Single Objective Constrained Optimization Problems Research Articles

Analysis and Optimization of Gait Cycle of 25-DOF NAO Robot Using Particle Swarm Optimization and Genetic Algorithms

The gait cycle of 25-degree of freedom (DOF) humanoid robot, namely NAO robot, consists of single support phase (SSP) and double support phase (DSP). Both dynamic and stability analyses are carried out for this robot to determine its power consumption and dynamic stability margin, respectively. Constrained single-objective optimization problems are formulated for the SSP and DSP separately and solved using particle swarm optimization (PSO) and genetic algorithms (GA). A performance index, other than the fitness function, consisting of constraint values and maximum swing height, is also considered to compare PSO and GA-obtained optimal solutions. PSO is able to find the trajectories that offer higher swing height for nearly similar power consumption during SSP. A performance assessment of each algorithm based on the best fitness values in each generation across several runs is also carried out. These values are compared using the Wilcoxon rank-sum test, and PSO is found to be statistically better than GA. The optimal solutions from the simulations are tested using the Webots simulator to validate their efficacy on stability. Moreover, an investigation of the influence of gait parameters on power consumption during SSP and DSP reveals that the humanoid robot with a higher hip height, lower swing height, and slow pace consumes less power. The methodology developed in this is generic and can be easily extended to other robots.

Hosting Capacity Assessment in Electrical Power Distribution Systems Using Genetic Algorithm

Environmental issues and the current global energy crisis serve as further motivators for the promotion of renewable energy sources. However, integrating these sources into existing power grids presents numerous challenges. As the connection capacity approaches its limits, it is imperative to employ innovative engineering methods to integrate distributed generation (DG) into resilient, self-healing smart grids of the future. One such tool is Hosting Capacity (HC) analysis, which is an emerging power system-planning tool used to position investments toward parts of the network that can absorb additional generation and promote efficient use of energy sources, avoiding overloading, inefficiencies, DG misallocations, and network failures. In this study, a technique for calculating the ideal HC in a power system is presented. The goal of this research is to develop a replicable optimization methodology for determining HC in smart distribution systems using a single objective constrained optimization problem solved through the use of genetic algorithm (GA). Detailed power system load and generation modeling and the use of advanced open-source research tool for load flow optimization improve the confidence in the proposed model. This research contributes to collective knowledge of the subject matter and establishes a reliable optimization methodology for determining HC in power systems.

Automatic detection of semantic primitives using optimization based on genetic algorithm.

In this article, we propose a method for the automatic retrieval of a set of semantic primitive words from an explanatory dictionary and a novel evaluation procedure for the obtained set of primitives. The approach is based on the representation of the dictionary as a directed graph with a single-objective constrained optimization problem via a genetic algorithm with the PageRank scoring model. The problem is defined as a subset selection. The algorithm is fit to search for the sets of words that should fulfil several requirements: the cardinality of the set should not exceed empirically selected limits and the PageRank word importance score is minimized with cycle prevention thresholding. In the experiments, we used the WordNet dictionary for English. The proposed method is an improvement over the previous state-of-the-art solutions.

Double-track particle swarm optimizer for nonlinear constrained optimization problems

Particle swarm optimization (PSO) is a popular stochastic algorithm for solving nonlinear optimization problems. It has been used in various industrial applications because of its few parameters and ease of implementation. Various optimal problems must be frequently formed as nonlinear constrained optimization (NCO) problems because of global resource limitations. These problem-specific nonlinear constraints can result in many infeasible regions in the search space. Current PSO-based approaches are inherently designed for unconstrained optimization problems and cannot directly handle the constraint issue; therefore, they add the constraint handling technique (CHT) to account for NCO problems. This study proposes a double-track schema inside PSO called double-track PSO (DTPSO) to address the NCO problem. When an infeasible region blocks a particle, the DTPSO creates a copy of the particle. The original and copied particles utilize different search strategies to move to feasible and infeasible regions. The results indicate that the proposed DTPSO outperforms the seven referenced PSO-based methods in all 33 NCO problems and five recent strong methods in 19 mechanical design problems belonging to the IEEE CEC 2020 competition on real-world single-objective constrained optimization problems. Furthermore, the experiment results demonstrate the quality of the solution and the effective computation of the proposed DTPSO.

