Harmony Search Algorithm

Harmony Search optimization algorithm has become popular in many fields of engineering research and practice during the last decade. This paper introduces three major rules of the algorithm: harmony memory considering (HMC) rule, random selecting (RS) rule, and pitch adjusting (PA) rule, and shows the effect of each rule on the algorithm performance. Application of example benchmark function proves that each rule has its own role in the exploration and exploitation processes of the search. Good balance between the two processes is very important, and the PA rule can be a key factor for the balance if used intelligently.

Generally speaking, it is not fully understood why and how metaheuristic algorithms work very well under what conditions. It is the intention of this paper to clarify the performance characteristics of some of popular algorithms depending on the fitness landscape of specific problems. This study shows the performance of each considered algorithm on the fitness landscapes with different problem characteristics. The conclusions made in this study can be served as guidance on selecting algorithms to the problem of interest.

Recently, Harmony Search Algorithm (HSA) is gaining prominence in solving real-world optimization problems. Like most of the evolutionary algorithms, finding optimal solution to a given numerical problem using HSA involves several evaluations of the original function and is prohibitively expensive. This problem can be resolved by amalgamating HSA with surrogate models that approximate the output behavior of complex systems based on a limited set of computational expensive simulations. Though, the use of surrogate models can reduce the original functional evaluations, the optimization based on the surrogate model can lead to erroneous results. In addition, the computational effort needed to build a surrogate model to better approximate the actual function can be an overhead. In this paper, we present a novel method in which HSA is integrated with an ensemble of low quality surrogate models. The proposed algorithm is referred to as HSAES and is tested on a set of 10 bound-constrained problems and is compared with conventional HSA.

The parameters of traditional PID controller cannot varies with load and environment for the precision motion control system. In this paper, an efficient scheme for proportional-integral-derivation (PID) controller using bee colony algorithm is applied to precision motion control system. The simulation results show that the feasibility of bee colony PID control algorithm in precision motion field. Furthermore, the bee colony PID control algorithm make the precision motion control system has faster response speed, high positioning accuracy, and its parameters can optimize automatically.

This paper discusses the resource availability cost problem (RACP) with the objective of minimizing the total cost of the unlimited renewable resources by a prespecified project deadline. A tabued scatter search (TSS) algorithm is developed to solve the RACP. The deadline constraint is handled in coding. A tabu search module is embedded in the framework of scatter search. A computational experiment was conducted and the computational results show that the proposed TSS hybrid algorithm is effective and advantageous for the RACP.

Harmony Search Algorithm (HSA) has shown to be simple, efficient and strong optimization algorithm. The exploration ability of any optimization algorithm is one of the key points. In this article a new methodology is proposed to measure the exploration ability of the HS algorithm. To understand the searching ability potential exploration range for HS algorithm is designed. Four HS variants are selected and their searching ability is tested based on the choice of improvised harmony. An empirical analysis of the proposed method is tested along with the justification of theoretical findings and experimental results.

The thermal error of the motorized spindle has great influence on the accuracy of the NC machine tools. In order to reduce the thermal error, the increase type PID control algorithm is adopted for the control system which can make the temperature controlled in reasonable range. In accordance with the control object features, the Application of the control algorithm is realized in MCU System. Finally, the experiments are carried out which verified the validity and effectiveness of the design of temperature control system by analysis of the experimental data.

The noise signal influences the stage positioning accuracy in the process of the nano stage motion, for which designs a Kalman filter to filter out noise effectively. The model of nano-positioning stage is established. Then the motion of stage is estimated by using Kalman filtering model, and the filtering effect of Kalman filter can be observed in the Matlab. Experimental results show that Kalman filtering can effectively reduce the positioning deviation, which is less than 4nm, and positioning accuracy has been improved significantly. Kalman filter has a good effect on filtering and can meet the requirement of positioning precision for nano-positioning stage.

