Spider Monkey Optimization Algorithm Research Articles

Application of Dandelion Optimization Algorithm in Pattern Synthesis of Linear Antenna Arrays

This paper introduces an application of the dandelion optimization (DO) algorithm in antenna arrays. This is the first time that the DO algorithm has been used for optimizing antenna arrays. For antenna array optimization, sidelobe level (SLL) and deep nulls are key technical indicators. A lower SLL can improve the signal-to-noise ratio and reduce the impact of clutter signals outside the main beam. Deep nulls need to be aligned with the direction of interference to eliminate the influence of interference sources. The combination of the two can effectively improve the anti-interference ability of the entire system. Therefore, antenna arrays with ultra-low sidelobes and ultra-deep nulls are currently hot in the field of antenna array design and are also some of the key technologies needed to achieve modern high-performance radar systems. As a new type of evolutionary algorithm inspired by nature, the DO algorithm is inspired by the wind propagation behavior of dandelions in nature. This algorithm iteratively updates the population from three stages of ascent, descent, and landing, ultimately finding the optimal position. It has good optimization ability in solving complex problems such as those involving nonlinearity, discreteness, and non-convexity, and the antenna array pattern synthesis optimization problem belongs to multivariate nonlinear problems. Therefore, the DO algorithm can be effectively applied in the field of antenna array optimization. In this work, we use the following method to obtain an optimized pattern of a linear array with the lowest sidelobe level (SLL), null placement in particular directions, and a lower notch in particular directions: by controlling the antenna array’s element spacing and leaving the phase unchanged to optimize the current amplitudes and by controlling the excitation current and phase fixation of the antenna array and changing the element spacing. In the first and second examples, different algorithms are used to reduce the SLL of the antenna. In the first example, the DO algorithm reduces the SLL to −33.37 dB, which is 2.67 dB, 2.67 dB, 3.77 dB, 2.74 dB, and 2.52 dB lower than five other algorithms. In the second example, the SLL optimized by the DO algorithm is −42.56 dB, which is 5.04 dB and 1.48 dB lower than two other algorithms. In both examples, the DO algorithm reduces the SLL lower than other algorithms when the main lobe of the antenna is not significantly widened. Examples 3, 4, and 5 use the DO algorithm to optimize the amplitude of the current, generating deep nulls and deep notches in specific directions. In Example 3, the DO algorithm obtains a depth of nulls equal to −187.6 dB, which is 66.7 dB and 44.3 dB lower than that of the flower pollination algorithm (FPA) and the chaotic colony predation algorithm (CCPA), respectively. In Example 4, the deep null obtained by the DO algorithm is as low as −98.69 dB, which is 6.67 dB lower than the deep null obtained by the grey wolf optimization (GWO) algorithm. In Example 5, the deep notch obtained by the DO algorithm is as low as −63.1 dB, which is 6.4 dB and 1.9 dB lower than the spider monkey optimization (SMO) algorithm and the grasshopper optimization algorithm (GOA), respectively. The data prove that the DO algorithm produces deeper nulls and notches than other algorithms. The last two examples involve reducing sidelobe levels and generating deep nulls by optimizing the spacing between elements. In Example 5, the SLL obtained using the DO algorithm is −22.8766 dB, which is 0.1998 dB lower than the lowest SLL of −22.6768 dB among other algorithms. In Example 6, the SLL obtained using the DO algorithm is −20.1012 dB, and the null depth is −125.1 dB, which is 1.592 dB lower than the SLL obtained by the cat swarm optimization (CSO) algorithm and 19.1 dB lower than the deep null obtained by the GWO algorithm, respectively. In summary, the results of six simulation experiments indicate that the DO algorithm has better optimization ability in linear array optimization than other evolutionary algorithms

Optimal allocation of solar PV and wind energy power for radial distribution system using spider monkey optimization

The integration of renewable energy sources, relatable as Solar Photovoltaic (PV) and Wind Power, into the radial distribution system has gained significant attention due to their eco-friendly and sustainable attributes. This article presents a narrative advent for achieving the finest share of Solar PV and Wind force power through a radial distribution system using the innovative Spider Monkey Optimization (SMO) algorithm. Multi-objective function for the minimization of distribution loss and voltage deviation with the constraints of power balance equation and boundary limits of voltage and power is considered. The Spider Monkey Optimization algorithm, stimulated via the community activities of spider monkeys, be employed to effectively search for the finest allotment of Solar PV and Wind Energy Power within the distribution network. The SMO algorithm exhibits robustness in handling non-linear and multi-dimensional optimization problems, making it suitable for this complex task. To authorize the usefulness and efficiency of the planned approach, it is functional to standard 33-bus radial division coordination. Comparative analyses of optimization techniques are reported and SMO reduces the losses to 104 KW and the voltage deviation is minimized to 0.0458 pu. The valuable perception is that incorporating Solar PV and Wind Energy sources into radial distribution systems improves the quality.

