Constrained Optimization Method Research Articles

Inaccurate search based sequential approximate constrained optimization method for Solid Rocket Motor design

Surrogate based constrained optimization methods are widely utilized in practical solid rocket motor (SRM) design problems. To improve the design performance, this paper proposes an inaccurate search based sequential approximate constrained optimization (ISSACO) method consisting of an efficient recursive evolution Latin hypercube design (RELHD) method and a three-stage constrained sampling method. The RELHD method divides large-sample experiment design problem into several small-sample design problems to ensure the computational efficiency and the design uniformity at the same time. The three-stage constrained sampling method employs the elite archives mechanism to balance the feasibility and the optimality in optimization. Results of the numerical cases indicate that the proposed ISSACO algorithm is competitive with other state-of-art constrained optimization method in efficiency and effectiveness. The finocyl grain design and the impulse mass ratio optimization are also conducted to make further verifications, and the ISSACO method can efficiently obtain feasible optimum and proves to be a potential method for computationally intensive solid rocket motor design problems.

Distributionally Robust Chance Constrained Optimization Method for Risk-Based Routing and Scheduling of Shared Mobile Energy Storage System With Variable Renewable Energy

Distributionally Robust Chance Constrained Optimization Method for Risk-Based Routing and Scheduling of Shared Mobile Energy Storage System With Variable Renewable Energy

The Knowledge and Application of Economics in Healthcare in a High-Income Country Today: The Case of Belgium.

Healthcare is a huge business sector in many countries, focusing on the social function of delivering quality health when people develop illness. The system is essentially financed by public funds based on the solidarity principle. With a large financial outlay, the sector must use economic evaluation methods to achieve better efficiency. The objective of our study was to evaluate and to understand how health economics is used today, taking Belgium as an example of a high-income country. The evaluation started with a historical view of healthcare development and ended with potential projections for its future. A literature review focused on country-specific evaluation reports to identify the health economic methods used, with a search for potential gaps. The first results indicated that Belgium in 2021 devoted 11% of its GDP, 17% of its total tax revenue, and 30% of the national Social Security Fund to health-related activities, totalizing EUR 55.5 billion spending. The main health economic method used was a cost-effectiveness analysis linked to budget impact, assigning reimbursable monetary values to new products becoming available. However, these evaluation methods only impacted at most 20% of the money circulating in healthcare. The remaining 80% was subject to financial regulations (70%) and budgeting (10%), which could use many other techniques of an economic analysis. The evaluation indicated two potentially important changes in health economic use in Belgium. One was an increased focus on budgeting with plans, time frames, and quantified treatment objectives on specific disease problems. Economic models with simulations are very supportive in those settings. The other was the application of constrained optimization methods, which may become the new standard of practice when switching from fee-for-service to pay-per-performance as promoted by value-based healthcare and value-based health management. This economic refocusing to a more constrained approach may help to keep the healthcare system sustainable and affordable in the face of the many future challenges including ageing, climate change, migration, pandemics, logistical limitations, and financial instability.

Modeling 3E-S sustainable development problem by an ambiguous chance constrained optimization method

The environmental-energy-economic-social (3E-S) sustainable development problem aims to balance the environment, energy, and economy upon which human society critically relies. However, it is further complicated by various ambiguous input parameters about greenhouse gas (GHG) emissions, electricity consumption, gross domestic product (GDP), and unemployment rate. To address this complexity, this paper develops an ambiguous chance constrained optimization model with multiple chance soft constraints for optimizing the 3E-S sustainable development problem by strategically allocating labor across key sectors. Tractable formulations of the proposed model are derived by constructing three types of ambiguity sets for input parameters with ambiguous probability distributions. The first is to construct support-mean ambiguous distribution sets with little known information, the second is to extend support-mean ambiguity sets to mean-covariance ambiguity sets by incorporating interactive relationships among sectors, and the third is to extend support-mean ambiguity sets to inner-outer ambiguity sets with Wasserstein metric from globalized distributionally robust perspective. The availability and computability of the proposed model have been illustrated by planning India’s 3E-S sustainability for the year 2030. The results suggest that (i) the proposed method exhibits the capability to offer flexible policy measures; (ii) India should prioritize the development of the Mining and quarrying sector, the Transport, storage, communication, and services sector, and the Constructions sector; (iii) India needs to make greater efforts for promoting GDP while controlling GHG emissions and energy consumption; (iv) The policy measures and objectives are influenced by tolerance levels, support intervals, interactive relationships among sectors, globalized sensitivity, and Wasserstein ball size.

