Solving Optimization Problems Research Articles

Event Based Control for Network Security Systems Subject to Actuator Saturation

Abstract As a typical nonlinear link, actuator saturation exists in most network security protection systems. It easily disrupts the closed-loop performance of the system, leading to instability. The event triggering control policy generally adopts an aperiodic sampling mechanism and transmits information only when the triggering condition is met, which can save system communication and computing resources. An event-triggered controller is designed for a network security system with actuator saturation, and the system stabilization is realized. The attractor domain of the system is estimated by solving optimization problems in the form of linear matrix inequalities. Simulation results show the validity of the conclusions obtained in this paper.

A Novel Reinforcement Learning-Based Particle Swarm Optimization Algorithm for Better Symmetry between Convergence Speed and Diversity

This paper introduces a novel Particle Swarm Optimization (RLPSO) algorithm based on reinforcement learning, embodying a fundamental symmetry between global and local search processes. This symmetry aims at addressing the trade-off issue between convergence speed and diversity in traditional algorithms. Traditional Particle Swarm Optimization (PSO) algorithms often struggle to maintain good convergence speed and particle diversity when solving multi-modal function problems. To tackle this challenge, we propose a new algorithm that incorporates the principles of reinforcement learning, enabling particles to intelligently learn and adjust their behavior for better convergence speed and richer exploration of the search space. This algorithm guides particle learning behavior through online updating of a Q-table, allowing particles to selectively learn effective information from other particles and dynamically adjust their strategies during the learning process, thus finding a better balance between convergence speed and diversity. The results demonstrate the superior performance of this algorithm on 16 benchmark functions of the CEC2005 test suite compared to three other algorithms. The RLPSO algorithm can find all global optimum solutions within a certain error range on all 16 benchmark functions, exhibiting outstanding performance and better robustness. Additionally, the algorithm’s performance was tested on 13 benchmark functions from CEC2017, where it outperformed six other algorithms by achieving the minimum value on 11 benchmark functions. Overall, the RLPSO algorithm shows significant improvements and advantages over traditional PSO algorithms in aspects such as local search strategy, parameter adaptive adjustment, convergence speed, and multi-modal problem handling, resulting in better performance and robustness in solving optimization problems. This study provides new insights and methods for the further development of Particle Swarm Optimization algorithms.

Data-driven multi-fidelity topology design of fin structures for latent heat thermal energy storage

This work develops a data-driven multi-fidelity topology design (MFTD) method for designing fins in a latent heat thermal energy storage tube. The high-fidelity simulation resolves the actual solid-liquid phase change process using the enthalpy method, while the low-fidelity topology optimization (TO) simply considers the natural convection with Darcy flow. The above MFTD method is integrated into the framework of evolutional algorithm, and the variational autoencoder is introduced to generate new offspring. Fins for accelerating the melting and solidification processes at different Grashof number (Gr) are designed. It is found that when the fin volume fraction is low, the melt designs exhibit strong heterogeneity due to the strong convection, while the solidification designs are almost isotropic. Along with the increase of the fin volume fraction, the fins are first getting longer, then having more branches or sub-branches and finally becoming thicker. The superiority of the present data-driven MFTD method to the gradient-based direct TO method for solving optimization problems with strong multimodality has been demonstrated in this work. Results find that compared with the designs from direct TO, the MFTD melt design can further reduce the melting time by at least 27 % and 20 % at Gr = 3.3 × 103 and Gr = 3.3 × 104 respectively, and the MFTD solidification design can further shorten the solidification time by at least 9 %.

ReLU surrogates in mixed-integer MPC for irrigation scheduling

Efficient water management in agriculture is important for mitigating the growing freshwater scarcity crisis. Mixed-integer Model Predictive Control (MPC) has emerged as an effective approach for addressing the complex scheduling problems in agricultural irrigation. However, the computational complexity of mixed-integer MPC still poses a significant challenge, particularly in large-scale applications. This study proposes an approach to enhance the computational efficiency of mixed-integer MPC-based irrigation schedulers by employing Rectified Linear Unit (ReLU) surrogate models to describe the soil moisture dynamics of the agricultural field. By leveraging the mixed-integer linear representation of the ReLU operator, the proposed approach transforms the mixed-integer MPC-based scheduler with a quadratic cost function into a mixed-integer quadratic program, which is the simplest class of mixed-integer nonlinear programming problems that can be efficiently solved using global optimization solvers. The effectiveness of this approach is demonstrated through comparative studies conducted on a large-scale agricultural field across two growing seasons, involving other machine learning surrogate models, specifically Long Short-Term Memory (LSTM) networks, and the triggered irrigation scheduling method. The ReLU-based approach significantly reduces solution times—by up to 99.5%—while achieving comparable performance to the LSTM approach in terms of water savings and Irrigation Water Use Efficiency (IWUE). Moreover, the ReLU-based approach achieves enhanced performance in terms of irrigation water savings and IWUE compared to the triggered approach.

