Particle-swarm harmony search for water network design

The optimal design of water distribution networks is a non-linear, multi-modal, and constrained problem classified as an NP-hard combinatorial problem. Because of the drawbacks of calculus-based algorithms, the problem has been tackled by assorted stochastic algorithms, such as the genetic algorithm, simulated annealing, tabu search, shuffled frog-leaping algorithm, ant colony optimization algorithm, harmony search, cross entropy, and scatter search. This study proposes a modified harmony search algorithm incorporating particle swarm concept. This algorithm was applied to the design of four bench-mark networks (two-loop, Hanoi, Balerma, and New York City networks), with good results.     

Self-adaptive multi-objective harmony search for optimal design of water distribution networks

In multi-objective optimization computing, it is important to assign suitable parameters to each optimization problem to obtain better solutions. In this study, a self-adaptive multi-objective harmony search (SaMOHS) algorithm is developed to apply the parameter-setting-free technique, which is an example of a self-adaptive methodology. The SaMOHS algorithm attempts to remove some of the inconvenience from parameter setting and selects the most adaptive parameters during the iterative solution search process. To verify the proposed algorithm, an optimal least cost water distribution network design problem is applied to three different target networks. The results are compared with other well-known algorithms such as multi-objective harmony search and the non-dominated sorting genetic algorithm-II. The efficiency of the proposed algorithm is quantified by suitable performance indices. The results indicate that SaMOHS can be efficiently applied to the search for Pareto-optimal solutions in a multi-objective solution space.     

Optimal cost design of water distribution networks using harmony search

This study presents a cost minimization model for the design of water distribution networks. The model uses a recently developed harmony search optimization algorithm while satisfying all the design constraints. The harmony search algorithm mimics a jazz improvisation process in order to find better design solutions, in this case pipe diameters in a water distribution network. The model also interfaces with a popular hydraulic simulator, EPANET, to check the hydraulic constraints. If the design solution vector violates the hydraulic constraints, the amount of violation is considered in the cost function as a penalty. The model was applied to five water distribution networks, and obtained designs that were either the same or cost 0.28–10.26% less than those of competitive meta-heuristic algorithms, such as the genetic algorithm, simulated annealing and tabu search under similar or less favorable conditions. The results show that the harmony search-based model is suitable for water network design.     

Improved mine blast algorithm for optimal cost design of water distribution systems

The design of water distribution systems is a large class of combinatorial, nonlinear optimization problems with complex constraints such as conservation of mass and energy equations. Since feasible solutions are often extremely complex, traditional optimization techniques are insufficient. Recently, metaheuristic algorithms have been applied to this class of problems because they are highly efficient. In this article, a recently developed optimizer called the mine blast algorithm (MBA) is considered. The MBA is improved and coupled with the hydraulic simulator EPANET to find the optimal cost design for water distribution systems. The performance of the improved mine blast algorithm (IMBA) is demonstrated using the well-known Hanoi, New York tunnels and Balerma benchmark networks. Optimization results obtained using IMBA are compared to those using MBA and other optimizers in terms of their minimum construction costs and convergence rates. For the complex Balerma network, IMBA offers the cheapest network design compared to other optimization algorithms.     

Research on Vehicle Routing Problem with Soft Time Windows Based on Hybrid Tabu Search and Scatter Search Algorithm

With the expansion of the application scope of social computing problems, many path problems in real life have evolved from pure path optimization problems to social computing problems that take into account various social attributes, cultures, and the emotional needs of customers. The actual soft time window vehicle routing problem, speeding up the response of customer needs, improving distribution efficiency, and reducing operating costs is the focus of current social computing problems. Therefore, designing fast and effective algorithms to solve this problem has certain theoretical and practical significance. In this paper, considering the time delay problem of customer demand, the compensation problem is given, and the mathematical model of vehicle path problem with soft time window is given. This paper proposes a hybrid tabu search (TS) & scatter search (SS) algorithm for vehicle routing problem with soft time windows (VRPSTW), which mainly embeds the TS dynamic tabu mechanism into the SS algorithm framework. TS uses the scattering of SS to avoid the dependence on the quality of the initial solution, and SS uses the climbing ability of TS improves the ability of optimizing, so that the quality of search for the optimal solution can be significantly improved. The hybrid algorithm is still based on the basic framework of SS. In particular, TS is mainly used for solution improvement and combination to generate new solutions. In the solution process, both the quality and the dispersion of the solution are considered. A simulation experiments verify the influence of the number of vehicles and maximum value of tabu length on solution, parameters’ control over the degree of convergence, and the influence of the number of diverse solutions on algorithm performance. Based on the determined parameters, simulation experiment is carried out in this paper to further prove the algorithm feasibility and effectiveness. The results of this paper provide further ideas for solving vehicle routing problems with time windows and improving the efficiency of vehicle routing problems and have strong applicability.     