A Fuzzy Congestion Control in Wireless Sensor Networks based on Spider Monkey Optimization Algorithm

Wireless Sensor Networks (WSN) have been broadly applied in various fields, such as medicine and agriculture. A network is likely to experience information congestion when many sensors initiate sending data concurrently. This could lead to maximizing in the packet loss ratio, thereby reducing efficiency and affecting the total system performance, so congestion control is an utmost challenge. To solve this problem, a Fuzzy Congestion Control in WSN based on the Spider Monkey Optimization Algorithm (FCC-WSN-SMOA) is proposed. The proposed method combines random early detection with the fuzzy proportional integral derivative controller. The proportional integral derivative (PID) and fuzzy logic conjointly together to help control the target buffer queue. FLC regulates the transmitting rate of every node. Then, FLC input and output parameters are optimized by SMOA. The simulation is activated in MATLAB. The FCC-WSN-SMOA method attains 21.28%, 32.20%, and 17.42% lower packet loss ratio and 16.25%, 26.07%, and 23.38% lower packet loss probability compared with existing methods, such as progressive fuzzy PSO-PID congestion control approach for WSN (FCC-WSN-PSO), optimized fuzzy clustering utilizing moth-flame optimization approach in WSNs (FCC-WSN-MFOA), and time synchronization depending on Improved Wolf Colony Algorithm-Cuckoo Search Optimized Fuzzy PID Controller for Smart Grid (FCC-WSN-IWCA-CSO), respectively.

A multi-objective fuzzy flexible job shop scheduling problem considering the maximization of processing quality

This paper analyzes practical production characteristics, including customer's stringent quality requirements and uncertain processing time in aircraft shaft parts manufacturing. Considering the above characteristics, we propose a multi-objective fuzzy aircraft shaft parts production scheduling problem considering the maximization of production quality. We define this problem as a multi-objective fuzzy flexible job shop scheduling problem (MO-fFJSP) with fuzzy processing time. To address this problem, we developed an improved multi-objective spider monkey optimization (IMOSMO) algorithm. IMOSMO integrates strategies such as genetic operators, variable neighborhood search and Pareto optimization theory on the framework of the conventional Spider Monkey Optimization (SMO) framework and discretize the continuous SMO algorithm to solve MO-fFJSP. To enhance the efficiency of the algorithm, we further adjust the sequence of the local leader learning phase and the global leader learning phase within the proposed IMOSMO framework. We conduct a comparative analysis between the performance of IMOSMO and NSGA-Ⅱ using 28 cases of varying scales. The computational results demonstrate the superiority of our algorithm over NSGA-Ⅱ in terms of both solution diversity and quality. Moreover, the performance of the proposed algorithm upgrades as the problem scale increases.

Multi-objective hybrid optimization for micro strip patch antenna design

Due to their low price, light weights, as well as simple installation, Micro strip Patch Antennas (MPAs) have been made to perform in a double and multi-band applications. The MP receiver is created with an Electromagnetic Band Gap (EBG) structure in order to decrease the micro strip patch cross-polarized radiation but also achieve the crucial radiation criteria. The polymeric liquid crystals substratum is employed to decrease raw material costs, and also the applicable shape framework are employed to enhance receiver execution. We have established a new optimization based method which has two operating stages. In the begining stage, we have designed a Micro strip patch antenna with certain parameters. Afterwards, these design parameters length, width, height, substrate thickness under area such as get optimized by the newly introduced Battle Royale Customized Spider Monkey Optimization (BRCSMO) algorithm in order to get an antenna with higher performance. We have evaluated the proposed method with regard to measures like receiver profit, productivity, bandwidth, decline loss as well as Total Active Reflection coefficient (TARC) and the outcomes showed that this proposed technique can offer superior outcomes than other approaches.

