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.     

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.     

A fuzzy discrete harmony search algorithm applied to annual cost reduction in radial distribution systems

Similarly to other optimization algorithms, harmony search (HS) is quite sensitive to the tuning parameters. Several variants of the HS algorithm have been developed to decrease the parameter-dependency character of HS. This article proposes a novel version of the discrete harmony search (DHS) algorithm, namely fuzzy discrete harmony search (FDHS), for optimizing capacitor placement in distribution systems. In the FDHS, a fuzzy system is employed to dynamically adjust two parameter values, i.e. harmony memory considering rate and pitch adjusting rate, with respect to normalized mean fitness of the harmony memory. The key aspect of FDHS is that it needs substantially fewer iterations to reach convergence in comparison with classical discrete harmony search (CDHS). To the authors’ knowledge, this is the first application of DHS to specify appropriate capacitor locations and their best amounts in the distribution systems. Simulations are provided for 10-, 34-, 85- and 141-bus distribution systems using CDHS and FDHS. The results show the effectiveness of FDHS over previous related studies.     

Applying tabu search and simulated annealing to the optimal design of sewer networks

Optimizations of sewer network designs create complicated and highly nonlinear problems wherein conventional optimization techniques often get easily bogged down in local optima and cannot successfully address such problems. In the past decades, heuristic algorithms possessing robust and efficient global search capabilities have helped to solve continuous and discrete optimization problems and have demonstrated considerable promise. This study applied tabu search (TS) and simulated annealing (SA) to the optimization of sewer network designs. For a case study, this article used the sewer network design of a central Taiwan township, which contains significantly varied elevations, and the optimal designs from TS and SA were compared with the original official design. The results show that, in contrast with the original design's failure to satisfy the minimum flow-velocity requirements, both TS and SA achieved least-cost solutions that also fulfilled all the constraints of the design criteria. According to the average performance of 200 trials, SA outperformed TS in both robustness and efficiency for solving sewer network optimization problems.     

Optimization of seismic isolation systems via harmony search

In this article, the optimization of isolation system parameters via the harmony search (HS) optimization method is proposed for seismically isolated buildings subjected to both near-fault and far-fault earthquakes. To obtain optimum values of isolation system parameters, an optimization program was developed in Matlab/Simulink employing the HS algorithm. The objective was to obtain a set of isolation system parameters within a defined range that minimizes the acceleration response of a seismically isolated structure subjected to various earthquakes without exceeding a peak isolation system displacement limit. Several cases were investigated for different isolation system damping ratios and peak displacement limitations of seismic isolation devices. Time history analyses were repeated for the neighbouring parameters of optimum values and the results proved that the parameters determined via HS were true optima. The performance of the optimum isolation system was tested under a second set of earthquakes that was different from the first set used in the optimization process. The proposed optimization approach is applicable to linear isolation systems. Isolation systems composed of isolation elements that are inherently nonlinear are the subject of a future study. Investigation of the optimum isolation system parameters has been considered in parametric studies. However, obtaining the best performance of a seismic isolation system requires a true optimization by taking the possibility of both near-fault and far-fault earthquakes into account. HS optimization is proposed here as a viable solution to this problem.     

Construction of nested maximin designs based on successive local enumeration and modified novel global harmony search algorithm

Engineering design often involves different types of simulation, which results in expensive computational costs. Variable fidelity approximation-based design optimization approaches can realize effective simulation and efficiency optimization of the design space using approximation models with different levels of fidelity and have been widely used in different fields. As the foundations of variable fidelity approximation models, the selection of sample points of variable-fidelity approximation, called nested designs, is essential. In this article a novel nested maximin Latin hypercube design is constructed based on successive local enumeration and a modified novel global harmony search algorithm. In the proposed nested designs, successive local enumeration is employed to select sample points for a low-fidelity model, whereas the modified novel global harmony search algorithm is employed to select sample points for a high-fidelity model. A comparative study with multiple criteria and an engineering application are employed to verify the efficiency of the proposed nested designs approach.     

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.     

A diversity-enriched variant of discrete PSO applied to the design of water distribution networks

The design of water distribution networks (WDNs) is addressed by using a variant of the particle swarm optimization (PSO) algorithm. This variant, which makes use of a discrete version of PSO already considered by the authors, overcomes one of the PSO's main drawbacks, namely its difficulty in maintaining acceptable levels of population diversity and in balancing local and global searches. The performance of the variant proposed here is investigated by applying the model to solve two standard benchmark problems: the Hanoi new water distribution network and the New York Tunnel water supply system. The results obtained show considerable improvements in both convergence characteristics and the quality of the final solutions, and near-optimal results are consistently achieved at reduced computational cost.     