A novel evolutionary meta-heuristic for the multi-objective optimization of real-world water distribution networks

Genetic algorithms are currently one of the state-of-the-art meta-heuristic techniques for the optimization of large engineering systems such as the design and rehabilitation of water distribution networks. They are capable of finding near-optimal cost solutions to these problems given certain cost and hydraulic parameters. Recently, multi-objective genetic algorithms have become prevalent in the water industry due to the conflicting nature of these hydraulic and cost objectives. The Pareto-front of solutions can aid decision makers in the water industry as it provides a set of design solutions which can be examined by experienced engineers. However, multi-objective genetic algorithms tend to require a large number of objective function evaluations to arrive at an acceptable Pareto-front. This article investigates a novel hybrid cellular automaton and genetic approach to multi-objective optimization (known as CAMOGA). The proposed method is applied to two large, real-world networks taken from the UK water industry. The results show that the proposed cellular automaton approach can provide a good approximation of the Pareto-front with very few network simulations, and that CAMOGA outperforms the standard multi-objective genetic algorithm in terms of efficiency in discovering similar Pareto-fronts.     

A jazz-based approach for optimal setting of pressure reducing valves in water distribution networks

This study presents a model for valve setting in water distribution networks (WDNs), with the aim of reducing the level of leakage. The approach is based on the harmony search (HS) optimization algorithm. The HS mimics a jazz improvisation process able to find the best solutions, in this case corresponding to valve settings in a WDN. The model also interfaces with the improved version of a popular hydraulic simulator, EPANET 2.0, to check the hydraulic constraints and to evaluate the performances of the solutions. Penalties are introduced in the objective function in case of violation of the hydraulic constraints. The model is applied to two case studies, and the obtained results in terms of pressure reductions are comparable with those of competitive metaheuristic algorithms (e.g. genetic algorithms). The results demonstrate the suitability of the HS algorithm for water network management and optimization.     

Optimal design of water distribution networks by a discrete state transition algorithm

In this study it is demonstrated that, with respect to model formulation, the number of linear and nonlinear equations involved in water distribution networks can be reduced to the number of closed simple loops. Regarding the optimization technique, a discrete state transition algorithm (STA) is introduced to solve several cases of water distribution networks. Firstly, the focus is on a parametric study of the ‘restoration probability and risk probability’ in the dynamic STA. To deal effectively with head pressure constraints, the influence is then investigated of the penalty coefficient and search enforcement on the performance of the algorithm. Based on the experience gained from training the Two-Loop network problem, a discrete STA has successfully achieved the best known solutions for the Hanoi, triple Hanoi and New York network problems.     

Optimal cost design of water distribution networks using a decomposition approach

Water distribution network decomposition, which is an engineering approach, is adopted to increase the efficiency of obtaining the optimal cost design of a water distribution network using an optimization algorithm. This study applied the source tracing tool in EPANET, which is a hydraulic and water quality analysis model, to the decomposition of a network to improve the efficiency of the optimal design process. The proposed approach was tested by carrying out the optimal cost design of two water distribution networks, and the results were compared with other optimal cost designs derived from previously proposed optimization algorithms. The proposed decomposition approach using the source tracing technique enables the efficient decomposition of an actual large-scale network, and the results can be combined with the optimal cost design process using an optimization algorithm. This proves that the final design in this study is better than those obtained with other previously proposed optimization algorithms.     