A Modified Spider Monkey Optimization Algorithm Based on Good-Point Set and Enhancing Position Update

A Modified Spider Monkey Optimization Algorithm Based on Good-Point Set and Enhancing Position Update

An improved spider monkey optimization algorithm for multi-objective planning and scheduling problems of PCB assembly line

In recent years, the demand for printed circuit boards (PCBs) with various electronic components has tremendously increased due to high customization in smart electronic devices. To meet the market competition, efficient and realistic decisions with optimum planning and scheduling are required to enhance the productivity of PCB industries. Processing time of surface mounting technology (SMT) machines defines the pace of PCB production because of time consuming and critical process. In addition, it is observed that various planning and scheduling problems exist in PCB assembly line which are required to emphasize to increase the productivity. Therefore, in this study critical planning and scheduling problems i.e., component allocation problem (CAP) and component placement sequence problem (CPSP) are considered to optimize. Moreover, the periodic maintenance (PM) is also considered to maintain the efficiency of machines and make the problem more realistic. A mathematical model is formulated to minimize the maximum completion time, total energy consumption and the total maintenance time simultaneously. To solve this multi-objective NP-hard problem, an improved spider monkey optimization (ISMO) algorithm is developed. The efficiency and effectiveness of ISMO algorithm is improved by embedding few additional features. a) Two heuristics to ensure better initial solutions; b) evolutionary state judgment based on change in Pareto entropy to ensure the tradeoff between exploration and exploitation; c) an archive-based Q-Learning strategy to ensure the parametric adaptive tuning. Finally, computational experiments and comprehensive performance comparisons with other well-known multi-objective algorithms are performed with several size problem instances. The statistical results and analysis demonstrate that the proposed ISMO algorithm outperforms the other competitors.

Discrete spider monkey optimization algorithm for latency‐sensitive VNF deployment and resource allocation

SummaryThe next‐generation networks are expected to support diverse latency‐sensitive services, that is, auto‐driving, telemedicine, and so on. Deploying these services in current hardware‐based networks faces significant challenges. The emergence of network function virtualization (NFV) and software defined network (SDN) makes network deployment flexible and agile. In order to meet the strict latency constraints, joint VNF deployment and resource allocation problems are needed. In this paper, we consider the resource‐delay interpendency and formulate the joint VNF deployment and resource allocation problems as linear programming (LP) problems. Discrete spider monkey optimization (DSMO) algorithm is proposed to solve this problem, which imitates spider monkeys' fission and fusion social behavior during foraging. The two‐phase decision update mechanism greatly increases the diversity of the spider monkey decision population and promotes the algorithm to perform a global search of the solution space. Evaluation results show that the proposed solutions achieve superior performance in terms of latency, CPU utilization and service acceptance rate.

An Optimized Reinforcement Learning-Based Routing Protocol Using Spider Monkey Optimization Algorithm

In Wireless Sensor Networks, numerous machine-learning algorithms are used in the packet routing strategy. The recommended routing approach is implemented using adaptive reinforcement learning and a spider monkey optimization algorithm. Data packets are sent over the network via optimum route establishment—the above attempts to save energy by changing the Q-value at each instance. Technology enables adaptive mechanisms to demonstrate intelligent behavior in complex and dynamic situations such as Wireless Sensor Networks (WSN). Recently, new routing methods for WSNs have been devised in response to such a notion. Due to user interference and overall network performance, the numerous routing pathways cause frequent channel-switching occurrences. The spider monkey optimization method obtains routing metrics such as bandwidth, end-to-end latency, throughput, overhead, and packet delivery ratio. Compared to other machine learning algorithms, such as RLBR, the performance of WSN is improved and obtained better performance results.