The mechanical structure and load changes of nano positioning stage cause a poor accuracy of the control system. For solving the problem, Adaptive PID control algorithm was applied to control the nano positioning stage. The model of nano positioning stage was established on the basis of Controlled Autoregressive Moving Average model (CARMA). The parameters of controller were identified based on Recursive Extended Least Squares algorithm (RELS). The control system of nano positioning stage was steady through 4ms after parameters identification, which static error was less than 5nm. The experimental results demonstrated that adaptive PID control algorithm was able to identify the parameters of controlled object and calculate the parameters of controller. The accuracy of control system can be at nanometer resolution.

Harmony Search is a metaheuristic technique for optimizing problems involving sets of continuous or discrete variables, inspired by musicians searching for harmony between instruments in a performance. Here we investigate two frameworks, using Harmony Search to select a mixture of continuous and discrete variables forming the components of a Memetic Algorithm for cross-domain heuristic search. The first is a single-point based framework which maintains a single solution, updating the harmony memory based on performance from a fixed starting position. The second is a population-based method which co-evolves a set of solutions to a problem alongside a set of harmony vectors. This work examines the behaviour of each framework over thirty problem instances taken from six different, real-world problem domains. The results suggest that population co-evolution performs better in a time-constrained scenario, however both approaches are ultimately constrained by the underlying metaphors.

In this paper, an improved harmony search (IHS) algorithm is proposed to solve the distributed two machine flow-shop scheduling problem (DTMFSP) with makespan criterion. First, a two-stage decoding rule is developed for the decimal vector based representation. At the first stage, a job-to-factory assignment method is designed to transform a continuous harmony vector to a factory assignment. At the second stage, the Johnson’s method is applied to provide a job sequence in each factory. Second, a new pitch adjustment rule is developed to adjust factory assignment effectively. The influence of parameter setting on the IHS is investigated based on the Taguchi method of design of experiments, and numerical experiments are carried out. The comparisons with the global-best harmony search and the original harmony search demonstrate the effectiveness of the IHS in solving the DTMFSP.

This paper addresses the nurse rostering problem (NRP), whose objective is to minimize a total penalty caused by the roster. A large number of constraints required to be considered could cause a great difficulty of handling the NRP. A hybrid harmony search algorithm (HHSA) with a greedy local search is proposed to solve the NRP. A personal schedule is divided into several blocks, in which a subset of constraints is considered in advance. Based on these blocks, the pitch adjustment and randomization are carried out. Every time a roster is improvised, a coverage repairing procedure is applied to make the shift constraints satisfied, and the greedy local search is used to improve the roster’s quality. The proposed HHAS was tested on many well known real-world problem instances and competitive solutions were obtained.

In the last years freight transportation has undergone a sharp increase in the scales of its underlying processes and protocols mainly due to the ever-growing community of users and the increasing number of on-line shopping stores. Furthermore, when dealing with the last stage of the shipping chain an additional component of complexity enters the picture as a result of the fixed availability of the destination of the good to be delivered. As such, business opening hours and daily work schedules often clash with the delivery times programmed by couriers along their routes. In case of conflict, the courier must come to an arrangement with the destination of the package to be delivered or, alternatively, drop it off at a local depot to let the destination pick it up at his/her time convenience. In this context this paper will formulate a variant of the so-called courier problem under economic profitability criteria including the cost penalty derived from the delayed drop-off. In this context, if the courier delivers the package to its intended destination before its associated deadline, he is paid a reward. However, if he misses to deliver in time, the courier may still deliver it at the destination depending on its availability or, alternatively, drop it off at the local depot assuming a certain cost. The manuscript will formulate the mathematical optimization problem that models this logistics process and solve it efficiently by means of the Harmony Search algorithm. A simulation benchmark will be discussed to validate the solutions provided by this meta-heuristic solver and to compare its performance to other algorithmic counterparts.

