Population-based Stochastic Search Algorithm Research Articles

A new empirical model and neural network-based approach for evaluation of isobaric heat capacity of natural gas

Isobaric heat capacity of natural gas is of prominent thermophysical property as it is directly related to thermodynamic energy functions, thereby its trustworthy prediction can open a new window for better establishment of the basis for its theoretical and engineering studies. In the present study, a new accurate and simple empirical correlation as a function of specific gravity (γg), temperature (T), and pressure (P) was developed to rapidly estimate the isobaric specific heat capacity (Cp) of natural gas without using gas composition. Due to the limitations of proposed experimental models and relations derived from gas compressibility factor (Z-factor) equations in the literature to a certain temperature, pressure and specific gravity range, an artificial neural network (ANN) based on back-propagation method was also applied for reliable prediction of Cp of natural gas. 847 sets of data from a diverse range of T, P, and γg were used to develop the neural network architecture and topology. Moreover, Genetic algorithm (GA) and Particle swarm (PS) optimization as population-based stochastic search algorithms were also utilized to optimize the weights and biases of networks to establish the best combination of input variables leading to the minimum Cp. The ANN demonstrated an accurate and promising prediction with a correlation coefficient of 0.99691 and 0.99518 for total dataset and test data, respectively.

PopDMMO: A general framework of population-based stochastic search algorithms for dynamic multimodal optimization

Dynamic multimodal optimization problems (DMMOPs) are a class of problems consisting of two characteristics, i.e., dynamic and multimodal natures. The former characteristic reveals that the properties of DMMOPs change over time, which is derived from dynamic optimization problems (DOPs). The latter one indicates that there exist multiple global or acceptable local optima, which comes from the multimodal optimization problems (MMOPs). Although there has been much attention to both DOPs and MMOPs in the field of meta-heuristics, there is little work devoting to the connection between the dynamic and multimodal natures in DMMOPs. To solve DMMOPs, the strategies dealing with dynamic and multimodal natures in the algorithms should cooperate with each other. Before looking deeply into the connections between two natures, there is necessary to measure the performances of the methods dealing with two natures in DMMOPs. In this paper, first, considering the dynamic and multimodal natures of DMMOPs, we design a set of benchmark problems to simulate various dynamic and multimodal environments. Then, we propose the optimization framework called PopDMMO containing several popular algorithms and methods to test and compare the performances of these algorithms, which gives a general view of solving DMMOPs.

EST-TSA: An effective search tendency based to tree seed algorithm

As a population-based stochastic search algorithm for continuous optimization problems, tree−seed algorithm (TSA) fails to balance capability of the exploitation and exploration of the algorithm effectively. Therefore, TSA has certain defects in local search capability. This paper proposes improvements of TSA in local search capability. Although TSA can achieve good performance in general, it does not fully consider the role of the current optimal position of the population in solving optimization problems. This slows down the convergence speed of the algorithm. This paper redesigns the balance rule between exploitation and exploration and improves the original position updating formula of TSA. EST-TSA can converge to the global optimal solution more effectively in the search process, which greatly strengthens the local search capability. Experimental results show that EST-TSA has better local search capability compared with the basic TSA. The improvements proposed in this paper are significant for TSA performance.

SNR-Constrained Heuristics for Optimizing the Scaling Parameter of Robust Audio Watermarking

In spread spectrum (SS) based robust audio watermarking, the scaling parameter is an important factor for balancing between robustness and imperceptibility. There have been intense studies of the embedded parameter optimization in light of the signal-to-noise ratio (SNR), but little attention has been given to the constrained SNR. Moreover, traditional population-based stochastic search algorithms for optimizing the embedded parameter significantly increase the computation pressure of the corresponding audio watermarking schemes. This paper comprehensively investigates the effect of the constrained SNR on the optimization of the scaling parameter, from both model and algorithmic perspectives. Specifically, the empirical relationship between the scaling parameter, robustness, and imperceptibility is first analyzed in detail. Next, an SNR-constrained optimization model is presented. Then, to solve the proposed model and find the current optimal scaling parameter for watermark embedding, a binary search algorithm and a heuristic search (HS) algorithm are, respectively, developed. Finally, we embed the proposed model and heuristics in the SS-based audio watermarking scheme and compare the integrated technique (called SS-SNR-HS) with the existing similar schemes. The experimental results demonstrate that SS-SNR-HS not only is computationally simple, but also achieves better balance between imperceptibility and robustness and, thus, seems promising in copyright protection of online digital audio.