Robotic arm trajectory optimization based on multiverse algorithm.

For inefficient trajectory planning of six-degree-of-freedom industrial manipulators, a trajectory planning algorithm based on an improved multiverse algorithm (IMVO) for time, energy, and impact optimization are proposed. The multi-universe algorithm has better robustness and convergence accuracy in solving single-objective constrained optimization problems than other algorithms. In contrast, it has the disadvantage of slow convergence and quickly falls into local optimum. This paper proposes a method to improve the wormhole probability curve, adaptive parameter adjustment, and population mutation fusion to improve the convergence speed and global search capability. In this paper, we modify MVO for multi-objective optimization to derive the Pareto solution set. We then construct the objective function by a weighted approach and optimize it using IMVO. The results show that the algorithm improves the timeliness of the six-degree-of-freedom manipulator trajectory operation within a specific constraint and improves the optimal time, energy consumption, and impact problems in the manipulator trajectory planning.

Adaptive heterogeneous particle swarm optimization with comprehensive learning strategy

This paper proposes an adaptive heterogeneous particle swarm optimization with a comprehensive learning strategy for solving single-objective constrained optimization problems. In this algorithm, particles can use an exploration strategy and an exploitation strategy to update their positions. The historical success rates of the two strategies are used to adaptively control the adoption rates of strategies in the next iteration. The search strategy in the canonical particle swarm optimization algorithm is based on elite solutions. As a result, when no particles can discover better solutions for several generations, this algorithm is likely to fall into stagnation. To respond to this challenge, a new strategy is proposed to explore the neighbors of the elite solutions in this study. Finally, a constraint handling method is equipped to the proposed algorithm to make it be able to solve constrained optimization problems. The proposed algorithm is compared with the canonical particle swarm optimization, differential evolution, and several recently proposed algorithms on the benchmark test suite. The Wilcoxon signed-rank test results show that the proposed algorithm is significantly better on most of the benchmark problems compared with the competitors. The proposed algorithm is also applied to solve two real-world mechanical engineering problems. The experimental results show that the proposed algorithm performs consistently well on these problems.

Population initialization techniques for evolutionary algorithms for single-objective constrained optimization problems: Deterministic vs. stochastic techniques

The population initialization step is a common step in the majority (or even all) of evolutionary algorithms (EAs). There are many population initialization techniques. Due to the limited population size and the high dimensionality of many problems, there is little chance to cover the promising regions in the search space. From different perspectives, this paper compares the stochastic and deterministic population initialization techniques through comparing five of the well-known population initializers: Random number generator (RNG), Latin Hypercube, Sobol, Halton, and Kronecker. Due to the presence of many constraints in real-world applications, in this paper, we are focusing only on single-objective constrained optimization problems. Specifically, the goal is to investigate if there is a significant difference between these population initialization methods. In this paper, we explain theoretically and mathematically these different population initialization techniques. Moreover, different illustrative examples and visualizations are introduced to explain the behavior of each technique and compare different techniques from different perspectives. The results show that due to the high uniformity of the low-discrepancy sequences such as the Halton and Sobol sequences, the generated points using these sequences are more evenly distributed over the space than RNG, which is the commonly used technique for initializing the populations in EAs. Practically, using a set of benchmark functions, we investigate the use of each population initialization technique for initializing different population-based evolutionary algorithms. The results of our experiments prove that with sufficient numbers of iterations, the EAs are not sensitive to the initialization methods and there are no significant differences between the mentioned population initialization methods. Further, the low discrepancy methods enhance the exploration ability of EAs in early iterations.

