significantly the control performance even in the presence of uncertainties and disturbances when compared to the PID, T1-FPID and self-tuning T1-FPID structures. Moreover, it has been shown that the reason for the superior control performance of the IT2-FPID under high levels of uncertainty and noise is not merely for its use of extra parameters, but rather its different way of dealing with the uncertainties and noise present in real world environments by comparing with a self-tuning T1-FPID structure.

Congestion Management Using Real and Reactive Power Rescheduling Based on Big Bang-Big Crunch Optimization Algorithm

With appearance of deregulated electricity markets, line congestions in transmission systems is considered as critical problem for power system which may prevent dispatching all of the contracted power transactions. Many studies have been carried out to express techniques for congestion management (CM). In this paper real and reactive power rescheduling of generators approach is utilized. This method includes two steps. First one is optimum selection of generators on the basis of sensitivities of generator to power flow on congested line/lines. Next step is optimal rescheduling of generators and identification of capacitors required to provide real and reactive power support for CM. Optimization process in this paper is carried out using big bang-big crunch (BB-BC) algorithm which is improved by particle swarm optimization (PSO) method as hybrid BB-BC (HBB-BC) optimization for the first time. Effectiveness of proposed method has been tested on IEEE 30-bus system, the 39-bus New England system, and 75-bus Indian system and compared with the other proposed methodologies.

Under Voltage Load Shedding Scheme Using Meta-heuristic Optimization Methods

Load shedding has been extensively studied because of multiple power system failure occurrences worldwide. Reliable techniques are required to provide rapid and precise load shedding to avert voltage collapse in power networks. Meta-heuristic optimization approaches are currently the widely developed methods because of their robustness and flexibility in dealing with complex and non-linear systems. These methods include genetic algorithm, fuzzy logic control, particle swarm optimization, artificial neural network, ant colony optimization, big-bang big-crunch optimization, and many others. This study provides an overview of all the meta-heuristic methods implemented for under voltage load shedding in power systems.

Environmental/economic power dispatch using a Hybrid Big Bang–Big Crunch optimization algorithm

The combined economic and emission dispatch (CEED) problem where objective function is highly non linear, non-differentiable and may have multiple local minima. Therefore, classical optimization methods may not converge or get trapped to any local minima. This paper proposes a Hybrid Big Bang–Big Crunch (HBB–BC) optimization algorithm technique for solving the CEED. Six generator test and IEEE 30 standard bus system was used for testing and validation purposes. The preference of the HBB–BC is compared with other heuristic methods. The results show, clearly, that the proposed method gives better optimal solution as compared to the other methods.

Optimisation of damping treatments based on big bang–big crunch and modal strain energy methods

A cost-effective methodology is needed in various applications in order to optimise damping treatments for structures. Although some methods appear to be applicable for structures with relatively simple geometries, it is still difficult to utilise them for general structures. This paper presents an efficient approach for optimisation of passive damping treatments that can be applied to general structures. First, an optimisation procedure based on big bang–big crunch optimisation method is introduced and its effectiveness for damping optimisation is evaluated. Then, a procedure based on modal strain energy method is presented for the prediction of modal damping levels for structures with damping treatments and its performance is assessed. After that, for validation purposes, the proposed optimisation methodology is used to maximise modal damping for a single mode of a structure whose optimised configurations are known for the individual modes. Finally, the performance of the proposed optimisation procedure is demonstrated for the maximisation of damping levels for multiple modes at the same time and the applicability of the approach for general structures with passive damping treatments is demonstrated. • An optimisation procedure based on Big Bang–Big Crunch algorithm is presented. • Modal strain energy method is used for damping prediction. • The performance of the damping prediction method is assessed. • The applicability of optimisation procedure for general structures is demonstrated.

Optimum design of steel frames with semi-rigid connections using Big Bang-Big Crunch method

The Big Bang-Big Crunch (BB-BC) optimization algorithm is developed for optimal design of non-linear steel frames with semi-rigid beam-to-column connections. The design algorithm obtains the minimum total cost which comprises total member plus connection costs by selecting suitable sections. Displacement and stress constraints together with the geometry constraints are imposed on the frame in the optimum design procedure. In addition, non-linear analyses considering the P- effects of beam-column members are performed during the optimization process. Three design examples with various types of connections are presented and the results show the efficiency of using semi-rigid connection models in comparing to rigid connections. The obtained optimum semi-rigid frames are more economical solutions and lead to more realistic predictions of response and strength of the structure.