The high data volumes being managed by and transferred through mobile networks in the last few years are the main rationale for the upsurge of research aimed at finding efficient technical means to offload exceeding traffic to alternative communication infrastructures with higher transmission bandwidths. This idea is solidly buttressed by the proliferation of short-range wireless communication technologies (e.g. mobile devices with multiple radio interfaces), which can be conceived as available opportunistic hotspots to which the operator can reroute exceeding network traffic depending on the contractual clauses of the owner at hand. Furthermore, by offloading to such hotspots a higher effective coverage can be attained by those operators providing both mobile and fixed telecommunication services. In this context, the operator must decide if data generated by its users will be sent over conventional 4G+/4G/3G communication links, or if they will instead be offloaded to nearby opportunistic networks assuming a contractual cost penalty. Mathematically speaking, this problem can be formulated as a spanning tree optimization subject to cost-performance criteria and coverage constraints. This paper will elaborate on the efficient solving of this optimization paradigm by means of the Harmony Search meta-heuristic algorithm and the so-called Dandelion solution encoding, the latter allowing for the use of conventional meta-heuristic operators maximally preserving the locality of tree representations. The manuscript will discuss the obtained simulation results over different synthetically modeled setups of the underlying communication scenario and contractual clauses of the users.

During the last two decades, parallel computing has drawn attention as an alternative to lessen computational burden in the engineering domain. Parallel computing has also been adopted for meta-heuristic optimization algorithms which generally require large number of functional evaluations because of their random nature of search. However, traditional parallel approaches, which distribute and perform fitness calculations concurrently on the processing units, are not intended to improve the quality of solution but to shorten CPU computation time. In this study, we propose a new parallelization scheme to improve the effectiveness and efficiency of harmony search. Four harmony searches are simultaneously run on the processors in a work station, sharing search information (e.g., a good solution) at the predefined iteration intervals. The proposed parallel HS is demonstrated through the optimization of an engineering planning problem.

A hybrid optimization method that combines the power of the harmony search (HS) algorithm with the mine blast algorithm (MBA) is presented in this study. The resulting mine blast harmony search (MBHS) utilizes the MBA for exploration and the HS for exploitation. The HS is inspired by the improvisation process of musicians, while the MBA is derived based on explosion of landmines. The HS used in the proposed hybrid method is an improved version, introducing a new concept for the harmony memory (HM) (i.e., dynamic HM), while the MBA is modified in terms of its mathematical formulation. Several benchmarks with many design variables are used to validate the MBHS, and the optimization results are compared with other algorithms. The obtained optimization results show that the proposed hybrid algorithm provides better exploitation ability (particularly in final iterations) and enjoys fast convergence to the optimum solution.

This paper proposes an Improved Modified Harmony Search Algorithm with constraint handling with application to redundancy allocation problems in reliability engineering. The performance of Improved Modified Harmony Search is being compared with that of the original Harmony Search, Modified Great Deluge Algorithm, Ant Colony Optimization, Improved Non-Equilibrium Simulated Annealing and Simulated Annealing. It is observed that Improved Modified Harmony Search requires less number of function evaluations compared to others.

As a meta-heuristic algorithm, Harmony Search (HS) algorithm is a population-based meta-heuristics approach that is superior in solving diversified large scale optimization problems. Several studies have pointed that Harmony Search (HS) is an efficient and flexible tool to resolve optimization problems in diversed areas of construction, engineering, robotics, telecommunication, health and energy. In this respect, the three main operators in HS, namely the Harmony Memory Consideration Rate (HMCR), Pitch Adjustment Rate (PAR) and Bandwidth (BW) play a vital role in balancing the local exploitation and the global exploration. These parameters influence the overall performance of HS algorithm, and therefore it is very crucial to fine turn them. However, when performing a local search, the harmony search algorithm can be easily trapped in the local optima. Therefore, there is a need to improve the fine tuning of the parameters. This research focuses on the HMCR parameter adjustment strategy using step function with combined Gaussian distribution function to enhance the global optimality of HS. The result of the study showed a better global optimum in comparison to the standard HS.

