A Comparative Study of Large-Scale Nonlinear Optimization Algorithms

Buildings contribute to more than 70% of overall U.S. electricity usage and greenhouse gas emissions. The future building control optimizes more connected devices and renewable energy equipment, which requires a rapid and accurate response. It also poses the challenge of solving non-linear problems with discrete variables in real time. In one study, we developed a novel optimization using quantum annealing for MPC of rooftop units in buildings. Our approach demonstrated significant improvements in computational speed from hours to seconds by considering day-ahead demand response signals. Our findings highlight the potential of quantum computing in solving large-scale non-linear discrete optimization problems for building energy systems. The other research presented a new framework for building-to-grid integration. We developed MPC for a commercial distribution grid for cost reduction. With similar solutions to traditional algorithms, quantum computing reduced computational time to less than 1.1%. We proved its potential to solve large-scale discrete optimization problems for urban energy systems

Genetic algorithms are able to search very large, variable complex spaces and locate the global optimum. However, there exist many difficulties in applying GA to large-scale nonlinear system optimization or "GA hard" problems. This paper presents an improved GA based on domain evolution model and fuzzy environment factor. Simulation study shows that it is a powerful search technique which can avoid premature convergence and locate the real global optimum. An example is given to show how this new algorithm can be successfully applied to solve large-scale industrial chemical separation process optimization problem.

Short-term scheduling and recipe optimization of blending processes

The growing penetration of renewable energy sources (RES) has boosted the necessity of cost-effective and flexible power system operations. Battery Energy Storage Systems (BESS) provide a real-world solution by improving grid reliability, facilitating flexible dispatch, and renewable integration. This paper models the Economic Dispatch (ED) problem with BESS integration, with an objective to minimize overall generation cost subject to operation constraints of thermal units and BESS. Two optimization methods are compared: (i) fmincon, a gradient-based constrained nonlinear solver, and (ii) the JAYA algorithm, a parameter-free metaheuristic that repeatedly pushes solutions towards best and away from worst. Simulation studies on a 6-bus system with six thermal units show that integration with BESS highly enhances operation flexibility and lowers costs. The total generation cost was reduced from Rs.23.74 million to Rs.21.21 million, corresponding to a saving of Rs.2.53 million (10.66%) using FMINCON whereas using JAYA algorithm the tota generation cost was reduced from Rs.23.68 million to Rs.20.83 million, corresponding to a saving of Rs.2.85 million (12.06%). The Jaya algorithm performs better consistently compared to fmincon in both cost minimization and the speed of convergence, showing its suitability for solving large-scale nonlinear power system optimization problems.

A techno-economic multi-objective model for hybrid harmonic filter planning considering uncertainty in non-linear loads

Conjugate gradient methods are widely acknowledged to be among the most efficient and robust methods for solving the large-scale unconstrained nonlinear optimization problems

This paper reports on a successful determination of the train travel schedule parameters for a rail system based on limited data, and thus provides a verification of the axiomatic safety-critical assessment process (ASCAP), a rail system simulator developed at the Center of Rail Safety-Critical Excellence at the University of Virginia. The train system considered is a corridor encompassing a territory of over 127 miles. It is divided into 37 train speed zones, with nine sidings. The only data available are the actual trip times of 171 trains dispatched over a period of 14 days. The problem of determining the 37 train-speed-zone average speeds and nine siding delay times was formulated as a constrained optimization problem. The cost to be minimized is the accumulated errors between the actual train trip times and the ASCAP simulated trip times resulting from a particular set of train-speed-zone average speeds and siding delay times. The constraints include allowable siding delays, permissible train-speed-zone average speeds and prohibition of southbound trains from entering the sidings. This large-scale non-linear optimization problem was then solved by a genetic algorithm developed by the present authors and referred to as the intelligent genetic algorithm. Simulation results demonstrate the effectiveness of this intelligent genetic algorithm.

Solids-based carbon dioxide (CO2)adsorption, where CO2 is adsorbed under high pressure/low temperature and desorbed at low pressure/high temperature, is a low energy consumption capture technology with high carbon uptake efficiency. Chemical looping combustion (CLC), where a solid oxygen carrier (OC) transports oxygen between two high-temperature reactors – a fuel and an air reactor –, is a low energy penalty, fuel-flexible technology with inherent CO2 capture for power/heat and syngas production. In this work, state-of-the-art equation-oriented (EO) mathematical models of a fixed-bed (FxB) contactor for CO2 adsorption and moving-bed (MB) reactors for gas-, and solid-fueled CLC processes are developed. The solid-fueled MB model is a multi-zonal model for the CLC of coal. Large-scale nonlinear optimization problems are solved for simultaneous optimization of design and operating conditions for the CLC processes. Further, a Bayesian parameter estimation and model building framework is proposed and used to quantify the parametric and model form uncertainty of CO2 adsorption isotherm and CLC OC reduction kinetic models based on experimental data. The model form discrepancy is described by a set of orthogonal functions which are naturally suitable and efficient for uncertainty propagation to the unit/process model in which the discrepancy-augmented models are implemented. By using the joint posterior distribution of the model and discrepancy function parameters and inserting discrepancy functions in the isotherm and kinetic models coupled with the EO unit/process reactor models, the effect of the uncertainty inherent to bench-scale adsorption/kinetic models on key process variables of the large-scale systems are evaluated.