A random-key encoded harmony search approach for energy-efficient production scheduling with shared resources

When seeking near-optimal solutions for complex scheduling problems, meta-heuristics demonstrate good performance with affordable computational effort. This has resulted in a gravitation towards these approaches when researching industrial use-cases such as energy-efficient production planning. However, much of the previous research makes assumptions about softer constraints that affect planning strategies and about how human planners interact with the algorithm in a live production environment. This article describes a job-shop problem that focuses on minimizing energy consumption across a production facility of shared resources. The application scenario is based on real facilities made available by the Irish Center for Manufacturing Research. The formulated problem is tackled via harmony search heuristics with random keys encoding. Simulation results are compared to a genetic algorithm, a simulated annealing approach and a first-come-first-served scheduling. The superior performance obtained by the proposed scheduler paves the way towards its practical implementation over industrial production chains.     

An improved version of the multiple trajectory search for real value multi-objective optimization problems

Multi-objective optimization is widely used in science, engineering and business. In this article, an improved version of the multiple trajectory search (MTS) called MTS2 is presented and successfully applied to real-value multi-objective optimization problems. In the first step, MTS2 generates M initial solutions distributed over the solution space. These solutions are called seeds. Some seeds with good objective values are selected as foreground seeds. Then, MTS2 chooses a suitable region search method for each foreground seed according to the landscape of the neighbourhood of the seed. During the search, MTS2 focuses its search on some promising areas specified by the foreground seeds. The performance of MTS2 was examined by applying it to solve the benchmark problems provided by the Competition of Performance Assessment of Constrained/Bound Constrained Multi-Objective Optimization Algorithms held at the 2009 IEEE Congress on Evolutionary Computation.     

A Pareto-based estimation of distribution algorithm for the multi-objective flexible job-shop scheduling problem

To solve the multi-objective flexible job-shop problem (MFJSP), an effective Pareto-based estimation of distribution algorithm (P-EDA) is proposed. The fitness evaluation based on Pareto optimality is employed and a probability model is built with the Pareto superior individuals for estimating the probability distribution of the solution space. In addition, a mechanism to update the probability model is proposed, and the new individuals are generated by sampling the promising searching region based on the probability model. To avoid premature convergence and enhance local exploitation, the population is divided into two sub-populations at certain generations according to a splitting criterion, and different operators are designed for the two sub-populations to generate the promising neighbour individuals. Moreover, multiple strategies are utilised in a combination way to generate the initial solutions, and a local search strategy based on critical path is proposed to enhance the exploitation ability. Furthermore, the influence of parameters is investigated based on the Taguchi method of design of experiment, and a suitable parameter setting is suggested. Finally, numerical simulation based on some well-known benchmark instances and comparisons with some existing algorithms are carried out. The comparative results demonstrate the effectiveness of the proposed P-EDA in solving the MFJSP.     

A guided search genetic algorithm using mined rules for optimal affective product design

Affective design is an important aspect of new product development, especially for consumer products, to achieve a competitive edge in the marketplace. It can help companies to develop new products that can better satisfy the emotional needs of customers. However, product designers usually encounter difficulties in determining the optimal settings of the design attributes for affective design. In this article, a novel guided search genetic algorithm (GA) approach is proposed to determine the optimal design attribute settings for affective design. The optimization model formulated based on the proposed approach applied constraints and guided search operators, which were formulated based on mined rules, to guide the GA search and to achieve desirable solutions. A case study on the affective design of mobile phones was conducted to illustrate the proposed approach and validate its effectiveness. Validation tests were conducted, and the results show that the guided search GA approach outperforms the GA approach without the guided search strategy in terms of GA convergence and computational time. In addition, the guided search optimization model is capable of improving GA to generate good solutions for affective design.     

基于遗传算法解决河流环境需水量优化调度的模糊多目标规划方法的研究

为实现城市受污染河流的环境需水量的合理调配,以各蓄水构筑物的调水量为决策变量,研究了在保证河流生态环境需求的基础上,实现整个流域的污染负荷的环境容量最大化、水量最大节约和调水成本最小化的方法,建立了环境需水调度的模糊多目标规划模型.模型中采用整合的非线性梯度隶属度函数作为目标函数,以遗传算法作为求解此模型的工具,并将该模型用于大庆市黎明河流域的环境水量调配,取得较好的效果.     