Investigation of static transmission expansion planning using the symbiotic organisms search algorithm

Transmission expansion planning (TEP) has become a complex problem in restructured electricity markets. This article presents the symbiotic organisms search (SOS) algorithm, a novel metaheuristic optimization technique for solving TEP problems in power systems. The SOS algorithm is inspired by the interactions among organisms in an ecosystem. The TEP problem is formulated here as an optimization problem to determine the cost-effective expansion planning of electrical power systems. Several constraints, such as power flow of the lines, right-of-way validity and maximum line addition, are taken into consideration. First, the SOS algorithm is tested with several benchmark functions. Then, it is applied on three standard power system networks (IEEE 24-bus system, Brazilian 46-bus system and Brazilian 87-bus system) in a TEP study to demonstrate the optimization capability of the proposed SOS algorithm. The results are compared with those produced by other state-of-the-art algorithms.     

基于环分布的频繁子图挖掘算法

频繁了图挖掘主要涉及到子图搜索和子图同构问题.对子图搜索问题,本文提出了环分布的概念,并构造了基于环分布的子图搜索算法:对了图同构问题,本文利用度序列和特征值构造了两种算法,分别用于对有向图和无向图的同构判别.利用同构算法对搜索出的子图进行同构分类,根据分类结果得到频繁了图.实验结果表明,本算法的效率优于现有算法.     

An effective hybrid cuckoo search and genetic algorithm for constrained engineering design optimization

This article presents an effective hybrid cuckoo search and genetic algorithm (HCSGA) for solving engineering design optimization problems involving problem-specific constraints and mixed variables such as integer, discrete and continuous variables. The proposed algorithm, HCSGA, is first applied to 13 standard benchmark constrained optimization functions and subsequently used to solve three well-known design problems reported in the literature. The numerical results obtained by HCSGA show competitive performance with respect to recent algorithms for constrained design optimization problems.     

Comparison between hybridized algorithm of GA–SA and ABC,GA, DE and PSO for vertical-handover in heterogeneous wireless networks

Genetic algorithms (GAs) and simulated annealing (SA) have emerged as leading methods for search and optimization problems in heterogeneous wireless networks. In this paradigm, various access technologies need to be interconnected; thus, vertical handovers are necessary for seamless mobility. In this paper, the hybrid algorithm for real-time vertical handover using different objective functions has been presented to find the optimal network to connect with a good quality of service in accordance with the user’s preferences. As it is, the characteristics of the current mobile devices recommend using fast and efficient algorithms to provide solutions near to real-time. These constraints have moved us to develop intelligent algorithms that avoid slow and massive computations. This was to, specifically, solve two major problems in GA optimization, i.e. premature convergence and slow convergence rate, and the facilitation of simulated annealing in the merging populations phase of the search. The hybrid algorithm was expected to improve on the pure GA in two ways, i.e., improved solutions for a given number of evaluations, and more stability over many runs. This paper compares the formulation and results of four recent optimization algorithms: artificial bee colony (ABC), genetic algorithm (GA), differential evolution (DE), and particle swarm optimization (PSO). Moreover, a cost function is used to sustain the desired QoS during the transition between networks, which is measured in terms of the bandwidth, BER, ABR, SNR, and monetary cost. Simulation results indicated that choosing the SA rules would minimize the cost function and the GA–SA algorithm could decrease the number of unnecessary handovers, and thereby prevent the ‘Ping-Pong’ effect.     

求解约束优化问题的改进布谷鸟搜索算法

为了提高约束优化问题的求解精度和收敛速度,提出求解约束优化问题的改进布谷鸟搜索算法。首先分析了基本布谷鸟搜索算法全局搜索和局部搜索过程中的不足,对其中全局搜索和局部搜索迭代公式进行重新定义,然后以一定概率在最优解附近进行搜索。对12个标准约束优化问题和4个工程约束优化问题进行测试并与多种算法进行对比,实验结果和统计分析表明所提算法在求解约束优化问题上具有较强的优越性。     

Pareto archived dynamically dimensioned search with hypervolume-based selection for multi-objective optimization

Pareto archived dynamically dimensioned search (PA-DDS) is a parsimonious multi-objective optimization algorithm with only one parameter to diminish the user's effort for fine-tuning algorithm parameters. This study demonstrates that hypervolume contribution (HVC) is a very effective selection metric for PA-DDS and Monte Carlo sampling-based HVC is very effective for higher dimensional problems (five objectives in this study). PA-DDS with HVC performs comparably to algorithms commonly applied to water resources problems (?-NSGAII and AMALGAM under recommended parameter values). Comparisons on the CEC09 competition show that with sufficient computational budget, PA-DDS with HVC performs comparably to 13 benchmark algorithms and shows improved relative performance as the number of objectives increases. Lastly, it is empirically demonstrated that the total optimization runtime of PA-DDS with HVC is dominated (90% or higher) by solution evaluation runtime whenever evaluation exceeds 10 seconds/solution. Therefore, optimization algorithm runtime associated with the unbounded archive of PA-DDS is negligible in solving computationally intensive problems.     

