Large-scale Optimization Research Articles

Large-scale stealth trajectory optimization based on hybrid A*-Gauss pseudospectral method

For airborne electronic countermeasures, a practical and feasible stealth trajectory with low observability significantly impacts mission success. However, for long-range and large-scale trajectory optimization problems, the significant increase in the state space size will affect the feasibility and optimality of the problem solution. This paper proposes a hybrid trajectory optimization method to address the above issues. First, the A* (A-star) algorithm and cubic B-spline curve fitting method are used to generate the corresponding waypoints in the predetermined grid map under the radar detection threat to satisfy the trajectory stealth effect at the macro level. Then, the optimal control model (OCP) with the shortest flight time is solved between the waypoints to obtain segmented trajectories. Finally, the above state-control variable sequences are further used to solve the optimal control problem of the micro-level stealth trajectory coupling the radar cross section (RCS) by Gauss pseudospectral method (GPM). The numerical simulation results validate the proposed hybrid optimization method.

Distributed Stochastic Gradient Tracking Algorithm With Variance Reduction for Non-Convex Optimization.

This article proposes a distributed stochastic algorithm with variance reduction for general smooth non-convex finite-sum optimization, which has wide applications in signal processing and machine learning communities. In distributed setting, a large number of samples are allocated to multiple agents in the network. Each agent computes local stochastic gradient and communicates with its neighbors to seek for the global optimum. In this article, we develop a modified variance reduction technique to deal with the variance introduced by stochastic gradients. Combining gradient tracking and variance reduction techniques, this article proposes a distributed stochastic algorithm, gradient tracking algorithm with variance reduction (GT-VR), to solve large-scale non-convex finite-sum optimization over multiagent networks. A complete and rigorous proof shows that the GT-VR algorithm converges to the first-order stationary points with O(1/k) convergence rate. In addition, we provide the complexity analysis of the proposed algorithm. Compared with some existing first-order methods, the proposed algorithm has a lower O(PMε⁻¹) gradient complexity under some mild condition. By comparing state-of-the-art algorithms and GT-VR in numerical simulations, we verify the efficiency of the proposed algorithm.

An Ensemble Surrogate-Based Coevolutionary Algorithm for Solving Large-Scale Expensive Optimization Problems.

Surrogate-assisted evolutionary algorithms (SAEAs) have shown promising performance for solving expensive optimization problems (EOPs) whose true evaluations are computationally or physically expensive. However, most existing SAEAs only focus on the problems with low dimensionality and they rarely consider solving large-scale EOPs (LSEOPs). To fill this research gap, this article proposes an ensemble surrogate-based coevolutionary optimizer for tackling LSEOPs. First, some local surrogate models are trained with low-dimensional data subsets by using feature selection on the large-scale decision variables, a part of which are used to build a selective ensemble surrogate for better approximating the target LSEOP. Then, a coevolutionary optimizer guided by the ensemble surrogate is designed by running two populations to cooperatively solve the target LSEOP and the simplified auxiliary problem. The information of offspring from the two populations is shared to facilitate the coevolution process, which can exploit the searching experience from the simplified auxiliary problem to help solving the target LSEOP. Finally, an effective infill selection criterion is used to update the ensemble surrogate and enhance its approximate performance. To evaluate the performance of the proposed algorithm, a number of well-known benchmark problems are used and the experimental results validate our superior performance over nine state-of-the-art SAEAs on most cases.

Security-Constrained Unit Commitment for Electricity Market: Modeling, Solution Methods, and Future Challenges

This paper summarizes the technical activities of the IEEE Task Force on Solving Large Scale Optimization Problems in Electricity Market and Power System Applications. This Task Force was established by the IEEE Technology and Innovation Subcommittee to first review the state-of-the-art of the security-constrained unit commitment (SCUC) business model, its mathematical formulation, and solution techniques in solving electricity market clearing problems. The Task Force then investigated the emerging challenges of future market clearing problems and presented efforts in building benchmark mathematical and business models.