Performance evaluation and comparative analysis of CrowWhale-energy and trust aware multicast routing algorithm

Multipath routing helps to establish various quality of service parameters, which is significant in helping multimedia broadcasting in the Internet of Things (IoT). Traditional multicast routing in IoT mainly concentrates on ad hoc sensor networking environments, which are not approachable and vigorous enough for assisting multimedia applications in an IoT environment. For resolving the challenging issues of multicast routing in IoT, CrowWhale-energy and trust-aware multicast routing (CrowWhale-ETR) have been devised. In this research, the routing performance of CrowWhale-ETR is analyzed by comparing it with optimization-based routing, routing protocols, and objective functions. Here, the optimization-based algorithm, namely the Spider Monkey Optimization algorithm (SMO), Whale Optimization Algorithm (WOA), Dolphin Echolocation Optimization (DEO) algorithm, Water Wave Optimization (WWO) algorithm, Crow Search Algorithm (CSA), and, routing protocols, like Ad hoc On-Demand Distance Vector (AODV), CTrust-RPL, Energy-Harvesting-Aware Routing Algorithm (EHARA), light-weight trust-based Quality of Service (QoS) routing, and Energy-awareness Load Balancing-Faster Local Repair (ELB-FLR) and the objective functions, such as energy, distance, delay, trust, link lifetime (LLT) and EDDTL (all objectives) are utilized for comparing the performance of CrowWhale-ETR. In addition, the performance of CrowWhale-ETR is analyzed in terms of delay, detection rate, energy, Packet Delivery Ratio (PDR), and throughput, and it achieved better values of 0.539 s, 0.628, 78.42%, 0.871, and 0.759 using EDDTL as fitness.

Short-Term EV Charging Demand Forecast with Feedforward Artificial Neural Network

The global increase in greenhouse gas emissions from automobiles has brought about the manufacture and usage of large quantities of electric vehicles (EVs). However, to ensure proper integration of EVs into the grid, there is a need to forecast the charging demand of EVs accurately. This paper presents a short-term electric vehicle charging demand forecast using a feedforward artificial neural network optimized with a modified local leader phase spider monkey optimization (MLLP-SMO) algorithm, a proposed variant of spider monkey optimization. A proportionate fitness selection is employed to improve the update process of the local leader phase of the spider monkey optimization. The proposed algorithm trains a feedforward neural network to forecast electric vehicle charging demand. The effectiveness of the proposed forecasting model was tested and validated with electric vehicle public charging data from the United Kingdom Power Networks Low Carbon London Project. The model's performance was compared to a feedforward neural network trained with particle swarm optimization, genetic algorithm, classical spider monkey optimization, and two conventional forecasting models, multi-linear regression and Monte Carlo simulation. The performance of the proposed forecasting model was assessed using the mean absolute percentage error of forecast and forecasting accuracy. The model produced a forecast accuracy and mean absolute percentage error of 99.88% and 3.384%, respectively. The results show that MLLP-SMO as a trainer predicted better than the other forecasting models and met industry standard forecast accuracy.

Variable Ordering in Binary Decision Diagram Using Spider Monkey Optimization for Node and Path Length Optimization

Binary Decision Diagrams (BDDs) are an important data structure for the design of digital circuits using VLSI CAD tools. The ordering of variables affects the total number of nodes and path length in the BDDs. Finding a good variable ordering is an optimization problem and previously many optimization approaches have been implemented for BDDs in a number of research works. In this paper, an optimization approach based on Spider Monkey Optimization (SMO) algorithm is proposed for the BDD variable ordering problem targeting number of nodes and longest path length. SMO is a well-known swarm intelligence-based optimization approach based on spider monkeys foraging behavior. The proposed work has been compared with other latest BDD reordering approaches using Particle Swarm Optimization (PSO) algorithm. The results obtained show significant improvement over the Particle Swarm Optimization method. The proposed SMO-based method is applied to different benchmark digital circuits having different levels of complexities. The node count and longest path length for the maximum number of tested circuits are found to be better in SMO than PSO.

Dynamic Kernel Clustering by Spider Monkey Optimization Algorithm

Dynamic Kernel Clustering by Spider Monkey Optimization Algorithm

An efficient multi-objective scheduling algorithm based on spider monkey and ant colony optimization in cloud computing

Due to easier access, improved performance, and lower costs, the use of cloud services has increased dramatically. However, cloud service providers are still looking for ways to complete users’ jobs at a high speed to increase profits and reduce energy consumption costs. To achieve such a goal, many algorithms for scheduling problem have been introduced. However, most techniques consider an objective in the scheduling process. This paper presents a new hybrid multi-objective algorithm, called SMO_ACO, for addressing the scheduling problem. The proposed SMO_ACO algorithm combines Spider Monkey Optimization (SMO) and Ant Colony Optimization (ACO) algorithm. Additionally, a fitness function is formulated to tackle 4 objectives of the scheduling problem. The proposed fitness function considers parameters like schedule length, execution cost, consumed energy, and resource utilization. The proposed algorithm is implemented using the Cloud Sim toolkit and evaluated for different workloads. The performance of the proposed technique is verified using several performance metrics and the results are compared with the most recent existing algorithms. The results prove that the proposed SMO_ACO approach allocates resources efficiently while maintaining cloud performance that increases profits.

