Even Search in a Promising Region for Constrained Multi-Objective Optimization

In recent years, a large number of approaches to constrained multi-objective optimization problems(CMOPs) have been proposed, focusing on developing tweaked strategies and techniques for handling constraints. However, an overly finetuned strategy or technique might overfit some problem types,resulting in a lack of versatility. In this article, we propose a generic search strategy that performs an even search in a promising region. The promising region, determined by obtained feasible non-dominated solutions, possesses two general properties.First, the constrained Pareto front(CPF) is included in the promising region. Second, as the number of feasible solutions increases or the convergence performance(i.e., approximation to the CPF) of these solutions improves, the promising region shrinks. Then we develop a new strategy named even search,which utilizes the non-dominated solutions to accelerate convergence and escape from local optima, and the feasible solutions under a constraint relaxation condition to exploit and detect feasible regions. Finally, a diversity measure is adopted to make sure that the individuals in the population evenly cover the valuable areas in the promising region. Experimental results on 45 instances from four benchmark test suites and 14 real-world CMOPs have demonstrated that searching evenly in the promising region can achieve competitive performance and excellent versatility compared to 11 most state-of-the-art methods tailored for CMOPs.

Generating of Test Data by Harmony Search Against Genetic Algorithms

Many search-based algorithms have been successfully applied in sev-eral software engineering activities.Genetic algorithms(GAs)are the most used in the scientific domains by scholars to solve software testing problems.They imi-tate the theory of natural selection and evolution.The harmony search algorithm(HSA)is one of the most recent search algorithms in the last years.It imitates the behavior of a musician tofind the best harmony.Scholars have estimated the simi-larities and the differences between genetic algorithms and the harmony search algorithm in diverse research domains.The test data generation process represents a critical task in software validation.Unfortunately,there is no work comparing the performance of genetic algorithms and the harmony search algorithm in the test data generation process.This paper studies the similarities and the differences between genetic algorithms and the harmony search algorithm based on the ability and speed offinding the required test data.The current research performs an empirical comparison of the HSA and the GAs,and then the significance of the results is estimated using the t-Test.The study investigates the efficiency of the harmony search algorithm and the genetic algorithms according to(1)the time performance,(2)the significance of the generated test data,and(3)the adequacy of the generated test data to satisfy a given testing criterion.The results showed that the harmony search algorithm is significantly faster than the genetic algo-rithms because the t-Test showed that the p-value of the time values is 0.026<α(αis the significance level=0.05 at 95%confidence level).In contrast,there is no significant difference between the two algorithms in generating the adequate test data because the t-Test showed that the p-value of thefitness values is 0.25>α.

Quantum walk search algorithm for multi-objective searching with iteration auto-controlling on hypercube

Shenvi et al.have proposed a quantum algorithm based on quantum walking called Shenvi-Kempe-Whaley(SKW)algorithm,but this search algorithm can only search one target state and use a specific search target state vector.Therefore,when there are more than two target nodes in the search space,the algorithm has certain limitations.Even though a multiobjective SKW search algorithm was proposed later,when the number of target nodes is more than two,the SKW search algorithm cannot be mapped to the same quotient graph.In addition,the calculation of the optimal target state depends on the number of target states m.In previous studies,quantum computing and testing algorithms were used to solve this problem.But these solutions require more Oracle calls and cannot get a high accuracy rate.Therefore,to solve the above problems,we improve the multi-target quantum walk search algorithm,and construct a controllable quantum walk search algorithm under the condition of unknown number of target states.By dividing the Hilbert space into multiple subspaces,the accuracy of the search algorithm is improved from p_(c)=(1/2)-O(1/n)to p_(c)=1-O(1/n).And by adding detection gate phase,the algorithm can stop when the amplitude of the target state becomes the maximum for the first time,and the algorithm can always maintain the optimal number of iterations,so as to reduce the number of unnecessary iterations in the algorithm process and make the number of iterations reach t_(f)=(π/2)(?).