An application of neural network modeling is described for generating hypotheses about the relationships between response properties of neurons and information processing in the auditory system. The goal is to study response properties that are useful for extracting sound localization information from directionally selective spectral filtering provided by the pinna. For studying sound localization based on spectral cues provided by the pinna, a feedforward neural network model with a guaranteed level of fault tolerance is introduced. Fault tolerance and uniform fault tolerance in a neural network are formally defined and a method is described to ensure that the estimated network exhibits fault tolerance. The problem of estimating weights for such a network is formulated as a large-scale nonlinear optimization problem. Numerical experiments indicate that solutions with uniform fault tolerance exist for the pattern recognition problem considered. Solutions derived by introducing fault tolerance constraints have better generalization properties than solutions obtained via unconstrained back-propagation.

Meta-heuristic algorithms are widely viewed as feasible techniques to solve continuous large-scale numerical optimization problems. Grey wolf optimizer (GWO) is a relatively new stochastic algorithm with only a few parameters to adjust that can be easily used for global optimization. This paper presents an efficient and robust GWO (ERGWO) variant to solve large-scale numerical optimization problems. Inspired by particle swarm optimization, a nonlinearly adjustment strategy for parameter control is designed to balance exploration and exploitation. Additionally, a modified position-updating equation is presented to improve convergence speed. The performance of ERGWO is verified on 18 benchmark large-scale numerical optimization problems with dimensions ranging from 30 to 10,000, 30 benchmarks from CEC 2014, 30 functions in CEC 2017, respectively. Numerical experiments are performed to compare ERGWO to the basic GWO algorithm, other GWO variants, and other well-known meta-heuristic search techniques. Simulations demonstrate that the proposed ERGWO algorithm can find high quality solutions with low computational cost and very fast convergence.

A view of the limitations, opportunities, and challenges in parallel nonlinear optimization

A large-scale continuous optimization benchmark suite with versatile coupled heterogeneous modules

Recently, the large-scale optimization problems have become a common research topic in the field of evolutionary computation. It is hard to find optimal solutions when solving large-scale multi-objective optimization problems (LSMOPs), due to the ineffectiveness of existing operators. In the other word, the search ability of most existing MOEAs on solving LSMOPs is still weak. To address this issue, an efficient competitive swarm optimizer with a strong exploration ability, denoted as E-CSO, is presented in this paper, which designs a novel three-particle-based particle updating strategy to improve the search efficiency. The experimental results validate the high efficiency and effectiveness of our proposed approach when solving various LSMOPs.

With the development of optimization heads toward large-scale problems, a series of optimization packages were developed for large-scale NLP optimization. The RSQP (reduced sequential quadratic programming) we concerned is one of best large scale NLP algorithm, and is especially efficient in process operation optimization. In this paper, the performance of our concerned algorithm RSQP, CONOPT2 and MINOS5 were tested by large-scale benchmarking COPS examples, the calculation was under the environment of GAMS. Computing results demonstrate that the performance of CONOPT2 was better than the others on robustness and efficiency. To problems with relatively small degrees of freedom, the performance of MINOS5 worked worst, though RSQP was not as robust as CONOPT2, its memory required reduced as half as CONOPT2. The results show that the RSQP we concerned has great advances for large scale optimization and further research for the algorithmpsilas stability is very necessary.

Although there are many studies on large-scale unconstrained optimization (e.g., with 100 to 1000 variables) and small-scale constrained optimization (e.g., with 10 to 30 variables) using nature-inspired algorithms (e.g., evolutionary algorithms and swarm intelligence algorithms), no publicly available nature-inspired algorithm is developed for large-scale constrained optimization. In this paper, we combine a cooperative coevolutionary particle swarm optimization (CCPSO) algorithm with the e constrained method to solve large-scale real-valued constrained optimization problems. The eCCPSO framework is proposed, and three different algorithms based on the framework, i.e., eCCPSOd, eCCPSOw and eCCPSOw2, are developed. The proposed algorithms compare favorably to the state-of-the-art constrained optimization algorithm eDEag on large-scale problems. The experimental results further suggest that eCCPSOw2 with adaptive improvement detection technique is highly competitive compared with the other algorithms considered in this work for solving large-scale real-valued constrained optimization problems.