A Big-Bang Big-Crunch Optimized General Type-2 Fuzzy Logic Approach for Multi-Criteria Group Decision Making

Abstract Multi-Criteria Group Decision Making (MCGDM) aims to find a unique agreement from a number of decision makers/users by evaluating the uncertainty in judgments. In this paper, we present a General Type-2 Fuzzy Logic based approach for MCGDM (GFLMCGDM). The proposed system aims to handle the high levels of uncertainties which exist due to the varying Decision Makers’ (DMs) judgments and the vagueness of the appraisal. In order to find the optimal parameters of the general type-2 fuzzy sets, we employed the Big Bang-Big Crunch (BB-BC) optimization. The aggregation operation in the proposed method aggregates the various DMs opinions which allow handling the disagreements of DMs’ opinions into a unique approval. We present results from an application for the selection of reading lighting level in an intelligent environment. We carried out various experiments in the intelligent apartment (iSpace) located at the University of Essex. We found that the proposed GFL-MCGDM effectively handle the uncertainties between the various decision makers which resulted in producing outputs which better agreed with the users’ decision compared to type 1 and interval type 2 fuzzy based systems.

A novel order diminution of LTI systems using Big Bang Big Crunch optimization and Routh Approximation

A novel computer aided method is presented that yields Linear Time Invariant Reduced Order System (LTI-ROS). This is accomplished by using the combined benefits of Big Bang Big Crunch (BBBC) optimization and Routh Approximation (RA) method. The applicability of the proposed method for both Single Input Single Output (SISO) and Multiple Input Multiple Output (MIMO) Linear Time Invariant (LTI) systems is verified by solving numerical examples. Furthermore, the results show that the realized LTI-ROS retain stability and steady state conditions of original system. The reduced order system also exhibits lower Integral Square Error (ISE) values.

A New Damage Detection Method: Big Bang-Big Crunch (BB-BC) Algorithm

The present paper aims to explore damage assessment methodology based on the changes in dynamic parameters properties of vibration of a structural system. The finite-element model is used to apply at an element level. Reduction of the element stiffness is considered for structural damage. A procedure for locating and quantifying damaged areas of the structure based on the innovative Big Bang-Big Crunch (BB-BC) optimization method is developed for continuous variable optimization. For verifying the method a number of damage scenarios for simulated structures have been considered. For the purpose of damage location and severity assessment the approach is applied in three examples by using complete and incomplete modal data. The effect of noise on the accuracy of the results is investigated in some cases. A great unbraced frame with a lot of damaged element is considered to prove the ability of proposed method. More over BB- BC optimization method in damage detection is compared with particle swarm optimizer with passive congregation (PSOPC) algorithm. This work shows that BB-BC optimization method is a feasible methodology to detect damage location and severity while introducing numerous advantages compared to referred method.

A New Damage Detection Method: Big Bang-Big Crunch (BB-BC) Algorithm

The present paper aims to explore damage assessment methodology based on the changes in dynamic parameters properties of vibration of a structural system. The finite-element model is used to apply at an element level. Reduction of the element stiffness is considered for structural damage. A procedure for locating and quantifying damaged areas of the structure based on the innovative Big Bang-Big Crunch (BB-BC) optimization method is developed for continuous variable optimization. For verifying the method a number of damage scenarios for simulated structures have been considered. For the purpose of damage location and severity assessment the approach is applied in three examples by using complete and incomplete modal data. The effect of noise on the accuracy of the results is investigated in some cases. A great unbraced frame with a lot of damaged element is considered to prove the ability of proposed method. More over BB-BC optimization method in damage detection is compared with particle swarm optimizer with passive congregation (PSOPC) algorithm. This work shows that BB-BC optimization method is a feasible methodology to detect damage location and severity while introducing numerous advantages compared to referred method.