Do Search and Selection Operators Play Important Roles in Multi-Objective Evolutionary Algorithms:A Case Study

Multi-objective Evolutionary Algorithm (MOEA) is becoming a hot research area and quite a few aspects of MOEAs have been studied and discussed. However there are still few literatures discussing the roles of search and selection operators in MOEAs. This paper studied their roles by solving a case of discrete Multi-objective Optimization Problem (MOP): Multi-objective TSP with a new MOEA. In the new MOEA, We adopt an efficient search operator, which has the properties of both crossover and mutation, to generate the new individuals and chose two selection operators: Family Competition and Population Competition with probabilities to realize selection. The simulation experiments showed that this new MOEA could get good uniform solutions representing the Pareto Front and outperformed SPEA in almost every simulation run on this problem. Furthermore, we analyzed its convergence property using finite Markov chain and proved that it could converge to Pareto Front with probability 1. We also find that the convergence property of MOEAs has much relationship with search and selection operators.

Hybrid heuristic algorithm for multi-objective scheduling problem

This research provides academic and practical contributions. From a theoretical standpoint, a hybrid harmony search(HS)algorithm, namely the oppositional global-based HS(OGHS), is proposed for solving the multi-objective flexible job-shop scheduling problems(MOFJSPs) to minimize makespan, total machine workload and critical machine workload. An initialization program embedded in opposition-based learning(OBL) is developed for enabling the individuals to scatter in a well-distributed manner in the initial harmony memory(HM). In addition, the recursive halving technique based on opposite number is employed for shrinking the neighbourhood space in the searching phase of the OGHS. From a practice-related standpoint, a type of dual vector code technique is introduced for allowing the OGHS algorithm to adapt the discrete nature of the MOFJSP. Two practical techniques, namely Pareto optimality and technique for order preference by similarity to an ideal solution(TOPSIS), are implemented for solving the MOFJSP.Furthermore, the algorithm performance is tested by using different strategies, including OBL and recursive halving, and the OGHS is compared with existing algorithms in the latest studies.Experimental results on representative examples validate the performance of the proposed algorithm for solving the MOFJSP.

A Hybrid Multi-Objective Evolutionary Algorithm for Optimal Groundwater Management under Variable Density Conditions

In this paper, a new hybrid multi-objective evolutionary algorithm （MOEA）, the niched Pareto tabu search combined with a genetic algorithm （NPTSGA）, is proposed for the management of groundwater resources under variable density conditions. Relatively few MOEAs can possess global search ability contenting with intensified search in a local area. Moreover, the overall searching ability of tabu search （TS） based MOEAs is very sensitive to the neighborhood step size. The NPTSGA is developed on the thought of integrating the genetic algorithm （GA） with a TS based MOEA, the niched Pareto tabu search （NPTS）, which helps to alleviate both of the above difficulties. Here, the global search ability of the NPTS is improved by the diversification of candidate solutions arising from the evolving genetic algorithm population. Furthermore, the proposed methodology coupled with a density-dependent groundwater flow and solute transport simulator, SEAWAT, is developed and its performance is evaluated through a synthetic seawater intrusion management problem. Optimization results indicate that the NPTSGA offers a tradeoff between the two conflicting objectives. A key conclusion of this study is that the NPTSGA keeps the balance between the intensification of nondomination and the diversification of near Pareto-optimal solutions along the tradeoff curves and is a stable and robust method for implementing the multi-objective design of variable-density groundwater resources.