A staged diversity enhancement method for constrained multiobjective evolutionary optimization

Optimizing the convergence and diversity of solutions simultaneously under constraints is a challenge in solving constrained multiobjective optimization problems. In existing multiobjective optimization algorithms, general diversity maintenance mechanisms have difficulty determining all optimal solutions in discrete feasible regions. This paper proposes a staged constrained multiobjective optimization algorithm with a diversity enhancement method (SDEM), which can explore potential discrete feasible regions by retaining well-distributed offspring. Specifically, after solutions have converged to optimal feasible regions by niching-based constraint dominance in the early stage, the SDEM improves the diversity of solutions through a proposed diversity enhancement dominance principle in the mid-term. Finally, the optimize objective functions and constraints of all solutions are optimized under constraint dominance to balance convergence, diversity, and feasibility during the three stages. Experiments on four well-known test suites and six real-world case studies demonstrate that the SDEM is competitive with or comparable to seven state-of-the-art constrained multiobjective evolutionary algorithms.

A decoupled probabilistic constrained topology optimization method based on the constraint shift

AbstractTopology optimization (TO) has recently emerged as an advanced design method. To ensure practical reliability in the design process, it is imperative to incorporate considerations of uncertainty. Consequently, performing reliability analysis (RA) during the design phase becomes necessary. However, RA itself constitutes an optimization problem. Combining these two optimization problems can result in inefficiency. To address this challenge, we propose a decoupled approach that integrates deterministic topology optimization (DTO) and RA cycles. The reliability‐based stress‐constrained TO (RBSCTO) problem is considered in this paper. The DTO constraint is derived based on shifting vectors derived from the previous cycle's RA outcomes, enabling low‐reliability constraint shift towards the feasible direction. The DTO is solved based on solid‐isotropic‐material‐with‐penalization (SIMP) and augmented Lagrangian method. Meanwhile, the optimization problem in RA is addressed using finite differences and the interior point method. To reduce the errors resulting from linear approximation and optimization in RA when the target reliability is very low, an outlier handling method is employed. Meantime, we utilize a probabilistic neural network to enhance the efficiency of reliability assessment. Comparative studies against traditional methods across four RBSCTO tasks are demonstrated to validate its effectiveness. Monte Carlo simulations are used to validate the reliability of results.

An inexact nonmonotone projected gradient method for constrained multiobjective optimization

An inexact nonmonotone projected gradient method for constrained multiobjective optimization

Stochastic nested primal-dual method for nonconvex constrained composition optimization

In this paper we study the nonconvex constrained composition optimization, in which the objective contains a composition of two expected-value functions whose accurate information is normally expensive to calculate. We propose a STochastic nEsted Primal-dual (STEP) method for such problems. In each iteration, with an auxiliary variable introduced to track the inner layer function values we compute stochastic gradients of the nested function using a subsampling strategy. To alleviate difficulties caused by possibly nonconvex constraints, we construct a stochastic approximation to the linearized augmented Lagrangian function to update the primal variable, which further motivates to update the dual variable in a weighted-average way. Moreover, to better understand the asymptotic dynamics of the update schemes we consider a deterministic continuous-time system from the perspective of ordinary differential equation (ODE). We analyze the Karush-Kuhn-Tucker measure at the output by the STEP method with constant parameters and establish its iteration and sample complexities to find an ϵ \epsilon -stationary point, ensuring that expected stationarity, feasibility as well as complementary slackness are below accuracy ϵ \epsilon . To leverage the benefit of the (near) initial feasibility in the STEP method, we propose a two-stage framework incorporating a feasibility-seeking phase, aiming to locate a nearly feasible initial point. Moreover, to enhance the adaptivity of the STEP algorithm, we propose an adaptive variant by adaptively adjusting its parameters, along with a complexity analysis. Numerical results on a risk-averse portfolio optimization problem and an orthogonal nonnegative matrix decomposition reveal the effectiveness of the proposed algorithms.