A Spring Search Algorithm Applied to Engineering Optimization Problems

At present, optimization algorithms are used extensively. One particular type of such algorithms includes random-based heuristic population optimization algorithms, which may be created by modeling scientific phenomena, like, for example, physical processes. The present article proposes a novel optimization algorithm based on Hooke’s law, called the spring search algorithm (SSA), which aims to solve single-objective constrained optimization problems. In the SSA, search agents are weights joined through springs, which, as Hooke’s law states, possess a force that corresponds to its length. The mathematics behind the algorithm are presented in the text. In order to test its functionality, it is executed on 38 established benchmark test functions and weighed against eight other optimization algorithms: a genetic algorithm (GA), a gravitational search algorithm (GSA), a grasshopper optimization algorithm (GOA), particle swarm optimization (PSO), teaching–learning-based optimization (TLBO), a grey wolf optimizer (GWO), a spotted hyena optimizer (SHO), as well as an emperor penguin optimizer (EPO). To test the SSA’s usability, it is employed on five engineering optimization problems. The SSA delivered better fitting results than the other algorithms in unimodal objective function, multimodal objective functions, CEC 2015, in addition to the optimization problems in engineering.

Fine-grained resource provisioning and task scheduling for heterogeneous applications in distributed green clouds

An increasing number of enterprises have adopted cloud computing to manage their important business applications in distributed green cloud &#x0028 DGC &#x0029 systems for low response time and high cost-effectiveness in recent years. Task scheduling and resource allocation in DGCs have gained more attention in both academia and industry as they are costly to manage because of high energy consumption. Many factors in DGCs, e.g., prices of power grid, and the amount of green energy express strong spatial variations. The dramatic increase of arriving tasks brings a big challenge to minimize the energy cost of a DGC provider in a market where above factors all possess spatial variations. This work adopts a G &#x002F G &#x002F 1 queuing system to analyze the performance of servers in DGCs. Based on it, a single-objective constrained optimization problem is formulated and solved by a proposed simulated-annealing-based bees algorithm &#x0028 SBA &#x0029 to find SBA can minimize the energy cost of a DGC provider by optimally allocating tasks of heterogeneous applications among multiple DGCs, and specifying the running speed of each server and the number of powered-on servers in each GC while strictly meeting response time limits of tasks of all applications. Realistic data-based experimental results prove that SBA achieves lower energy cost than several benchmark scheduling methods do.

Profit-Maximized Collaborative Computation Offloading and Resource Allocation in Distributed Cloud and Edge Computing Systems

Edge computing is a new architecture to provide computing, storage, and networking resources for achieving the Internet of Things. It brings computation to the network edge in close proximity to users. However, nodes in the edge have limited energy and resources. Completely running tasks in the edge may cause poor performance. Cloud data centers (CDCs) have rich resources for executing tasks, but they are located in places far away from users. CDCs lead to long transmission delays and large financial costs for utilizing resources. Therefore, it is essential to smartly offload users’ tasks between a CDC layer and an edge computing layer. This work proposes a cloud and edge computing system, which has a terminal layer, edge computing layer, and CDC layer. Based on it, this work designs a profit-maximized collaborative computation offloading and resource allocation algorithm to maximize the profit of systems and guarantee that response time limits of tasks are strictly met. In each time slot, this work jointly considers CPU, memory, and bandwidth resources, load balance of all heterogeneous nodes in the edge layer, maximum amount of energy, maximum number of servers, and task queue stability in the CDC layer. Considering the abovementioned factors, a single-objective constrained optimization problem is formulated and solved by a proposed simulated-annealing-based migrating birds optimization procedure to obtain a close-to-optimal solution. The proposed method achieves joint optimization of computation offloading between CDC and edge, and resource allocation in CDC. Realistic data-based simulation results demonstrate that it realizes higher profit than its peers. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This work considers the joint optimization of computation offloading between Cloud data center (CDC) and edge computing layers, and resource allocation in CDC. It is important to maximize the profit of distributed cloud and edge computing systems by optimally scheduling all tasks between them given user-specific response time limits of tasks. It is challenging to execute them in nodes in the edge computing layer because their computation resources and battery capacities are often constrained and heterogeneous. Current offloading methods fail to jointly optimize computation offloading and resource allocation for nodes in the edge and servers in CDC. They are insufficient and coarse-grained to schedule arriving tasks. In this work, a novel algorithm is proposed to maximize the profit of distributed cloud and edge computing systems while meeting response time limits of tasks. It explicitly specifies the task service rate and the selected node for each task in each time slot by considering resource limits, load balance requirement, and processing capacities of nodes in the edge, and server and energy constraints in CDC. Real-life data-driven simulations show that the proposed method realizes a larger profit than several typical offloading strategies. It can be readily implemented and incorporated into large-scale industrial computing systems.