A global harmony search algorithm for finding optimal capacitor location and size in distribution networks

Shunt capacitors are broadly applied in distribution systems to scale down power losses, improve voltage profile and boost system capacity. The amount of capacitors added and location of deployment in the system highly determine the advantage of compensation. A novel global harmony search(GHS) algorithm in parallel with the backward/ forward sweep power flow technique and radial harmonic power flow was used to investigate the optimal placement and sizing of capacitors in radial distribution networks for minimizing power loss and total cost by taking account load unbalancing, mutual coupling and harmonics. The optimal capacitor placement outcomes show that the GHS algorithm can reduce total power losses up to 60 k W and leads to more than 18% of cost saving. The results also demonstrate that the GHS algorithm is more effective in minimization of power loss and total costs compared with genetic algorithm(GA), particle swarm optimization(PSO) and harmony search(HS) algorithm. Moreover, the proposed algorithm converges within 800 iterations and is faster in terms of computational time and gives better performance in finding optimal capacitor location and size compared with other optimization techniques.

Annealing Harmony Search Algorithm to Solve the Nurse Rostering Problem

A real-life problem is the rostering of nurses at hospitals.It is a famous nondeterministic,polynomial time(NP)-hard combinatorial optimization problem.Handling the real-world nurse rostering problem(NRP)constraints in distributing workload equally between available nurses is still a difficult task to achieve.The international shortage of nurses,in addition to the spread of COVID-19,has made it more difficult to provide convenient rosters for nurses.Based on the literature,heuristic-based methods are the most commonly used methods to solve the NRP due to its computational complexity,especially for large rosters.Heuristic-based algorithms in general have problems striking the balance between diversification and intensification.Therefore,this paper aims to introduce a novel metaheuristic hybridization that combines the enhanced harmony search algorithm(EHSA)with the simulated annealing(SA)algorithm called the annealing harmony search algorithm(AHSA).The AHSA is used to solve NRP from a Malaysian hospital.The AHSA performance is compared to the EHSA,climbing harmony search algorithm(CHSA),deluge harmony search algorithm(DHSA),and harmony annealing search algorithm(HAS).The results show that the AHSA performs better than the other compared algorithms for all the tested instances where the best ever results reported for the UKMMC dataset.

Sensor Layout of Hoisting Machinery Vibration Monitoring Based on Harmony Genetic Search Algorithm

With the construction of automated docks,health monitoring technology as a parallel safety assurance technology for unmanned hoisting machinery has become a hot spot in the development of the industry.Hoisting machinery has a huge structure and numerous welded joints.The complexity and nonlinearity of the welded structure itself makes the structural failure parts random and difficult to arrange for monitoring sensors.In order to solve the problem of effectiveness and stability of the sensor arrangement method for monitoring the structure of hoisting machinery.Using the global and local search capabilities enhanced by the complementary search mechanism,a structural vibration monitoring sensor placement algorithm based on the harmony genetic algorithm is proposed.Firstly,the model is established for modal analysis to obtain the displacement matrix of each mode.Secondly,the optimal parameter combination is established through parameter comparison,and the random search mechanism is used to quickly search in the modal matrix to obtain the preliminary solution,and then the preliminary solution is genetically summed The mutation operation obtains the optimized solution,and the optimal solution is retained through repeated iterations to realize the decision of the vibration sensor layout of the crane structure monitoring.Combining the comparison test of harmony genetic algorithm,harmony search algorithm and genet-ic algorithm,the fitness of harmony genetic algorithm in X,Y and Z directions were 0.0045,0.0084 and 0.0058,respectively,which were all optimal.And the average probability of deviating from the optimal path is 1.10%,19.34%,and 54.43%,which are also optimal.Harmony genetic algorithm has the advantages of simplicity,fastness and strong global search ability,and can obtain better fitness value and better search stability.