Enhanced particle swarm optimization for size and shape optimization of truss structures

This article presents an enhanced particle swarm optimization (EPSO) algorithm for size and shape optimization of truss structures. The proposed EPSO introduces a particle categorization mechanism into the particle swarm optimization (PSO) to eliminate unnecessary structural analyses during the optimization process and improve the computational efficiency of the PSO-based structural optimization. The numerical investigation, including three benchmark truss optimization problems, examines the efficiency of the EPSO. The results demonstrate that the particle categorization mechanism greatly reduces the computational requirements of the PSO-based approaches while maintaining the original search capability of the algorithms in solving optimization problems with computationally cheap objective function and expensive constraints.     

SSABA: Search Step Adjustment Based Algorithm

Finding the suitable solution to optimization problems is a fundamental challenge in various sciences. Optimization algorithms are one of the effective stochastic methods in solving optimization problems. In this paper, a new stochastic optimization algorithm called Search Step Adjustment Based Algorithm (SSABA) is presented to provide quasi-optimal solutions to various optimization problems. In the initial iterations of the algorithm, the step index is set to the highest value for a comprehensive search of the search space. Then, with increasing repetitions in order to focus the search of the algorithm in achieving the optimal solution closer to the global optimal, the step index is reduced to reach the minimum value at the end of the algorithm implementation. SSABA is mathematically modeled and its performance in optimization is evaluated on twenty-three different standard objective functions of unimodal and multimodal types. The results of optimization of unimodal functions show that the proposed algorithm SSABA has high exploitation power and the results of optimization of multimodal functions show the appropriate exploration power of the proposed algorithm. In addition, the performance of the proposed SSABA is compared with the performance of eight well-known algorithms, including Particle Swarm Optimization (PSO), Genetic Algorithm (GA), Teaching-Learning Based Optimization (TLBO), Gravitational Search Algorithm (GSA), Grey Wolf Optimization (GWO), Whale Optimization Algorithm (WOA), Marine Predators Algorithm (MPA), and Tunicate Swarm Algorithm (TSA). The simulation results show that the proposed SSABA is better and more competitive than the eight compared algorithms with better performance.     

Hessian approximation algorithms for hybrid optimization methods

This article introduces Hessian approximation algorithms to estimate the search direction of the quasi-Newton methods for solving optimization problems of continuous parameters. The proposed algorithms are quite different from other well-known quasi-Newton methods, such as symmetric rank-one, Davidon–Fletcher–Powell, and Broyden–Fletcher–Goldfarb–Shanno, in that the Hessian matrix is not calculated from the gradient information, rather directly from the function values. The proposed algorithms are designed for a class of hybrid algorithms that combine evolutionary search with the gradient-based methods of quasi-Newton type. The function values calculated for the evolutionary search are used for estimation of the Hessian matrix (or its inverse) as well as the gradient vector. Since the estimation process of the Hessian matrix is independent of that of the gradient vector, more reliable Hessian estimation with a small population is possible compared with the previous methods based upon the classical quasi-Newton methods. Numerical experiments show that the proposed algorithms are very competitive with state-of-the-art evolutionary algorithms for continuous optimization problems.     

求解约束优化问题的退火遗传算法

针对基于罚函数遗传算法求解实际约束优化问题的困难与缺点,提出了求解约束优化问题的退火遗传算法。对种群中的个体定义了不可行度,并设计退火遗传选择操作。算法分三阶段进行,首先用退火算法搜索产生初始种群体,随后利用遗传算法使搜索逐渐收敛于可行的全局最优解或较优解,最后用退火优化算法对解进行局部优化。两个典型的仿真例子计算结果证明该算法能极大地提高计算稳定性和精度。