Optimal design of structures with multiple natural frequency constraints using a hybridized BB-BC/Quasi-Newton algorithm

A hybridization of the Quasi-Newton with Big Bang-Big Crunch (QN-BBBC) optimization algorithm is proposed to find the optimal weight of the structures subjected to multiple natural frequency constraints. The algorithm is based on hybridizing a mathematical algorithm (quasi-Newton) for local search and a meta-heuristic algorithm (Big Bang-Big Crunch) for global search, and to help to leave the traps. Four examples are proposed for the optimization of trusses and two examples are studied for the optimization of frames with frequency constraints. The examples are widely reported and used in the related literature as benchmarks. The numerical results reveal the robustness and high performance of the suggested methods for the structural optimization with frequency constraints.

An Efficient Hybrid Big Bang–Big Crunch Algorithm for Multi-objective Reconfiguration of Balanced and Unbalanced Distribution Systems in Fuzzy Framework

This article presents an efficient hybrid big bang–big crunch optimization algorithm to solve the multi-objective reconfiguration of balanced and unbalanced distribution systems in a fuzzy framework. The objectives considered are the minimization of total real power losses, the minimization of buses voltage deviation, and load balancing in the feeders. First, each objective is fuzzified, and then the overall fuzzy satisfaction function formed is considered as a fitness function and maximized during the optimization process. The hybrid big bang–big crunch algorithm is an effective and powerful method that has high accuracy and fast convergence, and its implementation is easy. This algorithm using particle swarm optimization capacities improves the capability of the big bang–big crunch algorithm for better exploration. In addition, the hybrid big bang–big crunch uses a mutation operator after position updating to avoid local optimum and to explore new search areas. The effectiveness of the proposed algorithm is demonstrated on balanced and unbalanced test distribution systems. The simulation results are compared with the solutions obtained by other approaches.

CO2 and cost optimization of reinforced concrete frames using a big bang-big crunch algorithm

A hybrid Big Bang-Big Crunch (BB-BC) optimization algorithm is applied to the design of reinforced concrete frames. The objective of the optimization is to minimize the total cost or the CO2 emissions associated with construction of reinforced concrete frames subjected to constraints based on the specifications and guidelines prescribed by the American Concrete Institute (ACI 318-08).Designs are presented for several reinforced concrete frames that minimize the cost and the CO2 emissions associated with construction. In the first frame example, low-cost designs developed using BB-BC optimization are compared to designs developed using a genetic algorithm. In the second set of frame designs, both low-cost designs using BB-BC optimization are compared to designs developed using simulated annealing. The BB-BC algorithm generated designs that reduced the cost and the CO2 emissions of construction for example frames.

Environment Friendly BB-BC Optimized Economic Dispatch with Real and Reactive Power Constraints

The basic objective of Economic Dispatch (ED) of electric power generation is to schedule the committed generating unit outputs to meet the load demand at minimum operating cost subject to equality and inequality constraints. In recent years with increasing awareness about environmental issues this problem has taken an essential development i.e. economic dispatch now includes the dispatch of power to minimize pollutants (from fossil fuel power generating units), as well as to achieve minimum cost. This paper presents comparative study of two algorithms namely Particle Swarm Optimization (PSO) and Big Bang-Big Crunch Optimization (BB-BC) which are implemented on Environment Friendly BB-BC Optimized Economic Dispatch with Real and Reactive Power Constraints problem. It is shown that the performance of BB- BC method demonstrates superiority over PSO algorithm. Keywords Particle Swarm Optimization, Big Bang–Big Crunch, economic Dispatch, emission dispatch, fuel cost function, total emission function, penalty factor.

Design of Retaining Walls Using Big Bang–Big Crunch Optimization

A procedure is developed for designing low-cost or low-weight cantilever reinforced concrete retaining walls, with base shear keys, using big bang–big crunch (BB-BC) optimization. The objective of the optimization is to minimize the total cost or total weight per unit length of the retaining structure subjected to constraints on the basis of stability, bending moment, and shear force capacities and the requirements of the American Concrete Institute (ACI 318-05). An iterative population-based heuristic search method, BB-BC optimization has a numerically simple algorithm with relatively few control parameters as compared with other evolutionary methods. Low-cost and low-weight designs for two retaining walls are presented. In addition, results are presented on the effects of surcharge load, backfill slope, and internal friction angle of the retained soil on the values of low-cost and low-weight designs with and without a base shear key.