An adaptive heuristic cross-entropy algorithm for optimal design of water distribution systems

The optimal design problem of a water distribution system is to find the water distribution system component characteristics (e.g. pipe diameters, pump heads and maximum power, reservoir storage volumes, etc.) which minimize the system's capital and operational costs such that the system hydraulic laws are maintained (i.e. Kirchhoff's first and second laws), and constraints on quantities and pressures at the consumer nodes are fulfilled. In this study, an adaptive stochastic algorithm for water distribution systems optimal design based on the heuristic cross-entropy method for combinatorial optimization is presented. The algorithm is demonstrated using two well-known benchmark examples from the water distribution systems research literature for single loading gravitational systems, and an example of multiple loadings, pumping, and storage. The results show the cross-entropy dominance over previously published methods.     

An efficient local improvement operator for the multi-objective wireless sensor network deployment problem

Wireless sensor network layout, also known as sensor node deployment, is a complex NP-complete optimization task that determines most of the functioning features of a wireless sensor network. Coverage, connectivity and lifetime (handled through its opposing parameter, power consumption), are three of the most important characteristics of the service, and are taken into consideration in this article within a multi-objective approach of the problem. Leveraging on the specific properties of the wireless sensor nodes and networks, the Proximity Avoidance Coverage-preserving Operator (PACO) for local improvement is presented, described and tested. The testbed consists of a set of state-of-the-art multi-objective optimization algorithms with different configurations, and problem instances of varying size. In all the scenarios, and more specially in the algorithmic settings that already produce high performance solutions, PACO has proven to be a robust enhancement to the raw optimization technique, without requiring additional computation, that easily scales through problem complexity.     

Game-theory approach for multi-objective optimal design of stationary flat-plate solar collectors

A game-theory approach has been used for the multi-objective optimum design of stationary flat-plate solar collectors. The clear-day solar-beam radiation and diffuse radiation at the location of the solar collector (Miami) are estimated. Three objectives are considered in the optimization-problem formulation: maximization of the annual average incident solar energy; maximization of the lowest month incident solar energy; and minimization of costs. The game-theory methodology is used for the solution of the three objective-constrained optimization problems to find a balanced solution. This solution represents the best compromise in terms of the super-criterion selected. Two types of sensitivity analyses are conducted on the optimum solution in this work. The sensitivity analysis with respect to the design variables indicates which design valuables are more important to different objective functions. The sensitivity analysis with respect to the solar constant shows that small fluctuations of solar constant experienced in practice affect the various objectives very little, thereby indicating that the mathematical model is robust. This work represents the first work aimed at the application of multi-objective optimization strategy, particularly the game theory approach, for the solution of the solar collector design problem.     

结构主动控制的一体化多目标优化研究

基于Pareto多目标遗传算法提出了结构主动控制系统的一体化多目标优化设计方法,对作动器位置与主动控制器进行同步优化设计.外界激励采用平稳过滤白噪声来模拟,在状态空间下通过求解Lyapunov方程,得到结构响应和主动控制力的均方值.主动控制器采用LQG控制算法来进行设计.以结构位移和加速度均方值最大值与相应无控响应均方值的最大值之比,以及所需控制力均方值之和作为多目标同步优化的目标函数.优化过程还考虑了结构与激励参数对优化结果的影响.最后以某6层平面框架有限元模型为例进行了计算机仿真分析,结果表明所提出的主动控制系统多目标一体化优化方法简单,高效,实用,具有较好的普适性.     

On the optimal design of water distribution networks: a practical MINLP approach

We propose a practical solution method for real-world instances of a water-network optimization problem with fixed topology using a nonconvex continuous NLP (NonLinear Programming) relaxation and a MINLP (Mixed Integer NonLinear Programming) search. Our approach employs a relatively simple and accurate model that pays some attention to the requirements of the solvers that we employ. Our view is that in doing so, with the goal of calculating only good feasible solutions, complicated algorithmics can be confined to the MINLP solver. We report successful computational experience using available open-source MINLP software on problems from the literature and on difficult real-world instances. An important contribution of this paper is that the solutions obtained, besides being low cost, are immediately usable in practice because they are characterized by an allocation of diameters to pipes that leads to a correct hydraulic operation of the network. This is not the case for most of the other methods presented in the literature.