Implementing an Optimal Energy Management System for a Set of Microgrids Using the Harmony Search Algorithm

A microgrid(MG)refers to a set of loads,generation resources and energy storage systems acting as a controllable load or a generator to supply power and heating to a local area.The MG-generated power management is a central topic for MG design and operation.The existence of dispersed generation(DG)resources has faced MG management with new issues.Depending on the level of exchanges between an MG and the main grid,the MG operation states can be divided into independent or grid-connected ones.Energy management in MGs aims to supply power at the lowest cost for optimal load response.This study examines MG energy management in two operational modes of islanded and grid-connected,and proposes a structure with two control layers(primary and secondary)for energy management.At the principal level of control,the energy management system is determined individually for all MG by taking into consideration the probability constraints and RES uncertainty by the Weibull the probability density function(PDF),generation resources’power as well as the generation surplus and deficit of each MG.Then,the information of the power surplus and deficit of each MG must be sent to the central energy management system.To confirm the proposed structure,a case system with two MGs and a condensive load is simulated by using a multi-time harmony search algorithm.Several scenarios are applied to evaluate the performance of this algorithm.The findings clearly show the effectiveness of the proposed system in the energy management of several MGs,leading to the optimal performance of the resources per MG.Moreover,the proposed control scheme properly controls the MG and grid’s performance in their interactions and offers a high level of robustness,stable behavior under different conditions and high quality of power supply.

Modeling the Proposal of the Simultaneous Purchases and Sales of Electricity and Gas for the Energy Market in a Microgrid Using the Harmony Search Algorithm

The use of different energy carriers together,known as an energy hub,has been a hot topic of research in recent years amongst scientists and researchers.The term energy hub refers to the simultaneous operation of various infrastructures for energy generation and transfer,which has gained momentum in the form of microgrids(MGs).This paper introduces a new strategy for the optimal performance of an MG consisting of different energy carriers for each day.In a smart distribution network(DN),MGs can reduce their own costs in the previous-day market by bidding on sales and purchases.The sales and purchases bidding problem is challenging due to different uncertainties,however.This paper proposes a two-stage strategy for making an optimal bid on electricity sales and purchases with electricity and gas price dependency in the previous-day and real-time markets for an energy hub.In this model,the MG behavior regarding the electricity and gas energy sales/purchase,the simultaneous effects of electricity and gas prices,as well as the energy carriers’dependence on one another are all examined.Due to the inherent uncertainty in the sources of clean energy production,the probabilistic model and the production and reduction scenario have been used in the paper to cover this issue.In the proposed grid,energy sales/purchases are presented in a multi-carrier MG in a two-stage model.This model is solved by using the harmony search algorithm in MATLAB.Numeric results demonstrate the benefits of this model in reducing energy hub costs of operation.

Design of Sharp 2D Multiplier-Less Circularly Symmetric FIR Filter Using Harmony Search Algorithm and Frequency Transformation

In this paper, we present a novel and efficient method for the design of a sharp, two dimensional (2D) wideband, circularly symmetric, FIR filter. First of all, a sharp one dimensional (1D) infinite precision FIR filter is designed using the Frequency Response Masking (FRM) technique. This filter is converted into a multiplier-less filter by representing it in the Canonic Signed Digit (CSD) space. The design of the FRM filter in the CSD space calls for the use of a discrete optimization technique. To this end, a new optimization approach is proposed using a modified Harmony Search Algorithm (HSA). HSA is modified in such a way that, in every exploitation and exploration phase, the candidate solutions turns out to be integers. The 1D FRM multiplier-less filter, is in turn transformed to the 2D equivalent using the recently proposed multiplier-less transformations namely, T1 and T2. These transformations are successful in generating circular contours even for wideband filters. Since multipliers are the most power consuming elements in a 2D filter, the multiplier-less realization calls for reduced power consumption as well as computation time. Significant reduction in the computational complexity and computation time are the highlights of our proposed design technique. Besides, the proposed discrete optimization using modified HSA can be used to solve optimization problems in other engineering disciplines, where the search space consists of integers.

