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.     

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.     

Scatter search heuristic for least-cost design of water distribution networks

The optimization problems of water distribution networks are complex, multi-modal and discrete-variable problems that cannot be easily solved with conventional optimization algorithms. Heuristic algorithms such as genetic algorithms, simulated annealing, tabu search and ant colony optimization have been extensively employed over the last decade. This article proposed an optimization procedure based on the scatter search (SS) framework, which is also a heuristic algorithm, to obtain the least-cost designs of three well-known looped water distribution networks (two-loop, Hanoi and New York networks). The computational results obtained with the three benchmark instances indicate that SS is able to find solutions comparable to those provided by some of the most competitive algorithms published in the literature.     

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.     

用于结构优化设计的改进多目标群搜索算法

在多目标群搜索算法（multi-objective group search optimization, MGSO）基本原理的基础上,结合Pareto最优解理论,提出了基于约束改进的多目标群搜索算法（IMGSO）,并应用于多目标的结构优化设计．算法的改进主要有3个方面：第一,引入过渡可行域的概念来处理约束条件;第二,利用庄家法来构造非支配解集;最后,结合禁忌搜索算法和拥挤距离机制来选择发现者,以避免解集过早陷入局部最优,并提高收敛精度．采用IMGSO优化算法分别对平面和空间桁架结构进行了离散变量的截面优化设计,并与MGSO优化算法的计算结果进行了比较,结果表明改进的多目标群搜索优化算法IMGSO与MGSO算法相比具有更好的收敛精度.通过算例表明：IMGSO算法得到的解集中的解能大部分支配MGSO算法的解,在复杂高维结构中IMGSO算法的优越性更加明显,且收敛速度也有一定的提高,可有效应用于多目标的实际结构优化设计．     

A modified harmony search algorithm for the multi-objective flowshop scheduling problem with due dates

This paper presents a modified harmony search optimisation algorithm (MHSO), specifically designed to solve two- and three-objective permutation flowshop scheduling problems, with due dates. To assess its capability, five sets of scheduling problems have been used to compare the MHSO with a known and highly efficient genetic algorithm (GA) chosen as the benchmark. Obtained results show that the new procedure is successful in exploring large regions of the solution space and in finding a significant number of Pareto non-dominated solutions. For those cases where the exhaustive evaluation of sequences can be applied the algorithm is able to find the whole non-dominated Pareto border, along with a considerable number of solutions that share the same optimal values for the considered optimisation parameters. To validate the algorithm, five sets of scheduling problems are investigated in-depth in comparison with the GA. Results obtained by both methods (exhaustive solutions have been provided as well for small sized problems) are fully described and discussed.     

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.     

Optimal long-term design,rehabilitation and upgrading of water distribution networks

Given a limited budget, the choice of the best water distribution network upgrading strategy is a complex optimization problem. A model for the optimal long-term design and upgrading of new and existing water distribution networks is presented. A key strength of the methodology is the use of maximum entropy flows, which reduces the size of the problem and enables the application of linear programming for pipe size optimization. It also ensures the reliability level is high. The capital and maintenance costs and hydraulic performance are considered simultaneously for a predefined design horizon. The timing of upgrading over the entire planning horizon is obtained by dynamic programming. The deterioration over time of the structural integrity and hydraulic capacity of every pipe are explicitly considered. The upgrading options considered include pipe paralleling and replacement. The effectiveness of the model is demonstrated using the water supply network of Wobulenzi town in Uganda.     

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.     

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.     

Pareto-based multi-objective node placement of industrial wireless sensor networks using binary differential evolution harmony search

The reliability and real time of industrial wireless sensor networks (IWSNs) are the absolute requirements for industrial systems, which are two foremost obstacles for the large-scale applications of IWSNs. This paper studies the multi-objective node placement problem to guarantee the reliability and real time of IWSNs from the perspective of systems. A novel multi-objective node deployment model is proposed in which the reliability, real time, costs and scalability of IWSNs are addressed. Considering that the optimal node placement is an NP-hard problem, a new multi-objective binary differential evolution harmony search (MOBDEHS) is developed to tackle it, which is inspired by the mechanism of harmony search and differential evolution. Three large-scale node deployment problems are generated as the benCHmarks to verify the proposed model and algorithm. The experimental results demonstrate that the developed model is valid and can be used to design large-scale IWSNs with guaranteed reliability and real-time performance efficiently. Moreover, the comparison results indicate that the proposed MOBDEHS is an effective tool for multi-objective node placement problems and superior to Pareto-based binary differential evolution algorithms, nondominated sorting genetic algorithm II (NSGA-II) and modified NSGA-II.     

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 multi-objective scatter search for a bi-criteria no-wait flow shop scheduling problem

The flow shop problem as a typical manufacturing challenge has gained wide attention in academic fields. This article considers a bi-criteria no-wait flow shop scheduling problem (FSSP) in which weighted mean completion time and weighted mean tardiness are to be minimized simultaneously. Since a FSSP has been proved to be NP-hard in a strong sense, a new multi-objective scatter search (MOSS) is designed for finding the locally Pareto-optimal frontier of the problem. To prove the efficiency of the proposed algorithm, various test problems are solved and the reliability of the proposed algorithm, based on some comparison metrics, is compared with a distinguished multi-objective genetic algorithm (GA), i.e. SPEA-II. The computational results show that the proposed MOSS performs better than the above GA, especially for the large-sized problems.     

An improved harmony search minimization algorithm using different slip surface generation methods for slope stability analysis

An improved harmony search algorithm is proposed which is found to be more efficient than the original harmony search algorithm for slope stability analysis. The effectiveness of the proposed algorithm is examined by considering several published cases. The improved harmony search method is applied to slope stability problems with five types of procedure for generating trial slip surfaces. It is demonstrated that the improved harmony search algorithm is efficient and effective for the minimization of factors of safety for various difficult problems, and the method of generating the trial failure surfaces can be important in the minimization process.     

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.