A novel locally statistical active contour model for SAR image segmentation and faster algorithm

Abstract In this paper, a novel locally statistical active contour model (LACM) based on the Aubert-Aujol (AA) denoising model and variational level set method is proposed, which can be used for SAR image segmentation with intensity inhomogeneity. By simple transformation, a fast segmentation algorithm with a global optimization solver can be obtained. Experiments using some challenging synthetic images and Envisat SAR images demonstrate the superiority of our proposed models with respect to classic models. Further, we can find that the structure of the proposed algorithm is the same as that of the Transformer or RNN. We will study the nature of the above two types of algorithms to propose a more effective segmentation algorithm based on the energy model.

Learning in Inverse Optimization: Incenter Cost, Augmented Suboptimality Loss, and Algorithms

Enhancing the Efficiency and Accuracy of Inverse Optimization Inverse optimization (IO) is used to model the behavior of decision-making agents who solve optimization problems in response to external signals. Inspired by the geometry of IO problems, in “Learning in Inverse Optimization: Incenter Cost, Augmented Suboptimality Loss, and Algorithms,” Zattoni Scroccaro, Atasoy, and Mohajerin Esfahani propose the “incenter” concept to solve IO problems, which unlike previously proposed approaches, can be used to derive computationally tractable solutions to this modeling problem. Moreover, they also propose a novel loss function for IO problems and a tailored optimization algorithm to optimize it. Extensive numerical experiments showcase the improved efficiency and accuracy of the proposed IO formulations and algorithm.

Optimizing Drone Delivery Paths from Shared Bases: A Location-Routing Problem with Realistic Energy Constraints

Recently, Amazon patented fulfillment centers for drones on a large scale in densely populated areas. A network of such shared centers can be used for landing and launching drones as an alternative to the traditional private bases in near future. This paper studies how a user of such a shared delivery infrastructure can optimally determine the required bases among the existing bases to perform her delivery tasks. To this end, a location-routing problem is studied where the problem determines the drone launching centers and their routes to deliver parcels. A realistic energy function is used that incorporates the effect of load weight for calculating energy consumption in all flight phases including take-off, level flight, hovering, and landing. Although the energy consumption is nonlinear, the problem is formulated as a mixed-integer linear programming model and strengthened by valid inequalities and a pre-processing algorithm that enables us to solve instances with up to 100 customers using off-the-shelf optimization solvers. Moreover, a heuristic method is presented to solve instances with up to 200 customers. Results indicate the importance of incorporating the load-dependent energy formula in contrast to using fixed flight duration constraints for drones. The value of allowing multiple visits on each trip versus only simple back-and-forth trips is also assessed. The advantage of using an integrated location-routing approach is shown over the sequential approach in which the locations of bases are decided first and the routes are constructed next. Moreover, to manage future demand uncertainty, the model is extended for the case that a number of demand scenarios are given.

Development of a GPU-based DEM solver for parameter optimization in the simulations of soil-sweep tool interactions

The Discrete Element Method (DEM) is a powerful technique for simulating granular materials in agricultural applications, yet it is notoriously computationally and memory-intensive. A typical DEM simulation of soil-sweep tool interactions involves tens of thousands of particles, each of which may potentially interact with many others. This results in hundreds of thousands of interactions being computed at every time step, while the need for numerical stability often requires very small time steps. Despite these challenges, DEM holds significant promise to allow the design of more efficient agricultural tools. This paper introduces an in-house-developed modular library based on CUDA C++ for GPUs, aimed at accelerating DEM simulations using a single GPU. The library is designed to facilitate efficient memory usage, employing a per-thread approach where each GPU thread computes one discrete-element particle. To accelerate particle–particle contact searches, we implemented a cell-linked-list algorithm. Our library utilizes the Hertz–Mindlin contact model, which has been widely adopted in agricultural DEM applications. Validation of the code was performed through comparisons with commercial software. Using our software, experimental measurements of a sweep tool moving through sandy soil were replicated with high accuracy by employing differential evolution for parameter calibration, achieving these results using 38912 particles and running 2700 instances within 16 h on a single GPU.