Each of six members of hydrosystem laboratory in Korea University (KU) invented either a new metaheuristic optimization algorithm or an improved version of some optimization methods as a class project for the fall semester 2014. The objective of the project was to help students understand the characteristics of metaheuristic optimization algorithms and invent an algorithm themselves focusing those regarding convergence, diversification, and intensification. Six newly developed/improved metaheuristic algorithms are Cancer Treatment Algorithm (CTA), Extraordinary Particle Swarm Optimization (EPSO), Improved Cluster HS (ICHS), Multi-Layered HS (MLHS), Sheep Shepherding Algorithm (SSA), and Vision Correction Algorithm (VCA). This paper describes the details of the six developed/improved algorithms. In a follow-up companion paper, the six algorithms are demonstrated and compared through well-known benchmark functions and a real-life engineering problem.

In the previous companion paper, six new/improved metaheuristic optimization algorithms developed by members of Hydrosystem laboratory in Korea University (KU) are introduced. The six algorithms are Cancer Treatment Algorithm (CTA), Extraordinary Particle Swarm Optimization (EPSO), Improved Cluster HS (ICHS), Multi-Layered HS (MLHS), Sheep Shepherding Algorithm (SSA), and Vision Correction Algorithm (VCA). The six algorithms are tested and compared through six well-known unconstrained benchmark functions and a pipe sizing problem of water distribution network. Performance measures such as mean, best, and worst solutions (under given maximum number of function evaluations) are used for the comparison. Optimization results are obtained from thirty independent optimization trials. Obtained Results show that some of the newly developed/improved algorithms show superior performance with respect to mean, best, and worst solutions when compared to other existing algorithms.

Biogeography-based optimization is a recent addition in the class of population based gradient free search algorithms. Due to its simplicity in implementation and presence of very few tuning parameters, it has become very popular in very short span of time. From its inception in 2008, it has seen many changes in different steps of the algorithms. This paper incorporates the modified blended migration and polynomial mutation in the basic version of BBO. The proposed BBO is named as BBO with modified blended crossover and polynomial mutation (BBO-MBLX-PM). The performance of proposed BBO is explored over 20 test problems and compared with basic BBO as well as blended BBO. Results show that BBO-MBLX-PM outperforms over BBO and other considered variants of BBO.

Biogeography based optimization (BBO) has recently gain interest of researchers due to its efficiency and existence of very few parameters. The BBO is inspired by geographical distribution of species within islands. However, BBO has shown its wide applicability to various engineering optimization problems, the original version of BBO sometimes does not perform up to the mark. Poor balance of exploration and exploitation is the reason behind it. Migration, mutation and elitism are three operators in BBO. Migration operator is responsible for the information sharing among candidate solutions (islands). In this way, the migration operator plays an important role for the design of an efficient BBO. This paper proposes a new migration operator in BBO. The so obtained BBO shows better diversified search process and hence finds solutions more accurately with high convergence rate. The BBO with new migration operator is tested over 20 test problems. Results are compared with that of original BBO and Blended BBO. The comparison which is based on efficiency, reliability and accuracy shows that proposed migration operator is competitive to the present one.

In this paper, a modified version of Spider Monkey Optimization (SMO) algorithm is proposed. This modified version is named as Tournament selection based Spider Monkey Optimization (TS-SMO). TS-SMO replaces the fitness proportionate probability scheme of SMO with tournament selection based probability scheme with an objective to improve the exploration ability of SMO by avoiding premature convergence. The performance of the proposed variant is tested over a large benchmark set of 46 unconstrained benchmark problems of varying complexities broadly classified into two categories: scalable and non-scalable problems. The performance of TS-SO is compared with that of SMO. Results for scalable and non-scalable problems have been analysed separately. A statistical test is employed to access the significance of improvement in results. Numerical and statistical results show that the proposed modification has a positive impact on the performance of original SMO in terms of reliability, efficiency and accuracy.

Bioactive compounds form different plant materials are used in a number of important pharmaceutical, food and chemical industries. Many conventional and unconventional methods are available to extract optimum yields of these bioactive compounds from various plant materials. This paper focuses on the extraction of bioactive compounds (crocin, geniposide and total phenolic compounds) from Gardenia

(Gardenia jasminoides

Ellis)

by modeling the problem as a nonlinear optimization problem with multiple objectives. There are three objective functions each representing the maximizing of three bioactive compounds i.e. crocin, geniposide and total phenolic compounds. Each of the bioactive compounds are dependent on three factors namely: concentration of ethanol, extraction temperature and extraction time. The solution methodology is a recently proposed Laplacian Biofeographical Based Optimization. The results obtained are compared with previously reported results and show a significant improvement, thus exhibiting not only the superior performance of Laplacian Biogeographical Based Optimization, but also the complexity of the problem at hand.