Deep facial emotion recognition model using optimal feature extraction and dual‐attention residual U‐Net classifier

AbstractHuman facial emotion recognition (FER) system has become an active research area and it has attracted various research communities for its wide ranging and promising applications especially in the cybersecurity field. Recognizing various facial expressions corresponding to the emotional forms is considered as a significant task in the system of FER. Typically, the automated system of FER consists of two major and important steps like feature extraction, and facial emotion recognition. In this work, initially the input data is acquired and the features are extracted from the input facial image with the use of Fuzzy Eigen Weighted based feature extraction model (FEW‐FE). Among the extracted features, an optimal and best features are selected by means of feature selection technique, which employs Chaotic Spider Monkey Optimization algorithm (CSMO) so as to find best fitness function solution. The use of this optimization technique for the feature subset selection aids the enhancement of classifier performance. Then, the recognition process is carried using Dual‐attention residual U‐Net classifier framework. The performance evaluation of this proposed model is carried over three input datasets considered such as CK+, FER2013, and JAFFE in terms of recognition accuracy, precision, recall, and F‐measure. The comparison is made for the feature extraction and classifier model with that of various existing methodologies which shows the effectiveness of proposed system over other traditional schemes. This proposed design is applicable in the cybersecurity system to detect a person's emotional state from their expression.

An energy-efficient multi-objective integrated process planning and scheduling for a flexible job-shop-type remanufacturing system

This study considers an energy-efficient multi-objective integrated process planning and scheduling (IPPS) problem for the remanufacturing system (RMS) integrating parallel disassembly, flexible job-shop-type reprocessing, and parallel reassembly shops with the goal of realizing the minimization of both energy cost and completion time. The multi-objective mixed-integer programming model is first constructed with consideration of operation, sequence, and process flexibilities in the RMS for identifying this scheduling issue mathematically. An improved spider monkey optimization algorithm (ISMO) with a global criterion multi-objective method is developed to address the proposed problem. By embedding dynamic adaptive inertia weight and various local neighborhood searching strategies in ISMO, its global and local search capabilities are improved significantly. A set of simulation experiments are systematically designed and conducted for evaluating ISMO’s performance. Finally, a case study from the real-world remanufacturing scenario is adopted to assess ISMO’s ability to handle the realistic remanufacturing IPPS problem. Simulation results demonstrate ISMO’s superiority compared to other baseline algorithms when tackling the energy-aware IPPS problem regarding solution accuracy, computing speed, solution stability, and convergence behavior. Meanwhile, the case study results validate ISMO’s supremacy in solving the real-world remanufacturing IPPS problem with relatively lower energy usage and time cost.

A Spider Monkey Optimization Based on Beta-Hill Climbing Optimizer for Unmanned Combat Aerial Vehicle (UCAV)

Unmanned Combat Aerial Vehicle (UCAV) path planning is a challenging optimization problem that seeks the optimal or near-optimal flight path for military operations. The problem is further complicated by the need to operate in a complex battlefield environment with minimal military risk and fewer constraints. To address these challenges, highly sophisticated control methods are required, and Swarm Intelligence (SI) algorithms have proven to be one of the most effective approaches. In this context, a study has been conducted to improve the existing Spider Monkey Optimization (SMO) algorithm by integrating a new explorative local search algorithm called Beta-Hill Climbing Optimizer (BHC) into the three main phases of SMO. The result is a novel SMO variant called SMOBHC, which offers improved performance in terms of intensification, exploration, avoiding local minima, and convergence speed. Specifically, BHC is integrated into the main SMO algorithmic structure for three purposes: to improve the new Spider Monkey solution generated in the SMO Local Leader Phase (LLP), to enhance the new Spider Monkey solution produced in the SMO Global Leader Phase (GLP), and to update the positions of all Local Leader members of each local group under a specific condition in the SMO Local Leader Decision (LLD) phase. To demonstrate the effectiveness of the proposed algorithm, SMOBHC is applied to UCAV path planning in 2D space on three different complex battlefields with ten, thirty, and twenty randomly distributed threats under various conditions. Experimental results show that SMOBHC outperforms the original SMO algorithm and a large set of twenty-six powerful and recent evolutionary algorithms. The proposed method shows better results in terms of the best, worst, mean, and standard deviation outcomes obtained from twenty independent runs on small-scale (D = 30), medium-scale (D = 60), and large-scale (D = 90) battlefields. Statistically, SMOBHC performs better on the three battlefields, except in the case of SMO, where there is no significant difference between them. Overall, the proposed SMO variant significantly improves the obstacle avoidance capability of the SMO algorithm and enhances the stability of the final results. The study provides an effective approach to UCAV path planning that can be useful in military operations with complex battlefield environments.