Multiobjective multiarea unit commitment using hybrid differential evolution algorithm considering import/export and tie-line constraints

Recent power system networks are characterized by large proportions, high interconnections, and high nonlinearities. Challenge of supplying the nation with high-quality, reliable electrical energy at a reasonable cost converted government policy into deregulation and restructuring environment. To achieve significant cost-savings, multiarea unit commitment strategies are employed, whose intention is to establish the optimal commitment stratagem for power generating units situated in numerous areas which are interconnected through tie-lines, and combined operation of generation resources can result in considerable operational cost-savings. Differential evolution is a population-based stochastic search algorithm, whose simple yet powerful and straightforward features make it gorgeous for optimization. Differential evolution uses somewhat greedy and less stochastic approach for optimization problem solution. Although global exploration ability of differential evolution (DE) algorithm is adequate, its local exploitation ability is feeble and convergence velocity is too low, and it suffers from the problem of untimely convergence for multimodal objective function, in which search process may be trapped in local optima and it loses its diversity. Also, it suffers from the stagnation problem, where the search process may infrequently stop proceeding toward the global optimum even though the population has not converged to a local optimum or any other point. To improve the exploitation ability and global performance of DE algorithm, a novel and hybrid version of differential evolution algorithm combined with random search algorithm is presented in the proposed research to solve multiobjective and multiarea unit commitment problem of electric power system. The performance of the proposed hybrid algorithm is tested with benchmark of three-area interconnected system, which consist of IEEE-30 Bus system. Experimental results show that proposed technique has the prospective for the solution of multiobjective and multiarea unit commitment problem and power generation scheduling in deregulated electricity market with import and export constraints.

A Modified Particle Swarm Optimization Algorithm for Global Optimizations of Inverse Problems

Particle swarm optimization (PSO) is a population-based stochastic search algorithm inspired from the natural behavior of bird flocking or fish schooling for searching their foods. Due to its easiness in numerical implantations, PSO has been widely applied to solve a variety of inverse and optimization problems. However, a PSO is often trapped into local optima while dealing with complex and real world design problems. In this regard, a new modified PSO is proposed by introducing a mutation mechanism and using dynamic algorithm parameters. According to the proposed mutation mechanism, one particle is randomly selected from all personal best ones to generate some trial particles to preserve the diversity of the algorithm in the final searching stage of the evolution process. Moreover, the random variations in the two learning factors will help the particles to reach an optimal solution. In addition, the dynamic variation in the inertia weight will facilitate the algorithm to keep a good balance between exploration and exploitation searches. The numerical experiments on different case studies have shown that the proposed PSO obtains the best results among the tested algorithms.

Accurate prediction of properties of carbon dioxide for carbon capture and sequestration operations

Development of robust predictive models to estimate the transport properties of gases (namely viscosity and thermal conductivity) is of immense help in many engineering applications. This study highlights the application of the artificial neural network (ANN) and least squares support vector machine (LSSVM) modeling approaches to estimate the viscosity and thermal conductivity of CO2. To propose the machine learning methods, a total of 800 data gathered from the literature covering a wide temperature range of 200–1000 K and a wide pressure range of 0.1–100 MPa were used. Particle swarm optimization (PSO) and genetic algorithm (GA) as population-based stochastic search algorithms were applied for training of ANNs and to achieve the optimum LSSVM model variables. For the purpose of predicting viscosity, the PSO-ANN and GA-LSSVM methods yielded the mean absolute error (MAE) and coefficient of determination (R2) values of 1.736 and 0.995 as well as 0.51930 and 0.99934, respectively for the whole data set, while for the purpose of predicting thermal conductivity, the PSO-ANN and GA-LSSVM models yielded the MAE and R2 values of 1.43044 and 0.99704 as well as 0.72140 and 0.99857, respectively for the whole data set. Both methods provide properly capable method for predicting the thermal conductivity and viscosity of CO2.