This study develops river stage forecasting models combining Support Vector Regression (SVR) and optimization algorithms. The SVR is applied for forecasting river stage, and the optimization algorithms, including Grid Search (GS), Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and Artificial Bee Colony (ABC), are applied for searching the optimal parameters of the SVR. For assessing the applicability of models combining SVR and optimization algorithms, the model performance is compared with ANN and ANFIS models. In terms of model efficiency, SVR-GS, SVR-GA, SVR-PSO and SVR-ABC models yield better results than ANN and ANFIS models. SVR-PSO and SVR-ABC models produce relatively better efficiency than SVR-GS and SVR-GA models. SVR-PSO and SVR-ABC yield the best performance in terms of model efficiency. Results indicate that river stage forecasting models combining SVR and optimization algorithms can be used as an effective tool for forecasting river stage accurately.

Support Vector Machine (SVM) is one of the fastest growing methods of machine learning due to its good generalization ability and good convergence performance; it has been successfully applied in various fields, such as text classification, statistics, pattern recognition, and image processing. However, for real-time data collection systems, the traditional SVM methods could not perform well. In particular, they cannot well cope with the increasing new samples. In this paper, we give a survey on online SVM. Firstly, the description of SVM is introduced, then the brief summary of online SVM is given, and finally the research and development of online SVM are presented.

The objective of this study is to apply a hybrid model for estimating solar radiation and investigate its accuracy. A hybrid model is wavelet-based support vector machines (WSVMs). Wavelet decomposition is employed to decompose the solar radiation time series components into approximation and detail components. These decomposed time series are then used as input of support vector machines (SVMs) modules in the WSVMs model. Based on statistical indexes, results indicate that WSVMs can successfully be used for the estimation of daily global solar radiation at Champaign and Springfield stations in Illinois.

In practice, many physics principles have been employed to derive various models of financial engineering. However, few studies have been done on the feature selection of finance on time series data. The purpose of this paper is to determine if the behavior of market participant can be detected from historical price. For this purpose, the proposed algorithm utilizes back propagation neural network (BPNN) and works with new feature selection approach in data mining, which is used to generate more information of market behavior. This study is design for exchange-traded fund (ETF) to develop the day-trade strategy with high profit. The results show that BPNN hybridized with financial physical feature, as compared with the traditional approaches such as random walk, typically result in better performance.

The value of the investment method is that investors who are anxious to pursue, there are many value investing methods have been proposed, but only a minority of the value investing method were proved to be effective. The study is based on messages generated defined value of the investment by Steidlmayer in 1984 proposed market profile theory. In order to extract trading behavior of dealer and product value by the huge financial trading information, the model used the trading data to capture feature patterns, and find the double distribution trend day generated by market profile. The experimental results show the single print as an entry point, and the reference to historical support and pressure line as an exit point. The results show the returns are 24.09 points and the accuracy achieved 57.45%.The results had shown the analysis model can find the investment goods real value from the huge trading information, and help investors obtain excess returns.

In our earlier researches we examined the reliability and accuracy of sensors used in outdoor positioning. Results have shown that they are not as reliable as many think. So the question rightly arises: what sensor could be the solution for indoor navigation. The sensitivity and resilience of smartphone sensors are currently unknown, and their reliability is also questionable because of the many distracting factors. However, studies also show that it is possible to decrease distraction-caused errors with the help of appropriate algorithms. Hence first we must define sensitivity of sensors and understand their operational principles to find the appropriate algorithms.