An algorithm for numerical nonlinear optimization: Fertile Field Algorithm (FFA)

Nature, as a rich source of solutions, can be an inspirational guide to answer scientific expectations. Seed dispersal mechanism as one of the most common reproduction method among the plants is a unique technique with millions of years of evolutionary history. In this paper, inspired by plants survival, a novel method of optimization is presented, which is called Fertile Field Algorithm. One of the main challenges of stochastic optimization methods is related to the efficiency of the searching process for finding the global optimal solution. Seeding procedure is the most common reproduction method among all the plants. In the proposed method, the searching process is carried out through a new algorithm based on the seed dispersal mechanisms by the wind and the animals in the field. The proposed algorithm is appropriate for continuous nonlinear optimization problems. The efficiency of the proposed method is examined in details through some of the standard benchmark functions and demonstrated its capability in comparison to other nature-inspired algorithms. Obtained results show that the proposed algorithm is efficient and accurate to find optimal solutions for multimodal optimization problems with few optimal points. To evaluate the effects of the key parameters of the proposed algorithm on the results, a sensitivity analysis is carried out. Finally, to illustrate the applicability of FFA, a continuous constrained single-objective optimization problem as an optimal engineering design is considered and discussed.

Azimuth Signal Multichannel Reconstruction and Channel Configuration Design for Geosynchronous Spaceborne–Airborne Bistatic SAR

In geosynchronous spaceborne-airborne bistatic synthetic aperture radar (GEO-BiSAR) system, the airborne platform achieves high-resolution imaging by passively receiving the signal from the interested scenario. In this paper, the Doppler characteristics of GEO-BiSAR and the individual contribution of the transmitter and the receiver are first analyzed. The airborne receiver is found to be the dominant contributor for the total Doppler bandwidth, which will lead to Doppler spectrum aliasing regarding the low pulse repetition frequency (PRF) adopted by the GEO-SAR. In order to suppress the Doppler ambiguity without adjusting the PRF of GEO-SAR, azimuth multichannel receiving technique is introduced to the airborne receiver. The multichannel transfer function is derived based on the method of series reversion and the spectrum reconstruction algorithm is then modified for multichannel GEO-BiSAR. Moreover, the reconstruction performance is closely related to the corresponding spacing between each channel (i.e., channel configuration). Therefore, the channel configuration design for GEO-BiSAR aims at optimizing the azimuth ambiguity-to-signal ratio with a satisfactory level of signal-to-noise ratio scaling factor by adjusting the channel configuration. The channel configuration design is modeled as a constrained single objective optimization problem (CSOP). Then, a channel configuration design method based on differential evolution and feasibility rule is proposed to solve the CSOP and obtain the channel configuration for the receiver with the optimal reconstruction performance. Finally, simulations results are presented to verify the effectiveness of the proposed method, and characteristics of channel configuration are analyzed in detail, which can be a practical guide for the implementation of multichannel GEO-BiSAR systems.

