Weighted Optimization Problem Research Articles

Development of a non-uniform cellular automata framework for sizing, topology and layout optimization of truss structures

This article presents a bi-level non-uniform cellular automata (CA) algorithm for the solution of sizing, topology and layout optimization of truss structures. The non-uniform CA was successfully used in a previous study to solve the weight optimization problem of truss structures for topology and sizing (El Bouzouiki, Sedaghati, and Stiharu 2021. Computers & Structures 242: 106394). In this article, an extended version of the non-uniform CA algorithm is proposed, based on the fully stressed design approach and the distribution of strain energy within the structure, to find the optimal position of the cell’s (joint’s) coordinates. The proposed non-uniform CA algorithm can solve the minimum weight optimization problem of truss structures subjected to both stress and displacement constraints. Several benchmark problems are presented to demonstrate the efficiency and accuracy of the proposed methodology.

Robust circuit optimization under PVT variations via weight optimization problem reformulation

Robust design in analog integrated circuits (ICs) is intricate due to process variations, culminating in notable performance uncertainties. Contemporary surrogate-based techniques depend on lengthy pre-training and are prone to prediction inaccuracies amidst process, voltage, and temperature (PVT) fluctuations. This paper introduces a framework that amalgamates a problem reformulation strategy with an evolutionary algorithm, expediting robust analog IC design in the face of PVT variations. Initially, by segmenting decision variables into subgroups and correlating them with weight variables, the decision space is adeptly reconstructed. An indicator function is subsequently utilized to minimize the objective space’s dimensionality, thereby reshaping the original problem into a low-dimensional single-objective optimization problem. Given the reduced dimensionality of both objective and decision spaces, the Bayesian optimization algorithm is invoked to efficiently diminish performance disparity under variations. Consequently, a collection of quasi-optimal, robust solutions is acquired. In the final phase, a multi-objective evolutionary algorithm ensures the even distribution of these quasi-optimal solutions along the approximate Pareto optimal front. To validate the effectiveness of our framework, we conducted tests on three integrated voltage references and compared the results with four cutting-edge methods. The empirical data highlight the superior performance of our framework, which yields a 3 to 40-fold increase in the quality factor and a 30% to 60% reduction in necessary function evaluations. Additionally, the framework led to a 40% to 70% decrease in the overall execution time.

On the Interplay Between Sensing and Communications for UAV Trajectory Design

The unmanned aerial vehicles (UAVs) are envisioned as promising aerial facilities for providing advanced communication services as well as sensing functionalities in the next-generation wireless system. This paper considers a UAV-enabled integrated sensing and communications (ISAC) system, where a moving ground user (GU) is simultaneously tracked by multiple UAVs and receives the downlink communication information transmitted from the UAV. In particular, to jointly enhance the sensing and communication (S&C) performance, optimizing the UAV moving trajectory is demanded. To achieve this goal, we first harness the extended Kalman filtering (EKF) method for predicting and tracking the motion parameters of GU at each time slot, which relies on the range measurements extracted from the sensing echoes at the base station (BS). Afterward, we formulate a weighted optimization problem that addresses the design of UAV trajectories and GU-UAV association simultaneously, incorporating the consideration of real-time downlink communication rates and the Cramér-Rao bound (CRB) for GU tracking. The problem further is constrained by the maximum consumed power, maximum traveling distance, and minimum collision avoidance distance. As a step forward, to address the resultant non-convex problem, we develop an efficient iterative algorithm to obtain a near-optimal solution by utilizing the successive convex approximate (SCA) technique. Specifically, we alternately solve the GU-UAV association and the real-time trajectory design problem at each time slot. Finally, our numerical simulations illustrate that our proposed algorithm can track the GU accurately while meeting the sensing-centric and/or communication-centric requirements.

Sparse neural network optimization by Simulated Annealing

The over-parameterization of neural networks and the local optimality of backpropagation algorithm have been two major problems associated with deep-learning. In order to reduce the redundancy of neural network parameters, the conventional approach has been to prune branches with small weights. However, this only solves the problem of parameter redundancy, not providing any global optimality guarantees. In this paper, we overturn back-propagation and combine the sparse network optimization problem and the network weight optimization problem using a non-convex optimization method, namely Simulated Annealing. This method can complete network training under the premise of controlling the amount of parameters. Different from simply updating network parameters using gradient descent, our method simultaneously optimizes the topology of the sparse network. With the guarantee of global optimality of Simulated Annealing solution, the performance of the sparse network optimized by our method has exceeded the one trained by backpropagation only.