Population Feasibility State Guided Autonomous Constrained Multi-Objective Evolutionary Optimization

Many practical problems can be classified as constrained multi-objective optimization problems. Although various methods have been proposed for solving constrained multi-objective optimization problems, there is still a lack of research considering the integration of multiple constraint handling techniques. Given this, this paper combines the objective and constraint separation method with the multi-operator method, proposing a population feasibility state guided autonomous constrained evolutionary optimization method. This method first defines the feasibility state of the population based on both feasibility and ε feasibility of the solutions. Subsequently, a reinforcement learning model is employed to construct a mapping model between the population state and reproduction operators. Finally, based on the real-time population state, the mapping model is utilized to recommend the promising reproduction operator for the next generation. This approach demonstrates significant performance improvement for ε constrained mechanisms in constrained multi-objective optimization algorithms, and shows considerable advantages in comparison with state-of-the-art constrained multi-objective optimization algorithms.

Riemannian Interior Point Methods for Constrained Optimization on Manifolds

Riemannian Interior Point Methods for Constrained Optimization on Manifolds

A Unified Distributed Method for Constrained Networked Optimization via Saddle-Point Dynamics

A Unified Distributed Method for Constrained Networked Optimization via Saddle-Point Dynamics

Minimum-Energy Conical Intersections by Compressed Multistate Pair-Density Functional Theory.

Compressed multistate pair-density functional theory (CMS-PDFT) is a multistate version of multiconfiguration pair-density functional theory that can capture the correct topology of coupled potential energy surfaces (PESs) around conical intersections. In this work, we develop interstate coupling vectors (ISCs) for CMS-PDFT in the OpenMolcas and PySCF/mrh electronic structure packages. Yet, the main focus of this work is using ISCs to calculate minimum-energy conical intersections (MECIs) by CMS-PDFT. This is performed using the projected constrained optimization method in OpenMolcas, which uses ISCs to restrain the iterations to the conical intersection seam. We optimize the S1/S0 MECIs for ethylene, butadiene, and benzene and show that CMS-PDFT gives smooth PESs in the vicinities of the MECIs. Furthermore, the CMS-PDFT MECIs are in good agreement with the MECI calculated by the more expensive XMS-CASPT2 method.

Process Knowledge-Guided Autonomous Evolutionary Optimization for Constrained Multiobjective Problems

Various real-world problems can be attributed to constrained multi-objective optimization problems. Although there are various solution methods, it is still very challenging to automatically select efficient solving strategies for constrained multi-objective optimization problems. Given this, a process knowledge-guided constrained multi-objective autonomous evolutionary optimization method is proposed. Firstly, the effects of different solving strategies on population states are evaluated in the early evolutionary stage. Then, the mapping model of population states and solving strategies is established. Finally, the model recommends subsequent solving strategies based on the current population state. This method can be embedded into existing evolutionary algorithms, which can improve their performances to different degrees. The proposed method is applied to 41 benchmarks and 30 dispatch optimization problems of the integrated coal mine energy system. Experimental results verify the effectiveness and superiority of the proposed method in solving constrained multi-objective optimization problems.

Multi-objective constrained robust design of a metamaterial vibration isolator with a limited budget

Many real-world engineering design optimisation problems encounter input uncertainties, which may introduce undesired fluctuations in design performance or even make the design solution infeasible. Robust design optimisation (RDO) is widely studied due to its ability to deal with uncertainties. RDO methods require many evaluations generally, which is prohibitive when relying on expensive simulations. Surrogate-assisted optimisation can help to reduce the number of simulation calls. An improved constrained multi-objective efficient robust global optimisation method (CMO-ERGO) is proposed in this work, which combines the robust expected improvement of ERGO with the probability of feasibility. CMO-ERGO improves the ERGO framework and quantifies the robustness of the objective and the constraint functions using an analytical uncertainty quantification based on the Kriging surrogate. The proposed method is tested on three numerical benchmark functions and applied to the robust design of a metamaterial vibration isolator with a honeycomb structure to explore its performance in solving engineering applications. The robustness of optimal solutions is demonstrated using the Monte Carlo Method. Moreover, comparisons between CMO-ERGO and several existing RDO methods illustrate the effectiveness and efficiency of CMO-ERGO.