Optimization of Thermal Aware VLSI Non-Slicing Floorplanning Using Hybrid Particle Swarm Optimization Algorithm-Harmony Search Algorithm

Floorplanning is a prominent area in the Very Large-Scale Integrated (VLSI) circuit design automation, because it influences the performance, size, yield and reliability of the VLSI chips. It is the process of estimating the positions and shapes of the modules. A high packing density, small feature size and high clock frequency make the Integrated Circuit (IC) to dissipate large amount of heat. So, in this paper, a methodology is presented to distribute the temperature of the module on the layout while simultaneously optimizing the total area and wirelength by using a hybrid Particle Swarm Optimization-Harmony Search (HPSOHS) algorithm. This hybrid algorithm employs diversification technique (PSO) to obtain global optima and intensification strategy (HS) to achieve the best solution at the local level and Modified Corner List algorithm (MCL) for floorplan representation. A thermal modelling tool called hotspot tool is integrated with the proposed algorithm to obtain the temperature at the block level. The proposed algorithm is illustrated using Microelectronics Centre of North Carolina (MCNC) benchmark circuits. The results obtained are compared with the solutions derived from other stochastic algorithms and the proposed algorithm provides better solution.

Harmony Search-Dijkstra混合算法在铁路物流中心分层选址中的应用

为了满足铁路集中化运输的要求,基于铁路物流中心的层级特点,结合分层选址的理论和方法,以铁路物流中心覆盖的总需求最大化为目标,提出了铁路物流中心分层选址分配模型.针对铁路物流中心选址分配模型的特点,提出采用求解效率较高的和声搜索算法(Harmony Search,HS)和Dijkstra算法相结合的混合算法进行求解,并通过算例验证了模型的可行性和算法的有效性.为了验证算法的性能,对不同规模下的算法进行多次测试,结果表明当规模较大时,HS-Dijkstra混合算法仍可以在可接受的时间范围内收敛.为了体现算法的计算效率,对大规模下的Harmony Search-Dijkstra混合算法与遗传算法(Genetic Algorithm,GA)进行比较,结果显示Harmony Search-Dijkstra混合算法收敛速度明显优于遗传算法.因此,Harmony Search-Dijkstra混合算法可以有效解决铁路物流中心选址分配问题.

Optimization Design of Halbach Permanent Magnet Motor Based on Multi-objective Sensitivity

The halbach permanent magnet synchronous motor(HPMSM)combines the advantages of permanent magnet motors and halbach arrays,which make it very suitable to act as a robot joint motor,and it can also be used in other fields,such as electric vehicles,wind power generation,etc.At first,the sizing equation is derived and the initial design dimensions are calculated for the HPMSM with the rated power of 275W,based on which the finite element parametric model of the motor is built up and the key structural parameters that affect the total harmonic distortion of air-gap flux density and output torque are determined by analyzing multi-objective sensitivity.Then the structure parameters are optimized by using the cuckoo search algorithm.Last,in view of the problem of local overheating of the motor,an improved stator slot structure is proposed and researched.Under the condition of the same outer dimensions,the electromagnetic performance of the HPMSM before and after the improvement are analyzed and compared by the finite element method.It is found that the improved HPMSM can obtain better performances.

Harmony search optimization applied to reservoir engineering assisted history matching

Based on the analysis of characteristics and advantages of HSO(harmony search optimization) algorithm, HSO was used in reservoir engineering assisted history matching of Kareem reservoir in Amal field in the Gulf of Suez, Egypt. HSO algorithm has the following advantages:(1) The good balance between exploration and exploitation techniques during searching for optimal solutions makes the HSO algorithm robust and efficient.(2) The diversity of generated solutions is more effectively controlled by two components, making it suitable for highly non-linear problems in reservoir engineering history matching.(3) The integration between the three components(harmony memory values, pitch adjusting and randomization) of the HSO helps in finding unbiased solutions.(4) The implementation process of the HSO algorithm is much easier. The HSO algorithm and two other commonly used algorithms(genetic and particle swarm optimization algorithms) were used in three reservoir engineering history match questions of different complex degrees, which are two material balance history matches of different scales and one reservoir history matching. The results were compared, which proves the superiority and validity of HSO. The results of Kareem reservoir history matching show that using the HSO algorithm as the optimization method in the assisted history matching workflow improves the simulation quality and saves solution time significantly.