Cutting Stock Problem (CSP) applied to Structural Optimization for the minimum waste cost

AbstractIn this study, an optimization method to design simple truss structures for the evaluation of the optimal stock of existing elements is introduced. To achieve this goal, the well‐known Bin Packing Problem (BPP) will be implemented within the structural optimization procedure. Specifically, among all the BPP variants, one of the most common applications in real‐world cases is the Cutting Stock Problem (CSP) in which the objective is to produce dj copies of each item type j by employing the minimum number of bins. In the civil engineering field, structural optimization is often employed aiming to improve the load‐bearing capacity of the structure itself, i.e. maximization of the performance ratio through the minimization of the structure weight. However, this goal doesn't guarantee maximum efficiency in terms of minimization of waste during the industrial production phase. To overcome these limits, authors propose a stock‐constrained structural optimization in which a heuristic search technique is adopted and the best arrangement of bars whit the lowest cut‐off waste is obtained for a 10‐bar‐truss case study. For completeness reasons, a comparison between the solution obtained by the classic minimum weight optimization problem and the stock‐constrained one is discussed.

Generative Design of A 6-Axis Quadcopter Drone for Weight Optimization

Unmanned aerial vehicles (UAVs), known as drones, can be remotely operated using embedded technology and software-controlled flight plans. A six-axis drone's main problem is that its significant weight limits how much it can be used. As a result, the flexibility and endurance of the drone's design are necessary for excellent performance during altitude displacement. In order to create a body frame for the quadcopter, the project intends to solve the weight optimization problem via generative design. The three main steps of the optimization attempts utilizing generative design procedures are (a) abstraction, (b) initialization, and (c) interpretation. These are accomplished by employing the five generative design processes. The stress analysis and the generative design process were used to confirm that the generative design technique will help reduce the drone's weight. The drone using three (3) generative designs, was set to a total weight of less than 1kg. The results show that Generative Design 2 shows good optimization as follows, (a)50.00% of parts of assembly optimized from eight parts to four parts, (b) 54.09% of the weight of the body frame optimized from 1.1565kg to 0.531kg, (c) 36.17% of the height of the body frame optimized from 94mm to 60mm, (d) 45.44% of stress analysis increased from 3.457MPa to 5.028MPa, (e) 83.00% reduction of displacement elongation from 3.918mm to 0.666mm and (f) 61.25% of production time optimized from 40 hours to 15.5 hours.

Hybrid Beamforming in mmWave Massive MIMO for IoV With Dual-Functional Radar Communication

The dual-functional radar communication (DFRC) has been regarded as one of the most attractive solutions for facilitating vehicle applications in internet of vehicles (IoV) by utilizing millimeter Wave (mmWave) and massive multiple-in-multiple-out (MIMO) technologies. In this paper, we propose a hybrid beamforming (HBF) scheme with low power consumption and fully directional beamforming gains. The proposed HBF scheme integrates digital beamforming (DBF) with analog beamforming (ABF) to adopt a fully connected (F-C) structure to realize high spectral efficiency (SE) and accurate target sensing. Specifically, for HBF in a single-user MIMO (SU-MIMO) system, we design a fast Riemannian manifold optimization (FRMO) method by minimizing the weighted summation of the communication beamforming error and radar beamforming error. The proposed method can achieve optimal DBF for downlink communication and guarantee the desired beampattern for radar sensing. For HBF in a multiuser MIMO (MU-MIMO) system, we formulate the weighted optimization problem to mitigate multiuser interference (MUI). We design a low-complexity method, namely, the adaptive particle swarm optimization (APSO) algorithm, to obtain a near-optimal solution for HBF based on the criteria of minimizing MUI and the radar beamforming error. We conduct excessive simulations to evaluate the proposed algorithms for the HBF design in both the SU-MIMO system and MU-MIMO system. The numerical results demonstrate that the proposed algorithms achieve near-optimal performance compared to existing HFB methods with high computational efficiency in terms of beamforming gains and SE.

Net-Zero Energy Dual-Functional Radar-Communication Systems

This paper proposes beamforming designs for net-zero energy multi-input multi-output (MIMO) dual-functional radar-communication (DFRC) systems that are powered through energy harvesting (EH) resources and aim to operate autonomously without access to the power grid. We propose a weighted optimization problem to jointly maximize the radar mutual information and minimum quality of service (QoS) requested by communication users subject to energy balancing constraints. The proposed problem is not convex, hence it is tough to solve. We exploit semidefinite relaxation (SDR) and first-order Taylor expansion techniques to relax its non-convexity issues. We then propose an iterative algorithm to obtain the beamforming matrices for the reference scenario when full channel state information (CSI) and energy arrival information (EAI) are available. For the single-target scenario, we show that the proposed optimization contains rank-one solutions. For the multiple targets scenario, by adding auxiliary optimization variables, we show that rank-one matrices can be achieved from the optimal solutions of the proposed optimization. We then propose a robust optimization for the case where only imperfect CSI and EAI are assumed to be known. Finally, numerical simulations show that the proposed DFRC designs are convergent and obtain a graceful trade-off between the radar and communication performances.