Cost optimization in structural design for reinforced concrete frames using Jaya algorithm

This study analyzes and optimizes the structural design of three-dimensional (3D) reinforced concrete framestructures to minimize the amount of two main materials, including concrete and steel reinforcement, used inreinforced concrete frames. Jaya algorithm was developed based on evolutionary algorithms to build the structural optimization model. The objective function (minimum material cost) with variables being column andbeam cross-sections was set up. In which, the constraints related to the maximum internal force and displacement being in the structural members satisfy limited strength and serviceability requirements. A subroutine written in Python was used to connect the optimization process to the structural analysis software, ETABS. The 3D reinforced concrete frame of a three-story building was selected for cost and design optimization analysis. In which, the optimization problem was solved in cases of three different maximum numbers of iterations, including 20, 35, and 50. In each iteration level, a setting of five independent runs was performed. The subroutine proved to be fast, robust, and convenient manner for solving optimization problems in designing 3D reinforced concrete frames. In which, the best optimal cost might be obtained after twenty iterations and the better convergence behavior occurred at higher numbers of iterations. The study results showed that, for this reinforced concrete frame, applying optimal design led to a materials cost reduction (success rate) by 33.67% compared to that of the conventional design. This success rate would fluctuate according to different nations’ design codes.

Assuring optimality in surrogate‐based optimization: A novel theorem and its practical implementation in pressure swing adsorption optimization

AbstractSurrogate‐based optimization has gained significant traction in several engineering fields, given its ability to handle complex systems without significant computational burdens. However, surrogate models are approximations and may have limitations, including the possibility of artificial minima. The main contribution of this work is the derivation of a robustness test that guarantees the optimality of surrogate‐based optimization. The derivation of this metric is based on the universal approximation theorem. The full framework proposed in this work is also composed by a sampling sizing methodology to randomly select samples within a feasible operating region (FOR) resulting from the optimization population, reducing the computational cost of the analysis and avoiding biases in the robustness calculation. The applicability and importance of this methodology are demonstrated through a case study of a complex chemical process—a pressure swing adsorption (PSA) unit—which presents a high computational cost to solve optimization problems. The results highlight the need and importance of evaluating the optimality of surrogate‐based optimization schemes.

First-Order Algorithms for Robust Optimization Problems via Convex-Concave Saddle-Point Lagrangian Reformulation

Robust optimization (RO) is one of the key paradigms for solving optimization problems affected by uncertainty. Two principal approaches for RO, the robust counterpart method and the adversarial approach, potentially lead to excessively large optimization problems. For that reason, first-order approaches, based on online convex optimization, have been proposed as alternatives for the case of large-scale problems. However, existing first-order methods are either stochastic in nature or involve a binary search for the optimal value. We show that this problem can also be solved with deterministic first-order algorithms based on a saddle-point Lagrangian reformulation that avoid both of these issues. Our approach recovers the other approaches’ [Formula: see text] convergence rate in the general case and offers an improved [Formula: see text] rate for problems with constraints that are affine both in the decision and in the uncertainty. Experiment involving robust quadratic optimization demonstrates the numerical benefits of our approach. History: Accepted by Antonio Frangioni, Area Editor for Design & Analysis of Algorithms–Continuous. Funding: This work was supported by the Nederlandse Organisatie voor Wetenschappelijk Onderzoek [Grant VI.Veni.191E.035] and the Israel Science Foundation [Grant 1460/19]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0200 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0200 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Fixed points of regular set-valued mappings in quasi-metric spaces

Metric fixed point theory is becoming increasingly significant across various fields, including data science and iterative methods for solving optimization problems. This paper aims to introduce new fixed point theorems for set-valued mappings under novel regularity conditions, such as orbital regularity and orbital pseudo-Lipschitzness. Instead of traditional metric spaces, we adopt the framework of quasi-metric spaces, motivated by the need to address problems in spaces that are not necessarily metric, such as function spaces of homogeneous type. We also explore the stability of the set of fixed points under variations of the set-valued mapping. Additionally, we provide estimates for the distances from a given point to the set of fixed points and between two sets of fixed points. Building on these findings, we extend the discussion to similar problems involving fixed, coincidence, and cyclic/double fixed points within this framework. Our results generalize recent findings from the literature, including those in Ait Mansour M, Bahraoui MA, El Bekkali A. [Metric regularity and Lyusternik-Graves theorem via approximate fixed points of set-valued maps in noncomplete metric spaces. Set-Valued Var Anal. 2022;30(1):233–256. doi: 10.1007/s11228-020-00553-1], Dontchev AL, Rockafellar RT. [Implicit functions and solution mappings. a view from variational analysis. Dordrecht: Springer; 2009. Springer Monographs in Mathematics], Ioffe AD. [Variational analysis of regular mappings. Springer, Cham; 2017. Springer Monographs in Mathematics; theory and applications. doi: 10.1007/978-3-319-64277-2], Lim TC. [On fixed point stability for set-valued contractive mappings with applications to generalized differential equations. J Math Anal Appl. 1985;110(2):436–441. doi: 10.1016/0022-247X(85)90306-3] and Tron NH. [Coincidence and fixed points of set-valued mappings via regularity in metric spaces. Set-Valued Var Anal. 2023;31(2):22. Paper No. 17. doi: 10.1007/s11228-023-00680-5].