Accelerate Population-Based Stochastic Search Algorithms With Memory for Optima Tracking on Dynamic Power Systems

Existing population-based Stochastic Search Algorithms (SSAs) are too time-consuming to solve dynamic optimal power flow (OPF). The solution proposed in this paper is to accelerate SSAs with memory. Two memory schemes, the similarity retrieval scheme and the mean-based immigrants scheme, are proposed and applied together to the Differential Evolution and Particle Swarm Optimizer, which are two representatives of SSAs. Experiments are conducted on modified IEEE 30-bus and IEEE 118-bus systems with changing load buses and the objective of minimizing real power transmission loss. The results show that the proposed schemes significantly improve the performance of the two existing algorithms, and that SSAs could be practical for tracking optima of dynamic OPF.

Dynamic Population Size and Mutation Round Strategy Assisted Modified Particle Swarm Optimization with Mutation and Reposition

Particle swarm optimization (PSO) is a population-based stochastic search algorithm. This algorithm is utilized to solve the optimization problem. It suffers the problems of trapping in local optimum and premature convergence. Nowadays, both problems can be solved by mutation and reposition techniques apply with PSO (MRPSO). However, this technique use over evaluation calls for solution searching. This research paper proposed a technique to minimized evaluation call. This proposed is called DPM-MRPSO. The concept of adaption evaluation call depends on results from improvement solution of mutation technique and PSO technique. The proposed technique is tested on twenty-four benchmark functions and obtains satisfied search results.

A novel hybrid DE–random search approach for unit commitment problem

Differential evolution (DE) is a population-based stochastic search algorithm, whose simple yet powerful and straightforward features make it very attractive for numerical optimization. DE uses a rather greedy and less stochastic approach to problem-solving than other evolutionary algorithms. DE combines simple arithmetic operators with the classical operators of recombination, mutation and selection to evolve from a randomly generated starting population to a final solution. Although global exploration ability of DE algorithm is adequate, its local exploitation ability is feeble and convergence velocity is too low and it suffers from the problem of untime convergence for multimodal objective function, in which search process may be trapped in local optima and it loses its diversity. Also, it suffers from the stagnation problem, where the search process may infrequently stop proceeding toward the global optimum even though the population has not converged to a local optimum or any other point. To improve the exploitation ability and global performance of DE algorithm, a novel and hybrid version of DE algorithm is presented in the proposed research. This research paper presents a hybrid version of DE algorithm combined with random search for the solution of single-area unit commitment problem. The hybrid DE–random search algorithm is tested with IEEE benchmark systems consisting of 4, 10, 20 and 40 generating units. The effectiveness of proposed hybrid algorithm is compared with other well-known evolutionary, heuristics and meta-heuristics search algorithms, and by experimental analysis, it has been found that proposed algorithm yields global results for the solution of unit commitment problem.

Rapid optimization of drug combinations for the optimal angiostatic treatment of cancer.