Research on Optimization Algorithm of Single-block Train Formation Plan of Technical Station

The optimization of train formation plan is a large-scale combinatorial optimization problem, which is difficult to solve. This paper mainly studies the optimization algorithm of the single-block train formation plan. The corresponding mathematical model is established by consulting relevant literature, and a positive feedback search algorithm based on absolute conditions is proposed. First of all, the wagon flow that meets the absolute conditions directly runs through train flow without making other choices. For the wagon flow that does not meet the absolute conditions, select the target station to reach directly according to the probability. The probability of wagon flow selecting a station is calculated according to the pheromone of the wagon flow at the station. At the same time, a pheromone update strategy with positive feedback mechanism is proposed to make the search process converge. Finally, the feasibility of the algorithm and the necessity of introducing absolute conditions into the algorithm are verified by taking eight technical stations in the linear direction of the road network as examples.

An Adaptive Dimension Weighting Spherical Evolution to Solve Continuous Optimization Problems

The spherical evolution algorithm (SE) is a unique algorithm proposed in recent years and widely applied to new energy optimization problems with notable achievements. However, the existing improvements based on SE are deemed insufficient due to the challenges arising from the multiple choices of operators and the utilization of a spherical search method. In this paper, we introduce an enhancement method that incorporates weights in individuals’ dimensions that are affected by individual fitness during the iteration process, aiming to improve SE by adaptively balancing the tradeoff between exploitation and exploration during convergence. This is achieved by reducing the randomness of dimension selection and enhancing the retention of historical information in the iterative process of the algorithm. This new SE improvement algorithm is named DWSE. To evaluate the effectiveness of DWSE, in this study, we apply it to the CEC2017 standard test set, the CEC2013 large-scale global optimization test set, and 22 real-world problems from CEC2011. The experimental results substantiate the effectiveness of DWSE in achieving improvement.

Hierarchical shape optimization for large deployable membrane reflector with spatial skirt cable

In the shape optimization analysis of electrostatically controlled deployable membrane reflector (ECDMR), the poor balance of the membrane with spatial skirt cable is the main reason for the degradation of the reflector surface precision. At the same time, while in the optimization of the pre-stress of large deployable reflectors, the membrane structure has strong geometric nonlinearity, and the lack of necessary gradient information leads to low efficiency of the calculation. Therefore, according to the structural characteristics of the cable-membrane reflector, the two optimization objectives of the highest surface precision and the most uniform stress distribution is considered, and a hierarchical shape optimization method is proposed based on membrane theory and unbalance force analysis, which realizes the solution of the multi-objective optimization problem when the three optimization objectives have different priorities. The interior effective membrane reflective surface is analyzed using membrane theory, and the external membrane with spatial skirt cable is analyzed using nonlinear finite element method. The gradient information required for optimization is also obtained by unbalance force analysis, which ensures better optimization efficiency and can solve large-scale optimization problems. Therefore, the node positions and element equilibrium stresses of the structure can be optimized simultaneously, which further expands the search space of the equilibrium state and reduces the possibility of falling into local optimal solutions. Finally, a numerical example of a 30 m aperture ECDMR is calculated and analyzed, and the results show that the proposed method can obtain a high surface precision with a fast solution speed.

An efficient simulation procedure for the expected opportunity cost using metamodels

Many decision problems in modern industries involve the performance optimization of discrete-event dynamic systems. Because of the stochasticity of these systems, performance usually is evaluated through simulation. Finding the optimal designs of these systems can be modeled as a ranking and selection problem. This research considers the problem of selecting the best design from among numerous designs. We minimized the expected opportunity cost (EOC) of incorrect selection with a limited computing budget. The entire domain of designs could be divided into several adjacent partitions, and the performances of designs in each partition were estimated using a regression metamodel. We assumed the underlying function in each partition to be quadratic. Using large deviations theory, we then derived an asymptotically optimal budget allocation rule and developed a sequential allocation algorithm to implement the allocation rule. The EOC measure was compared with the probability of correct selection measure in a set of large-scale simulation optimization problems. Numerical experiments verified the effectiveness of our proposed simulation procedure.