Complementary Mismatch Filter Group Design for Integrated Radar and Communications Waveforms Observed in Colored Noise

To improve the processing performance of the integrated radar and communications (IRC) waveforms in colored noise scenario with range ambiguity, a complementary mismatch filter group (CMFG) design method is proposed by using the philosophy of the complementary sequence. The proposed method can decrease the sidelobe level (SLL) of unambiguous output and the energy of range ambiguous returns, and improve the output signal to noise ratio (SNR). To achieve this, a weighted optimization problem is developed, and the closed-form solution is derived. Finally, several simulation results are presented to show the effectiveness of the designed CMFG.

Ultra-Low-Complexity Algorithms With Structurally Optimal Multi-Group Multicast Beamforming in Large-Scale Systems

In this work, we propose ultra-low-complexity design solutions for multi-group multicast beamforming in large-scale systems. For the quality-of-service (QoS) problem, by utilizing the optimal multicast beamforming structure obtained recently in [2], we convert the original problem into a non-convex weight optimization problem of a lower dimension and propose two fast first-order algorithms to solve it. Both algorithms are based on successive convex approximation (SCA) and provide fast iterative updates to solve each SCA subproblem. The first algorithm uses a saddle point reformulation in the dual domain and applies the extragradient method with an adaptive step-size procedure to find the saddle point with simple closed-form updates. The second algorithm adopts the alternating direction method of multipliers (ADMM) method by converting each SCA subproblem into a favorable ADMM structure. The structure leads to simple closed-form ADMM updates, where the problem in each update block can be further decomposed into parallel subproblems of small sizes, for which closed-form solutions are obtained. We also propose efficient initialization methods to obtain favorable initial points that facilitate fast convergence. Furthermore, taking advantage of the proposed fast algorithms, for the max-min fair (MMF) problem, we propose a simple closed-form scaling scheme that directly uses the solution obtained from the QoS problem, avoiding the conventional computationally expensive method that iteratively solves the inverse QoS problem. We further develop lower and upper bounds on the performance of this scaling scheme. Simulation results show that the proposed algorithms offer near-optimal performance with substantially lower computational complexity than the state-of-the-art algorithms for large-scale systems.

The aircraft nacelle brace strength under some static types of loads

The problem of calculating the stress-strain state and solving the problem of weight optimization of a single-engine transport aircraft nacelle fasteners is relevant In connection with the development of aircraft construction. One of the fastening elements is the brace, which is under the action of static loads.. The method of calculation of the transport aircraft nacelle brace, which is based on the finite element method, is considered in the work. A tetrahedral finite element was chosen as the element. The stresses and strains of the brace were determined, the stress-strain state was analyzed and recommendations for optimization of structural elements were given.

A surrogate merit function developed for structural weight optimization problems

In this paper, a surrogate merit function (SMF) is proposed to be evaluated instead of the traditional merit functions (i.e., penalized weight of the structure). The standard format of the conventional merit functions needs several expensive trial-and-error tuning processes to enhance optimization convergence quality, retuning for different structural model configurations, and final manual local search in case optimization converges to infeasible vicinity of global optimum. However, on the other hand, SMF has no tunning factor but shows statistically stable performance for different models, converges directly to outstanding feasible points, and shows other superior advantages such as reduced required iterations to achieve convergence. In other words, this new function is a no-hassle one due to its brilliant user-friendly application and robust numerical results. SMF might be a revolutionary step in commercializing design optimization in the real-world construction market.