Large facilities in urban areas generate lots of traffic and cause congestion that waste social time and become a major source of greenhouse gas (GHG). To overcome a shortcoming of the fixed transportation cost in conventional facility models, the congestion effect by facility users as well as general drivers in networks, with increased GHG emission is considered. In this paper, several Harmony Search algorithms with local search are developed and compared to the existing Tabu Search algorithm in a variety of networks. The results demonstrate that the proposed approach and local search method can find better or comparable solution than other methods within a given time.

Helical piles are a manufactured steel foundation composed of one or multiple helix plates affixed to a central shaft. A helical pile is installed by rotating the central shaft with hydraulic torque motors. There are three representative theoretical predictions for the bearing capacity of helical piles: individual bearing method, cylindrical shear method, and torque correlation method. The bearing capacity of helical piles is governed by the helical pile’s configuration, geologic conditions and penetration depth. The high variability of influence factors makes an optimum design for helical pile configuration difficult in practice. In this paper, the harmony search algorithm is adopted to minimize the material cost of helical piles by optimizing the components composing a helical pile based on the proposed bearing capacity prediction. The optimization process based on the combined prediction method with the aid of the harmony search algorithm leads to an economical design by saving about 27percent of the helical pile material cost.

Construction site layout planning is a dynamic multi-objective optimization problem since there are various temporary facilities (TFs) employed in the different construction phase. This paper proposes the use of harmony search algorithm (HSA) to solve the problem that assigning TFs to inside of the building. The suggested algorithm shows a rapid convergence to an optimal solution in a short time. In addition, comparative analysis with Genetic Algorithm (GA) is conducted to prove the efficiency of the proposed algorithm quantitatively.

This paper presents a simulation-optimization model integrating particle swarm optimization (PSO) algorithm and sequential streamflow routing (SSR) method to maximize the net present value (NPV) of a hydropower storage development project. In the PSO-SSR model, the SSR method simulates the operation of reservoir and its powerplant on a monthly basis over long term for each set of controllable design and operational variables, which includes dam reservoir and powerplant capacities as well as reservoir rule curve parameters, being searched for by the PSO algorithm. To evaluate the project NPV for each set of the controllable variables, the “alternative thermal powerplant (ATP)” approach is employed to determine the benefit term of the project NPV. The PSO-SSR model has been used in the problem of optimal design and operation of Garsha hydropower development project in Iran. Results show that the model with a simple, hydropower standard operating policy results in an NPV comparable to another model optimizing operating policies.

Water transfer development projects (WTDPs) could be considered in arid and semi-arid areas in response to uneven distribution of available water resources over space. This paper presents a simulation-optimization model by linking Water Evaluation and Planning System (WEAP) to particle swarm optimization (PSO) algorithm for optimal design and operation of the Karoon-to- Zohreh Basin WTDP in Iran. PSO searches for optimal values of design and operation variables including capacities of water storage and transfer components as well as priority numbers of reservoirs target storage levels, respectively; And WAEP evaluates the system operation for any combinations of the design and operation variables. The results indicate that the water transfer project under consideration can supply water for the development of Dehdash and Choram Cropland (DCCL) in an undeveloped area located in Kohkiloyeh Province.

We investigate performance of the Genetic Landscape Evolution (GLE) model by changing number of crossover points, which controls spatial cohesiveness of topological information in generated offspring. Simulation results show that 1) GLE performance is insensitive to the number of crossover points, implying that the spatial cohesiveness does not significantly affect efficiency to find better solution sets; and 2) the method to generate randomness in GLE is a significant element for its performance.

The permeable pavement is one of representative Low Impact Development (LID) facilities which were used to reduce flooding and recover the water cycle in urban environments. Since the unit cost of porous pavement is greater than that of non-porous pavement, the designs of permeable pavement need to consider reduction effect of rainwater runoff and cost of facilities. These are determined by the size and location of facilities. In this study, the optimal design of permeable pavement, considering the size and location of that, was simulated in a developed optimization model using the Harmony Search (HS)algorithm connected to the Storm Water Management Model (SWMM) to calculate urban Rainfall-Runoff.