Thermal analysis of parabolic trough collectors via a swarm intelligence optimizer

The current study deals with developing an efficient strategy to solve the governing equations of the parabolic trough collectors’ heat transfer. In the proposed approach, available system of equations is converted into a single objective constrained optimization problem. Subsequently, the thermal properties of the system are gained via solving proposed optimization problem. This target should be met via implementing an appropriate optimization technique as a solver tool. In this respect, integrated particle swarm optimization (iPSO) is utilized as an efficient optimization method. The objective function of the proposed optimization problem computes the heat losses through the discretized cross-section of the receiver tube. To reduce the model complexity, the receiver tube is modeled in one-dimensional form. In addition, the thermal equilibrium of the entire system is implemented as the constraint of the optimization problem. The validity of the obtained outcomes is assessed via comparing them with existing practical results addressed in Sandia National Laboratory (SNL) reports. The comparison reveals that the achieved theoretical outcomes are in the good agreement with the experimental results.

Relaxed I-SHOT trust-region algorithm for solving multi-objective economic emission load dispatch problem

ABSTRACTIn this paper, a new algorithm for tackling nonlinear constrained multi-objective optimization problems is introduced. This algorithm, which we call relaxed the interactive sequential hybrid optimization technique (relaxed I-SHOT), is based on a hybrid method between the I-SHOT method and step method (STEM) to transform a multi-objective problem into a single-objective one. An active set strategy is used together with a suggested penalty method to transform a single-objective constrained optimization problem into unconstrained one. A trust-region globalization strategy is added to the algorithm to solve the obtained unconstrained problem to ensure global convergence. The suggested approach is utilized to solve the multi-objective economic emission load dispatch (EELD) problems to assert the effectiveness of the proposed algorithm. The proposed algorithm is tested on the standard IEEE 30-bus 6-generator test system. The results of the proposed approach are compared against those reported in the literature. The comparison asserts the potential of the proposed algorithm to solve the EELD problem.

Cooperative Differential Evolution Framework for Constrained Multiobjective Optimization.

This paper presents a cooperative differential evolution framework (CCMODE) for constrained multiobjective optimization, and two instantiations of the CCMODE framework are implemented. The proposed framework has (M+1) populations, including M subpopulations for constrained single-objective optimization and an archive population for constrained M -objective optimization. Each subpopulation performs its own constrained single-objective differential evolution to optimize the assigned constrained single-objective optimization problem. For the archive population, the constraint handling techniques (CHTs) are modified for constrained multiobjective optimization. The proposed framework takes the advantage of existing effective constrained single-objective optimization algorithms, and extends them to deal with constrained multiobjective optimization problems. In two instantiations, two CHTs are implemented in CCMODE framework, respectively. Experiment results on several sets of benchmark problems with two, three, and many objectives show that the proposed algorithm is better than existing state-of-the-art constrained multiobjective evolutionary algorithms. The effectiveness of the subpopulations is also discussed.

Quantum seeded evolutionary computational technique for constrained optimization in engineering design and manufacturing

In this paper an attempt is made to develop a new Quantum Seeded Hybrid Evolutionary Computational Technique (QSHECT) that is general, flexible and efficient in solving single objective constrained optimization problems. It generates initial parents using quantum seeds. It is here that QSHECT incorporates ideas from the principles of quantum computation and integrates them in the current framework of Real Coded Evolutionary Algorithm (RCEA). It also incorporates Simulated Annealing (SA) in the selection process of Evolutionary Algorithm (EA) for child generation. The proposed algorithm has been tested on standard test problems and engineering design problems taken from the literature. In order to test this algorithm on domain-specific manufacturing problems, Neuro-Fuzzy (NF) modeling of hot extrusion is attempted and the NF model is incorporated as a fitness evaluator inside the QSHECT to form a new variant of this technique, i.e. Quantum Seeded Neuro Fuzzy Hybrid Evolutionary Computational Technique (QSNFHECT) and is effectively applied for process optimization of hot extrusion process. The neuro-fuzzy model (NF) is also compared with statistical regression analysis (RA) model for evaluating the extrusion load. The NF model was found to be much superior. The optimal process parameters obtained by Quantum Seeded Neuro Fuzzy Hybrid Evolutionary Technique (QSNFHECT) are validated by the finite element model. The proposed methodology using QSNFHECT is a step towards meeting the challenges posed in intelligent manufacturing systems and opens new avenues for parameter estimation and optimization and can be easily incorporated in existing manufacturing setup.