Integrated optimization of vessel dispatching and empty container repositioning considering turnover time uncertainty

The global trade disproportion results in the accumulation of containers in import-dominated ports and shortages in export-dominated ports, causing congestion and high freight costs, thus hindering maritime shipping economy development. To address these issues, this study develops a stochastic programming model considering uncertain container turnover times. The model integrates decisions for vessel deployment and empty container repositioning over multiple planning periods through a two-stage decision process, aiming to minimize the total cost, including vessel deployment, container leasing, and penalty costs for unfulfilled demand. By formulating the scenario selection problem as a p-median problem, we effectively reduce the model size. We propose an accelerated Benders decomposition algorithm which leverages the independence of sub-problems in the second stage to enable parallel computation. Numerical experiments show that our Benders decomposition algorithm improves solution speed by over 63% compared to the Gurobi optimization solver. Furthermore, our integrated optimization approach proves to be more cost-effective than the reactive method used by shipping lines, achieving an average cost savings of 0.72%. Additionally, our method of constructing turnover time scenarios to address uncertainty saves approximately 0.45% in costs compared to using the probability distribution of container turnover time.

Data-driven approach for design and optimization of rotor–stator mixers for miscible fluids with different viscosities

Rotor–stator mixers (RSMs) are essential equipment used in the food, pharmaceutical, and cosmetic industries. The performance of RSMs is conventionally analyzed using three approaches based on empirical correlations and experimental and numerical analyses. This paper introduces a new approach based on a multifidelity data-driven framework for designing and optimizing RSMs that systematically combines elements of experimental and high-resolution computational fluid dynamics (CFD) models to train a machine learning model to predict RSM performance. It was subsequently coupled to an optimization solver based on a genetic algorithm. The developed framework was applied to a small-scale RSM with variable rotor blade radius, rotor speed, stator mesh width, and mass flow rate that is operated to mix two miscible fluids with different viscosities. The RSM was optimized at two regimes of low and high viscosities to achieve the best performance in terms of shaft power and mixing indices. The results demonstrate the successful application of the developed frameworks. The optimization of the mixing of high-viscosity fluids yielded a higher improvement than that for low-viscosity fluids. A decrease in shaft power of approximately 50% was obtained for the high-viscosity fluids, whereas the mixing indices increased up to 20% by the optimization of the geometrical input design parameters. The proposed framework can be advantageous for designers and operators at the industrial scale.

An adaptive gravitational search algorithm for optimizing mechanical engineering design and machining problems

The gravitational search algorithm (GSA) is widely used for solving optimization problems because it performs in a superior manner as compared to various competing evolutionary and swarm-based metaheuristics. However, GSA frequently gets trapped in local optima due to a lack of solution diversity. Although chaotic gravitational search algorithm (CGSA) can resolve this issue to some extent but its degraded exploitation rate and convergence speed may not result in desired outcome. To this end, diversity-based chaotic GSA (DCGSA) has exhibited its capability to resolve the issues encountered with GSA and CGSA to a certain extent for unconstrained problems. DCGSA achieves this characteristic through the use of an adaptive gravitational constant, which varies according to the diversity values of the population. Since most real-world problems are subjected to some constraints, it is prudent to improve the performance of GSA in solving constrained optimization problems. The present study integrates the enhanced search capability of DCGSA with a generalized constraint handling mechanism to improve the performance of GSA in solving constrained problems. It is observed that DCGSA significantly outperforms GSA on both CEC (Congress on evolutionary computation) 2006, 2010 and 2017 functions and competes strongly with CGSA. Diversity analysis shows that the capability to balance exploration and exploitation rates is enhanced using CGSA and DCGSA. Furthermore, DCGSA algorithms outperform GSA and CGSA on real-world machining and CEC 2020 mechanical design problems. Comparison with state-of-the-art algorithms is made to analyze the performance of the algorithms from a larger perspective.