Drug combinations can improve angiostatic cancer treatment efficacy and enable the reduction of side effects and drug resistance. Combining drugs is non-trivial due to the high number of possibilities. We applied a feedback system control (FSC) technique with a population-based stochastic search algorithm to navigate through the large parametric space of nine angiostatic drugs at four concentrations to identify optimal low-dose drug combinations. This implied an iterative approach of in vitro testing of endothelial cell viability and algorithm-based analysis. The optimal synergistic drug combination, containing erlotinib, BEZ-235 and RAPTA-C, was reached in a small number of iterations. Final drug combinations showed enhanced endothelial cell specificity and synergistically inhibited proliferation (p < 0.001), but not migration of endothelial cells, and forced enhanced numbers of endothelial cells to undergo apoptosis (p < 0.01). Successful translation of this drug combination was achieved in two preclinical in vivo tumor models. Tumor growth was inhibited synergistically and significantly (p < 0.05 and p < 0.01, respectively) using reduced drug doses as compared to optimal single-drug concentrations. At the applied conditions, single-drug monotherapies had no or negligible activity in these models. We suggest that FSC can be used for rapid identification of effective, reduced dose, multi-drug combinations for the treatment of cancer and other diseases.Electronic supplementary materialThe online version of this article (doi:10.1007/s10456-015-9462-9) contains supplementary material, which is available to authorized users.

Hybrid particle swarm optimisation with adaptively coordinated local searches for multimodal optimisation

Particle swarm optimisation PSO is a population-based stochastic search algorithm. Two common criticisms exist. First, PSO suffers premature convergence. Second, several existing PSO variants are designed for a specific search space thus an algorithm performing well on a diverse set of problems is lacking. In this paper, we propose a hybrid particle swarm optimisation with adaptively coordinated local searches, called NMRM-PSO, to make up the above demerits. These local search algorithms are the Nelder mead algorithm and the Rosenbrock method. NMRM-PSO has two alternative phases: the exploration phase realised by PSO and the exploitation phase completed by two adaptively coordinated local searches. Experiment results show that NMRM-PSO outperforms all of the tested PSO algorithms on most of multimodal functions in terms of solution quality, convergence speed and success rate.

Multi-strategy based bare bones particle swarm for numerical optimisation

Particle swarm optimisation PSO is a population-based stochastic search algorithm, which simulates the social behaviour of bird flocking or fish schooling. Many previous studies have shown that PSO is an effective optimisation technique in evolutionary optimisation community. However, the standard PSO still suffers from premature convergence when solving complex multimodal problems. In this paper, we propose a new PSO algorithm called multi-strategy based bare bones PSO MPSO. The MPSO introduces generalised opposition-based learning GOBL and two neighbourhood search strategies into the original bare bones PSO. Simulation study is conducted on 13 well-known benchmark functions. The results show that MPSO achieves better results than the standard PSO and two other PSO algorithms.

A new multi-population-based differential evolution

Differential evolution DE is an efficient population-based stochastic search algorithm, which has shown good search abilities on many real-world and benchmark optimisation problems. In this paper, we propose a new multi-population-based DE MDE algorithm. In MDE, the original population is divided into multiple subpopulations. For each subpopulation, two DE mutation schemes are alternatives to be conducted. Moreover, a Cauchy mutation operator is utilised to enhance the global search. To verify the performance of MDE, 12 well-known benchmark functions are used in the experiments. Simulation results show that MDE performs better than the standard DE and several other DE variants.

Dynamic partition search algorithm for global numerical optimization

This paper presents a novel evolutionary algorithm entitled Dynamic Partition Search Algorithm (DPSA) for global optimization problems with continuous variables. The DPSA is a population-based stochastic search algorithm in nature, which mainly consists of initialization process and evolution process. In the initialization process, the DPSA randomly generates an initial population of members from a specific search space and finds a leader. In the evolution process, the DPSA applies two groups to balance exploration ability and exploitation ability, in which one group is in charge of exploring new region via a dynamic partition strategy, and the other group relies on Cauchy distributions to exploit the region around the best member. Later, numerical experiments are conducted for 24 classical benchmark functions with 100, 1000 or even 10000 dimensions. And the performance of the proposed DPSA is compared with a state-of-the-art cooperative coevolving particle swarm optimization (CCPSO2), and two existing differential evolution (DE) algorithms. The experimental results show that DPSA has a better performance than the algorithms used for comparison, especially for high dimensional optimization problems. In addition, the numerical computational results also demonstrate that the DPSA has good scalability, and it is an effective evolutionary algorithm for solving large-scale global optimization problems.