A Precoding Approach for Dual-Functional Radar-Communication System With One-Bit DACs

In this paper, we investigate the precoder design for multiple-input multiple-output (MIMO) dual-functional radar-communication (DFRC) system with one-bit digital-to-analog converters (DACs). In order to form the dual-functional beam-pattern, we formulate the precoding problem as a weighted optimization problem with the constant modulus constraint, which aims at minimizing the average error power and guaranteeing radar waveform similarity. The problem is divided into three sub-problems corresponding to the multiple variables, i.e., the precoding factor, transmit signal matrix, and radar waveform matrix. Due to the discrete and non-convex properties of the optimization problem, we propose a multi-variable alternating minimization (MVAM) framework to achieve the near-optimal solutions. The precoding factor and radar waveform can be solved in closed-forms. For the transmit signal matrix, we devise a binary particle swarm optimization-simulated annealing (BPSO-SA) algorithm to obtain it under the MVAM framework. Extensive simulations validate the effectiveness of the proposed approach under various scenarios, including the case without perfect channel state information. The simulation results show that, compared with existing non-linear precoders, the proposed approach achieves 7dB SNR gain at the bit error rate of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−4</sup> in the 8-antenna system, and the gain of SNR is 0.2dB in the massive MIMO system with 128 antennas.

Optimal design of shell constructions taking into account the evolution of corrosion damage

An algorithm for computer modeling of the evolution of corrosion wear of the surface material of shell elements in the conditions of joint action of mechanical external loads and the impact of aggressive environments has been developed.&#x0D; A mathematical model of deformation of shells of rotation with variable as a result of corrosion of external and internal components of wall thickness is constructed.&#x0D; The proposed algorithm allows to trace in time the process of corrosion degradation of the surface material of the shells in accordance with arbitrary (existing) mathematical models of corrosion from the initial moment of time to complete destruction due to corrosion loss of material.&#x0D; An original algorithm for selecting the optimal parameters of the rotation shells and the study of their durability taking into account the corrosion degradation of the surface material has been developed.The essence of the algorithm is to optimize the design parameters at the end of its durability, further reverse bilateral build-up of the "sacrificial" layer of material and rational refinement of the project according to technological requirements.&#x0D; The solution of the problem of weight optimization of the shell under conditions of asymmetric bilateral non-uniformto the surface material, as a result of corrosion damage, is carried out using the necessary conditions of optimality in the form of the principle of maximum L. S. Pontryagin with phase constraints.The problem of satisfying technological requirements at the initial moment of time is formulated as the problem of the best quadratic approximation of the obtained continuous controls in the form of optimally variable thickness of the shell wall with a piecewise constant function.&#x0D; Numerical results of computer modeling of corrosion degradation of surface material and selection of optimal parameters of a cylindrical reservoir for storage of petroleum products under conditions of simultaneous action of force loading and influence of aggressive environment are given.

Ant Colony Optimization Tuned Closed-Loop Optimal Control Intended for Vehicle Active Suspension System

In recent years, the suspension system in modern vehicles has played a key role both as far as driving safety and comfort is concerned. To satisfy these vehicle performance specifications, active suspension is currently studied and implemented in practice in recent decades. In contrast to passive suspensions, by introducing force into system, active suspension can alter the suspension dynamic in real-time. A design of a controller is needed for real-time tuning of the control force in an active suspension system (ASS) to fulfill the challenging control objectives of suspension system comprising road handling, ride convenience, and travel suspension. This research proposed a novel ant colony optimization (ACO) algorithm for solving multi-objective weight optimization problem of the linear quadratic regulator (LQR) for automobiles ASS. The optimization problem of ASS is to design a state-feedback controller (SFC) as a result ACO is used to find optimal LQR weights. Here both Q and R weight matrix of LQR is tuned. On a quarter-car ASS (QCASS) system, the effectiveness of ACO-tuned LQR is analytically checked with hardware in loop (HIL) analysis for an irregular road surface. Here, for experiment, ISO road D rough runway, bumpy path, and pulse-type road profile are taken into account. Experimental findings illustrate that the proposed procedure can substantially reduce the acceleration of the Car body due to irregular road profiles compared to classical tuned LQR and model predictive control (MPC). The proposed controller shows the profound impact on the efficiency of the control schemes for three different road profiles.

Iterative Learning Tracking for Multisensor Systems: A Weighted Optimization Approach.

Multisensor systems are widely applied to realize the comprehensive monitoring and control as they feature multiple individual sensors/outputs. In such systems, different sensors can receive different types of operation signals, such as pressure, temperature, and volume. The desired references for different sensors may conflict in that an input signal that can precisely track all references simultaneously does not exist yet. This gap has motivated us to consider the incompatible multiobjective tracking problem for multisensor systems with random process disturbances and measurement noises. Our primary approach is to solve the problem as a weighted optimization problem using iterative learning control (ILC). First, the best achievable trajectory based on multiple references, as well as the weighted optimal tracking index, is carefully defined and then the ILC algorithms with both fixed and decreasing steps are proposed to generate the input sequence. The output driven by the proposed algorithms has been strictly proven to converge to the best achievable trajectory in both the mean square and almost-sure senses. Extensions to a networked implementation, in which the networks between the sensors and the learning controller suffer random data dropouts, are also detailed. Illustrative simulations are provided to verify the theoretical results.