A Method for Constrained Multiobjective Optimization Based on SQP Techniques

We propose a method for constrained and unconstrained nonlinear multiobjective optimization problems that is based on an SQP-type approach. The proposed algorithm maintains a list of nondominated points that is improved both for spread along the Pareto front and optimality by solving single-objective constrained optimization problems. These single-objective problems are derived as SQP problems based on the given nondominated points. Under appropriate differentiability assumptions we discuss convergence to local optimal Pareto points. We provide numerical results for a set of unconstrained and constrained multiobjective optimization problems in the form of performance and data profiles, where several performance metrics are used. The numerical results confirm the superiority of the proposed algorithm against a state-of-the-art multiobjective solver and a classical scalarization approach, both in the quality of the approximated Pareto front and in the computational effort necessary to compute the approximation.

Uniform adaptive scaling of equality and inequality constraints within hybrid evolutionary-cum-classical optimization

The holy grail of constrained optimization is the development of an efficient, scale invariant and generic constraint handling procedure. To address these, the present paper proposes a unified approach of constraint handling, which is capable of handling all inequality, equality and hybrid constraints in a coherent manner. The proposed method also automatically resolves the issue of constraint scaling which is critical in real world and engineering optimization problems. The proposed unified approach converts the single-objective constrained optimization problem into a multi-objective problem. Evolutionary multi-objective optimization is used to solve the modified bi-objective problem and to estimate the penalty parameter automatically. The constrained optimum is further improved using classical optimization. The efficiency of the proposed method is validated on a set of well-studied constrained test problems and compared against without using normalization technique to show the necessity of normalization. The results establish the importance of scaling , especially in constrained optimization and call for further investigation into its use in constrained optimization research.

Optimal reactive power dispatch by particle swarm optimization with an aging leader and challengers

This study presents a particle swarm optimization (PSO) with an aging leader and challengers (ALC-PSO) for the solution of optimal reactive power dispatch (ORPD) problem. The ORPD problem is formulated as a nonlinear constrained single-objective optimization problem where the real power loss and the total voltage deviations are to be minimized separately. In order to evaluate the performance of the proposed algorithm, it has been implemented on IEEE 30-, 57- and 118-bus test power systems and the optimal results obtained are compared with those of the other evolutionary optimization techniques surfaced in the recent state-of-the-art literature. The results presented in this paper demonstrate the potential of the proposed approach and show its effectiveness and robustness for solving the ORPD problem of power system.

Multi-objective economic emission load dispatch problem with trust-region strategy

In this paper, we present a trust region algorithm for solving multi-objective economic emission load dispatch problem (EELD). The trust region algorithm has proven to be a very successful globalization technique for solving a single objective constrained optimization problems. The proposed approach is suitable for multi-objective problem (EELD) such that its objective functions may be ill- defined or having a non convex pareto-optimal front. Also, we identify the weight values which reflect the degree of satisfaction of each objective. The proposed approach is carried out on the standard IEEE 30-bus 6-generator test systems to confirm the effectiveness of the algorithm used to solve the multi-objective problem (EELD). Our results with the proposed approach have been compared to those reported in the literature. The comparison demonstrates the superiority of the proposed approach and confirm its potential to solve the multi-objective problem (EELD).A Matlab implementation of our algorithm was used in solving one case study and the results are reported.