Occupational Exposure Limits (OELs) are representing the amount of a workplace health hazard that most workers can be exposed to without harming their health. In this work, a new Quantitative Structure Property Relationships (QSPR) model to estimate occupational exposure limits values has been developed. The model was developed based on a set of 100 exposure limit values, which were published by the American Conference of Governmental Industrial Hygienists (ACGIH). MATLAB software was employed to develop the model based on a combination between Multiple Linear Regression (MLR) and polynomial models. The results showed that the model is able to predict the exposure limits with high accuracy,

R

2

= 0.9998. The model can be considered scientifically useful and convenient alternative to experimental assessments.

Occupational Exposure Limits (OELs) are representing the amount of a workplace health hazard that most workers can be exposed to without harming their health. In this work, a new Quantitative Structure Property Relationships (QSPR) model to estimate occupational exposure limits values has been developed. The model was developed based on a set of 100 exposure limit values, which were published by the American Conference of Governmental Industrial Hygienists (ACGIH). MATLAB software was employed to develop the model based on a combination between Multiple Linear Regression (MLR) and polynomial models. The results showed that the model is able to predict the exposure limits with high accuracy,

R

2

= 0.9998. The model can be considered scientifically useful and convenient alternative to experimental assessments.

The design of an artificial satellite requires an optimization of multiple objectives with respect to performance, reliability, and weight. In order to consider these objectives simultaneously, multi-objective optimization technique can be considered. In this chapter, a multi-objective method considering both thermal conductance and heat pipe mass is explained for the design of a satellite heat pipe. This method has two steps: at first, each single objective function is optimized; then multi-objective function, which is the sum of individual error between current function value and optimal value in terms of single objective, is minimized. Here, the multi-objective function, representing thermal conductance and heat pipe mass, has five design parameters such as 1) length of conduction fin, 2) cutting length of adhesive attached area, 3) thickness of fin, 4) adhesive thickness, and 5) operation temperature of the heat pipe. Study results showed that the approach using harmony search found better solution than traditional calculus-based algorithm, BFGS.

In this paper, a Pareto-based discrete harmony search (P-DHS) algorithm is proposed to solve the reentrant hybrid flowshop scheduling problem (RHFSP) with the makespan and the total tardiness criteria. For each job, the operation set of each pass is regarded as a sub-job. To adopt the harmony search algorithm to solve the RHFSP, each harmony vector is represented by a discrete sub-job sequence, which determines the priority to allocate all the operations. To handle the discrete representation, a novel improvisation scheme is designed. During the search process, the explored non-dominated solutions are stored in the harmony memory with a dynamic size. The influence of the parameter setting is investigated, and numerical tests are carried out based on some benchmarking instances. The comparisons to some existing algorithms in terms of several performance metrics demonstrate the effectiveness of the P-DHS algorithm.

Lack of available surface water resources and increasing depletion of groundwater are the major challenges of urban water systems (UWSs) in semi-arid regions. This paper presents a long term multi-objective optimisation model to identify optimal water allocation in UWS. The objectives are to maximize reliability of water supply and minimize total operational costs while restricting the annual groundwater withdrawal. Pumping water from a dam reservoir and water recycling schemes are two alternatives for supplying water to increasing water demands over the planning horizon. The developed approach is demonstrated through its application to the UWS of Kerman City in Iran. The Pareto-optimal solutions are obtained as a trade-off between reliability of water supply and operational costs in the Kerman UWS. The results show that addition of recycled water to the water resources can provide the least cost-effective and most efficient way for meeting future water demands in different states of groundwater abstractions.

In the last four decades, many studies have been conducted for least-cost and maximum-reliability design of water supply systems. Most models employed multi-objective genetic algorithm (e.g., non-dominated sorting genetic algorithm-II, NSGA-II) in order to explore trade-off relationship between the two objectives. This study proposes a reliability-based design model that minimizes total cost and maximizes seismic reliability. Here, seismic reliability is defined as the ratio of available demand to required water demand under earthquakes. Multi-objective Harmony Search Algorithm (MoHSA) is developed to efficiently search for the Pareto optimal solutions in the two objectives solution space and incorporated in the proposed reliability-based design model. The developed model is applied to a well-known benchmark network and the results are analyzed.