Automatic source code generation for deterministic global optimization with parallel architectures

Trends over the past two decades indicate that much of the performance gains of commercial optimization solvers is due to improvements in x86 hardware. To continue making progress, it is critical to consider alternative/specialized massively parallel computing architectures. In this work, we detail the development of an open-source source code transformation approach built using Symbolics.jl to construct McCormick-based relaxations of functions that enables their effective parallelized evaluation. We then apply this approach in a novel parallelized branch-and-bound routine that offloads lower- and upper-bounding problems to a GPU. The effectiveness of this new approach is demonstrated on three nonconvex problems of interest, where it yields convergence time improvements of 22–118x compared to an equivalent serial CPU implementation and in two cases outperforms vanilla branch-and-bound versions of existing state-of-the-art solvers that use tighter bounding techniques. This work exemplifies how deterministic global optimizers using alternative hardware architectures can compete with—or eventually outclass—even the most powerful serial CPU implementations, and to the best of the authors' knowledge, represents the first successful demonstration of deterministic global optimization using a GPU.

Numerical methods for shape optimal design of fluid–structure interaction problems

We consider the method of mappings for performing shape optimization for unsteady fluid–structure interaction (FSI) problems. In this work, we focus on the numerical implementation. We model the optimization problem such that it takes several theoretical results into account, such as regularity requirements on the transformations and a differential geometrical point of view on the manifold of shapes. Moreover, we discretize the problem such that we can compute exact discrete gradients. This allows for the use of general purpose optimization solvers. We focus on problems derived from an FSI benchmark to validate our numerical implementation. The method is used to optimize parts of the outer boundary and the interface. The numerical simulations build on FEniCS, dolfin-adjoint and IPOPT. Moreover, as an additional theoretical result, we show that for a linear special case the adjoint attains the same structure as the forward problem but reverses the temporal flow of information.

Engineered dissipation to mitigate barren plateaus

Variational quantum algorithms represent a powerful approach for solving optimization problems on noisy quantum computers, with a broad spectrum of potential applications ranging from chemistry to machine learning. However, their performances in practical implementations crucially depend on the effectiveness of quantum circuit training, which can be severely limited by phenomena such as barren plateaus. While, in general, dissipation is detrimental for quantum algorithms, and noise itself can actually induce barren plateaus, here we describe how the inclusion of properly engineered Markovian losses after each unitary quantum circuit layer allows for the trainability of quantum models. We identify the required form of the dissipation processes and establish that their optimization is efficient. We benchmark the generality of our proposal in both a synthetic and a practical quantum chemistry example, demonstrating its effectiveness and potential impact across different domains.

The Research on Self-Excited Oscillating Jet Cleaning Technology

Abstract Self-oscillating nozzles have gained wide popularity due to their ability to generate powerful impact forces, long-range projection, and concentrated, stable jets in applications such as water-jet drilling and rust removal. However, the nozzle’s efficient operation relies heavily on specific structural designs and operational parameters, which necessitates further indepth research. By studying the characteristics of self-excited oscillating pulse cavitation jet within the nozzle cavity structure. Analyzing the evolution characteristics of internal flow field. Solving optimization problems in a targeted manner. The purpose of this study is to reveal the resonance principle behind the self-excited oscillation of nozzle. It also explores the regularities of the effects that the cavity diameter has on jet performance, ultimately seeking to find the optimal configuration of nozzle structure and operating conditions.

Orientation optimization of the Halbach PMG for the levitation and guidance performance of the HTS maglev system

High-temperature superconducting maglev technology has great application potential in rail transit applications due to its advantages such as passive stable levitation and green environmental protection. As one of the key components of the HTS maglev system, the Halbach-type permanent magnet guideway (PMG) enhances the magnetic field on one side of the guideway and weakens that on the other side. Optimizing the PMG, including the geometry and magnetic properties of the magnet, is an effective method to improve the levitation and guidance performance of the system. In addition, since NdFeB permanent magnets are expensive, optimizing the design of the PMG for the HTS maglev system is also an important work to reduce the application cost. In this paper, the Nelder–Mead Simplex method (NMS) in the optimization solver in COMSOL software is used to optimize the geometric parameters of the Halbach PMG according to the different objective requirements of the HTS maglev system. The optimization objectives include the maximum levitation force and guidance force under the constraint of the maximum cross-sectional area of the PMG, as well as the minimum cross-sectional area of the PMG with a minimum levitation force constraint. The results indicate that the NMS method is effective. By comparing four PMGs during the optimization process, it is found that this method can fully improve the utilization of the magnetic field by changing the geometric parameters of the Halbach PMG. This study can provide a valuable reference for the optimal design of the PMG for HTS maglev systems in the future.