求解燃气轮机制造车间调度的混合和声搜索算法

燃气轮机生产属于典型的离散型制造,其多品种小批量的生产特点给车间作业调度带来挑战,导致企业生产效率低下,不能满足产品交货期。因和声搜索算法结构简单易操作,常用于解决此类作业车间调度问题。然而传统和声搜索算法收敛速度较慢,易陷入局部最优。本文构建以最小化最大完工时间为目标的燃气轮机制造车间调度数学模型,提出一种离散型改进多种群混合和声搜索算法进行求解。结合和声搜索算法与变邻域搜索算法的优点,采用基于工序的编码方式进行编码,在种群更新部分引入模拟退火的Metropolis接受准则,提高种群多样性;提出自适应的记忆库保留概率和音调调节率来调节参数,以提高算法的全局寻优能力;加入变邻域搜索以提高算法的收敛速度。通过性能测试及实例验证表明,相较于已有算法,所提算法具有更好的性能。

基于混合和谐搜索算法的自压滴灌田间管网多目标优化设计

为了综合考虑管网投资和水压分布,合理进行管网布置和管径选择,以满足管网的经济性和可靠性,使自压滴灌管网系统达到投资最低和灌水均匀度最高的目的。以管网投资最低(管网经济性)和节点富余水头均值最小(管网可靠性)为目标,建立了自压滴灌“梳子”形和“丰字”形田间管网系统的多目标优化数学模型,提出了混合和谐搜索算法求解多目标优化模型的方法和步骤。以新疆某自压滴灌工程为例,采用该方法对其田间管网系统进行优化,优化方案的管网总投资为47.63万元,与原设计方案相比降低了9.86%;管网节点富余水头均值为8.87 m,与原设计方案相比降低了28.37%。该优化设计方法得到的优化结果,不仅节省投资明显,而且节点富余水头均值显著减小,说明管网系统的压力偏差小,灌水的均匀度显著提高。优化结果表明,混合和谐搜索算法收敛速度快,计算精度高,在自压滴灌管网的多目标优化设计中具有很好的应用价值。

基于改进和声搜索的配电网WSNs多路径QoS路由算法

针对智能配电网(Smart distribution network,SDN)中无线通信数据传输不可靠且网络寿命低等问题,提出一种基于改进和声搜索的无线传感器网络(Wireless sensor networks,WSNs)多路径QoS路由算法(Multipath QoS routing algorithm,MQRA)。首先,分析配电网的通信需求并建立数据传输模型;然后,针对无线传感器路由问题的特点对和声搜索算法(Harmony search,HS)做出改进;再将其自适应参数公式进行改进以避免算法陷入局部最优;通过在源节点与目的节点之间构建前传区域来优化转发节点集以避免数据回传,提升算法的运行效率;最后,在初始和声库生成阶段,综合考虑距离、丢包率以及节点剩余能量来改进轮盘法中的概率公式。仿真结果表明MQRA算法能有效降低数据传输的时延,提升数据可靠性并均衡节点能耗延长网络使用寿命。

基于改进和声搜索算法的移动机器人调度

为了提高药物管理系统中移动机器人集群调度的速度和精度,建立一种以移动机器人为载体的集群调度模型,并采用离散-连续双映射编码方式进行调度编码。为了提高调度算法解算性能,提出一种融合最优估计优化方法的改进和声搜索(improved harmony search,IHS)算法,结合最优迭代和有向搜索进行调度最优搜索,提高算法的计算速度和精度;根据全局最优和声进行自适应带宽调整和全随机交叉变异,扩大算法搜索范围和样本多样性,提高算法搜索和计算全局最优解的能力;同时,使用标准测试函数进行改进算法在连续区间上的验证,效果良好。对比试验结果表明,同一测试条件下,所提改进算法和对照算法相比具有更加优异的最优解搜索能力,调度结果精确度均有不同程度提高。可见,IHS算法对于优化自动药物系统调度系统性能具备良好的效果。