Groundwater vulnerability mapping using the modified DRASTIC model: the metaheuristic algorithm approach.

Vulnerability assessment and mapping is a significant tool for sustainable management of the precious natural groundwater resources. DRASTIC is an extensively used index model to map groundwater vulnerable zones. However, the original DRASTIC model rates and weights used in most of the research depict the poor correlation between nitrate concentration and groundwater vulnerability index. Wilcoxon test and five population-based metaheuristic (MH) algorithms, namely, firefly algorithm (FA), invasive weed optimization (IWO), teaching learning-based optimization (TLBO), shuffled frog leaping algorithm (SFLA), and particle swarm optimization (PSO), were used to optimize the rates and weights of the DRASTIC model to improve its accuracy. The performance of all the employed metaheuristic algorithms converges to a global optimal solution at different iterations, and to choose the best algorithm for DRASTIC weights optimization, a ranking methodology was proposed. The algorithms were ranked by calculating the relative closeness of alternatives with computational speed and the number of iterations as attributes in the TOPSIS method.This study identifies FA as the outperforming algorithm among the employed for this specified weight optimization problem based on ranking. The result of the optimization model proposed depicts significant improvement in the correlation coefficient between the groundwater vulnerability index and nitrate concentration from 0.0545 for the original DRASTIC model to 0.7247 for the Wilcoxon-MH- DRASTIC. Hence, this ranking approach can be adopted when global optimal solution is found by all employed algorithms in DRASTIC weight optimization.

Hardware in the Loop Testing of Adaptive Inertia Weight PSO-Tuned LQR Applied to Vehicle Suspension Control

This paper presents an adaptive inertia weight particle swarm optimization (AIWPSO) employed for solving the multiobjective weight optimization problem of LQR applied for the vehicle active suspension system (ASS). To meet the competing control objectives of ASS including the ride comfort, road handling, and suspension travel, the state feedback controller design for ASS is formulated as an optimization problem and an improved PSO is employed for finding the optimal weights of the linear-quadratic regulator (LQR). Specifically, for solving the premature convergence of the particles and imbalance between exploration and exploitation capabilities of PSO, an adaptive inertia weight that updates the velocity of the particles based on the success rate is used. The efficacy of the AIWPSO-tuned LQR is experimentally tested on a quarter-car ASS plant using the hardware in loop (HIL) testing for an uneven road surface. Experimental results highlight that, compared to conventional PSO-tuned LQR, the proposed scheme can significantly minimize the vehicle body acceleration due to irregular road profile while guaranteeing the minimum tire friction for passenger safety. The ISO 2361-1 standards adopted to evaluate the ride and health criteria substantiate that the proposed scheme reduces the vibration dose value by 25.34% for a bumpy road profile. Moreover, the cumulative power spectral density (CPSD) of vehicle body acceleration assessed in both low- and high-frequency regions manifests the significant improvement in the ride comfort.

A non-uniform cellular automata framework for topology and sizing optimization of truss structures subjected to stress and displacement constraints

The conventional Cellular Automata (CA) approach has the disadvantage of being particularly suited for design optimization of uniform truss ground structures with identical cells. Moreover, the conventional CA algorithms, which are intrinsically local, have to be modified in order to be able to tackle problems involving displacement constraints. This paper presents a new non-uniform Cellular Automata algorithm, which is based on non-identical cells and a modified FSD/FUD approach. The new algorithm can solve the minimum weight optimization problem of truss structures including both stress and displacement constraints. The efficiency and accuracy of the proposed methodology are proved on a number of benchmark truss design problems.

Non-linear optimization of frames with variable section stiffness of columns using Genetic Algorithm

Recently, in structural engineering, many main elements in structural systems such as columns or girders are designed with variable cross-section for certain purposes. In addition, in order to determine the appropriate sizes or suitable shapes of structural elements for optimal volume of material under the effect of certain loading or with the given sizes of elements the structures can be subjected maximum loading, it is required to studied the optimization problem. This paper presents the non-linear weight optimization problem of frames with variable section stiffness of columns according to the strength, stiffness and stability criteria with the help of finite element method. The non-linear optimization problem is solved by the Genetic Algorithm. The calculation procedure of non-linear optimization of plane frames with variable section stiffness of columns is established and implemented using Matlab calculation programming software. From the results of numerical examples, the conclusions and recommendations will be proposed.