Heterogeneous Differential Evolution for Numerical Optimization

Differential evolution (DE) is a population-based stochastic search algorithm which has shown a good performance in solving many benchmarks and real-world optimization problems. Individuals in the standard DE, and most of its modifications, exhibit the same search characteristics because of the use of the same DE scheme. This paper proposes a simple and effective heterogeneous DE (HDE) to balance exploration and exploitation. In HDE, individuals are allowed to follow different search behaviors randomly selected from a DE scheme pool. Experiments are conducted on a comprehensive set of benchmark functions, including classical problems and shifted large-scale problems. The results show that heterogeneous DE achieves promising performance on a majority of the test problems.

Human group optimiser for global numerical optimisation

In this paper, the previously proposed seeker optimisation algorithm (SOA) is renamed as human group optimisation (HGO) algorithm, which is a novel population-based heuristic stochastic search algorithm by simulating human group searching behaviours. In this algorithm, the choice of search direction is based on empirical gradients by evaluating the responses to the position changes, and the decision of step length is based on human-unique uncertainty reasoning by using a simple fuzzy rule. Furthermore, a canonical version of HGO is proposed. Based on the benchmark functions provided by CEC2005, the canonical HGO is compared with differential evolution (DE) algorithms, particle swarm optimisation (PSO) algorithms and covariance matrix adaptation evolution strategy (CMA-ES). The simulation results show that the proposed HGO is competitive or even superior to the listed other algorithms for some employed functions.

Particle swarm optimization with adaptive mutation for multimodal optimization

Particle swarm optimization (PSO) is a population-based stochastic search algorithm, which has shown a good performance over many benchmark and real-world optimization problem. Like other stochastic algorithms, PSO also easily falls into local optima in solving complex multimodal problems. To help trapped particles escape from local minima, this paper presents a new PSO variant, called AMPSO, by employing an adaptive mutation strategy. To verify the performance of AMPSO, a set of well-known complex multimodal benchmarks are used in the experiments. Simulation results demonstrate that the proposed mutation strategy can efficiently improve the performance of PSO.

An intelligent approach for optimal prediction of gas deviation factor using particle swarm optimization and genetic algorithm

The measurement of PVT properties of natural gas in gas pipelines, gas storage systems, and gas reservoirs require accurate values of compressibility factor. Although equation of state and empirical correlations were utilized to estimate compressibility factor, but the demands for novel, more reliable, and easy-to-use models encouraged the researchers to introduce modern tools such as artificial intelligent systems.This paper introduces Particle swarm optimization (PSO) and Genetic algorithm (GA) as population-based stochastic search algorithms to optimize the weights and biases of networks, and to prevent trapping in local minima. Hence, in this paper, GA and PSO were used to minimize the neural network error function.A database containing 6378 data was employed to develop the models. The proposed models were compared to conventional correlations so that the model predictions indicated a good accuracy for the results in training and testing stages. The results showed that artificial neural networks (ANNs) remarkably overcame the inadequacies of the empirical models where PSO–ANN improved the performance significantly. Additionally, the regression analysis released the efficiency coefficient (R2) of 0.999 which can be considered very promising.

Heuristic-Based Pipe Dimensioning Model for Water Distribution Networks

An economic design of water distribution system components plays an important role in the water-supplying agency because of the requirement of a large financial investment on construction, operation, and maintenance. Population-based stochastic search algorithms have become a futuristic method for optimal design of water distribution networks. However, the effectiveness of population-based stochastic search algorithms purely depends on several factors, such as population size, degree of randomness involved, penalty function, algorithm operators, and search space size. An analysis of published research shows that a large number of evaluations is required to arrive at the least cost combination of pipe diameters. This paper proposes a new approach, in which flow velocity in a pipe is considered as implicit information for pipe sizing. Three well-known benchmark networks were used to illustrate the applicability of the proposed approach for least-cost pipe sizing of water distribution networks. The result of the model application reveals that the computational effort required to arrive at an economical design is very minimal.