A two-level surrogate framework for demand-objective time-variant reliability-based design optimization

Complex engineering problems in the real world often involve uncertainties and require time-consuming simulations and experiments, hindering the efficiency of constraints processing. Additionally, practical engineering problems may have varying demands that pose new challenges for dealing with dynamic environments. However, most existing methods focus on immediate demands, making it inevitable to undergo tedious procedures to find feasible solutions. To address these issues, this paper proposes a demand-objective time-variant reliability-based design optimization framework to meet different demands in varying environments. Meanwhile, a corresponding two-level surrogate-based solving strategy is developed to reduce the computational resources required. The framework consists of two stages: time-variant reliability-based constraint handling and demand-objective optimization. An adaptive two-level surrogate method is proposed for time-variant reliability-based constraint handling by combining Kriging to reduce computational costs associated with evaluating constraints. This paper introduces moderate, conservative, and radical models for demand-objective optimization, combining the two-level surrogate method to deal with dynamic cost functions with different demands. Also, a new constrained minimax optimization method is developed for the radical model, which is the trickiest but very useful in practical engineering problems so that the algorithm can converge quickly. Finally, some examples are demonstrated to specify the proposed framework in applications.

Energy-efficient torque distribution strategy for four wheel drive electric vehicles based on Traffic zone

This paper presents a four-wheel electric vehicle control system. It incorporates a two-level control strategy for stability and optimal torque distribution to improve fuel efficiency and extend the vehicle’s operational range. The control architecture is structured hierarchically, with a higher level responsible for determining yaw moment and traction forces based on the desired vehicle dynamics. At the lower level, a multi-criteria constrained optimization method is employed, considering both vehicle stability and energy consumption. Additionally, this study takes into consideration the vehicle’s operational context, such as the specific Traffic zone, and the adhesion properties of the tires. This ensures a delicate balance between instantaneous power consumption and overall vehicle stability. The control system’s performance is tested and assessed through three distinct scenarios within the Matlab/Simulink environment. The co-simulation involves the nonlinear vehicle model simulation software, Carsim, and the results are comprehensively compared to the literature.

Linear Constrained Optimization Method (LiCOM): A Novel Paradigm to Handle Engineering Optimization Problems

Linear Constrained Optimization Method (LiCOM): A Novel Paradigm to Handle Engineering Optimization Problems

Gaussian Distribution–Based Control Vector Parameterization Method for Constrained Hypersonic Vehicle Reentry Trajectory Optimization

Gaussian Distribution–Based Control Vector Parameterization Method for Constrained Hypersonic Vehicle Reentry Trajectory Optimization

Solving multiphysics-based inverse problems with learned surrogates and constraints

Solving multiphysics-based inverse problems for geological carbon storage monitoring can be challenging when multimodal time-lapse data are expensive to collect and costly to simulate numerically. We overcome these challenges by combining computationally cheap learned surrogates with learned constraints. Not only does this combination lead to vastly improved inversions for the important fluid-flow property, permeability, it also provides a natural platform for inverting multimodal data including well measurements and active-source time-lapse seismic data. By adding a learned constraint, we arrive at a computationally feasible inversion approach that remains accurate. This is accomplished by including a trained deep neural network, known as a normalizing flow, which forces the model iterates to remain in-distribution, thereby safeguarding the accuracy of trained Fourier neural operators that act as surrogates for the computationally expensive multiphase flow simulations involving partial differential equation solves. By means of carefully selected experiments, centered around the problem of geological carbon storage, we demonstrate the efficacy of the proposed constrained optimization method on two different data modalities, namely time-lapse well and time-lapse seismic data. While permeability inversions from both these two modalities have their pluses and minuses, their joint inversion benefits from either, yielding valuable superior permeability inversions and CO2 plume predictions near, and far away, from the monitoring wells.

Trajectory Deformation With Constrained Optimization for Bilateral Rehabilitation Robots

Robot-aided bilateral treatment has been verified to be an effective training program for hemiplegic rehabilitation. In this article, a reference-free active control framework based on optimal trajectory deformation is proposed to ensure the safety requirements in the leader–follower paradigm of bilateral treatment. A constrained optimization method is developed to handle the motion constraints, which are constructed by quantitative assessments of typical impairment in stroke patients, such as reduced range of motion, resistance to passive movement, and disturbed quality of movement. Then, by optimally deforming the robotic trajectory, abnormal motion patterns that lead to safety issues can be rectified. Furthermore, the physically interactive trajectory deformation is employed to achieve active control without a predefined trajectory. At last, all approaches are verified on a robotic platform with a 2-DoF lower-limb exoskeleton. Experimental results demonstrate the effectiveness of proposed control scheme in rectifying abnormal motion patterns and enhancing human–robot interaction.