Multi-Strategy Boosted Spider Monkey Optimization Algorithm for Feature Selection

To solve the problem of slow convergence and easy to get into the local optimum of the spider monkey optimization algorithm, this paper presents a new algorithm based on multi-strategy (ISMO). First, the initial population is generated by a refracted opposition-based learning strategy to enhance diversity and ergodicity. Second, this paper introduces a non-linear adaptive dynamic weight factor to improve convergence efficiency. Then, using the crisscross strategy, using the horizontal crossover to enhance the global search and vertical crossover to keep the diversity of the population to avoid being trapped in the local optimum. At last, we adopt a Gauss-Cauchy mutation strategy to improve the stability of the algorithm by mutation of the optimal individuals. Therefore, the application of ISMO is validated by ten benchmark functions and feature selection. It is proved that the proposed method can resolve the problem of feature selection.

Hyperparameter Tuned Deep Hybrid Denoising Autoencoder Breast Cancer Classification on Digital Mammograms

Breast Cancer (BC) is considered the most commonly scrutinized cancer in women worldwide, affecting one in eight women in a lifetime. Mammography screening becomes one such standard method that is helpful in identifying suspicious masses’ malignancy of BC at an initial level. However, the prior identification of masses in mammograms was still challenging for extremely dense and dense breast categories and needs an effective and automatic mechanisms for helping radiotherapists in diagnosis. Deep learning (DL) techniques were broadly utilized for medical imaging applications, particularly breast mass classification. The advancements in the DL field paved the way for highly intellectual and self-reliant computer-aided diagnosis (CAD) systems since the learning capability of Machine Learning (ML) techniques was constantly improving. This paper presents a new Hyperparameter Tuned Deep Hybrid Denoising Autoencoder Breast Cancer Classification (HTDHDAE-BCC) on Digital Mammograms. The presented HTDHDAE-BCC model examines the mammogram images for the identification of BC. In the HTDHDAE-BCC model, the initial stage of image preprocessing is carried out using an average median filter. In addition, the deep convolutional neural network-based Inception v4 model is employed to generate feature vectors. The parameter tuning process uses the binary spider monkey optimization (BSMO) algorithm. The HTDHDAE-BCC model exploits chameleon swarm optimization (CSO) with the DHDAE model for BC classification. The experimental analysis of the HTDHDAE-BCC model is performed using the MIAS database. The experimental outcomes demonstrate the betterments of the HTDHDAE-BCC model over other recent approaches.

Joint optimization of production and maintenance scheduling for unrelated parallel machine using hybrid discrete spider monkey optimization algorithm

This paper considers an unrelated parallel machine scheduling problem with variable maintenance based on machine reliability to minimize the maximum completion time. To obtain the optimal solution of small-scale problems, we firstly establish a mixed integer programming model. To solve the medium and large-scale problems efficiently and effectively, we develop a hybrid discrete spider monkey optimization algorithm (HDSMO), which combines discrete spider monkey optimization (DSMO) with genetic algorithm (GA). A few additional features are embedded in the HDSMO: a three-phase constructive heuristic is proposed to generate better initial solution, and an individual updating method considering the inertia weight is used to balance the exploration and exploitation capabilities. Moreover, a problem-oriented neighborhood search method is designed to improve the search efficiency. Experiments are conducted on a set of randomly generated instances. The performance of the proposed HDSMO algorithm is investigated and compared with that of other existing algorithms. The detailed results show that the proposed HDSMO algorithm can obtain significantly better solutions than the DSMO and GA algorithms.