Large-Scale Multi-Objective Imaging Satellite Task Planning Algorithm for Vast Area Mapping

With satellite quantity and quality development in recent years, remote sensing products in vast areas are becoming widely used in more and more fields. The acquisition of large regional images requires the scientific and efficient utilization of satellite resources through imaging satellite task planning technology. However, for imaging satellite task planning in a vast area, a large number of decision variables are introduced into the imaging satellite task planning model, making it difficult for existing optimization algorithms to obtain reliable solutions. This is because the search space of the solution increases the exponential growth with the increase in the number of decision variables, which causes the search performance of optimization algorithms to decrease significantly. This paper proposes a large-scale multi-objective optimization algorithm based on efficient competition learning and improved non-dominated sorting (ECL-INS-LMOA) to efficiently obtain satellite imaging schemes for large areas. ECL-INS-LMOA adopted the idea of two-stage evolution to meet the different needs in different evolutionary stages. In the early stage, the proposed efficient competitive learning particle update strategy (ECLUS) and the improved NSGA-II were run alternately. In the later stage, only the improved NSGA-II was run. The proposed ECLUS guarantees the rapid convergence of ECL-INS-LMOA in the early evolution by accelerating particle update, introducing flight time, and proposing a binary competitive swarm optimizer BCSO. The results of the simulation imaging experiments on five large areas with different scales of decision variables show that ECL-INS-LMOA can always obtain the imaging satellite mission planning scheme with the highest regional coverage and the lowest satellite resource consumption within the limited evaluation times. The experiments verify the excellent performance of ECL-INS-LMOA in solving vast area mapping planning problems.

Multi-period optimization for the design and operation of a flexible power-to-methanol process

The increasing share of renewable resources in the context of energy transition scenarios requires new methodologies for the design and operation of chemical production facilities, which must adapt to the unsteady nature of their power supply. In this contribution, a highly flexible, fully electrified Power-to-Methanol process, supplied with unsteady wind power generated within the system boundaries, is designed by means of a large-scale NLP multi-period optimization for profit maximization. The problem is constrained by detailed models of interconnected units, feasibility conditions, and discretized power loads (periods) associated with their probability of occurrence. External power must be integrated into the plant to sustain feasible operations when the renewable input is not sufficiently available. Results show that the price at which the external power is purchased determines whether the resulting flexible-plant configuration is competitive with a comparable plant, optimized for steady-state operations ensured by large hydrogen or electricity buffers. Intermediate configurations represented by small buffers and semi-flexible operations constitute an important compromise for future applications of this novel approach.

Dynamic matrix-based evolutionary algorithm for large-scale sparse multiobjective optimization problems

Dynamic matrix-based evolutionary algorithm for large-scale sparse multiobjective optimization problems

A stochastic policy algorithm for seasonal hydropower planning

AbstractHydropower producers need to plan several months or years ahead to estimate the opportunity value of water stored in their reservoirs. The resulting large-scale optimization problem is computationally intensive, and model simplifications are often needed to allow for efficient solving. Alternatively, one can look for near-optimal policies using heuristics that can tackle non-convexities in the production function and a wide range of modelling approaches for the price- and inflow dynamics. We undertake an extensive numerical comparison between the state-of-the-art algorithm stochastic dual dynamic programming (SDDP) and rolling forecast-based algorithms, including a novel algorithm that we develop in this paper. We name it Scenario-based Two-stage ReOptimization abbreviated as STRO. The numerical experiments are based on convex stochastic dynamic programs with discretized exogenous state space, which makes the SDDP algorithm applicable for comparisons. We demonstrate that our algorithm can handle inflow risk better than traditional forecast-based algorithms, by reducing the optimality gap from 2.5 to 1.3% compared to the SDDP bound.

Research on key technologies of large-scale wind-solar hybrid grid energy storage capacity big data configuration optimization

Due to the uncertainty and randomness of large-scale wind and light, the output power of the power grid has great fluctuations. If it is directly connected to the grid, it will affect the main grid. In addition, when the grid switches between on-grid/off-grid operation modes, there will be power shortages, shocks and oscillations. The scientific and reasonable configuration of energy storage system capacity big data can reduce the load power shortage rate, improve the utilization rate of renewable energy, and ensure the reliable operation of the power grid. For this reason, the key technology of large-scale wind-solar hybrid grid energy storage capacity big data configuration optimization is studied. A large-scale wind-solar hybrid grid energy storage structure is proposed, and the working characteristics of photovoltaic power generation and wind power generation are analyzed, and the probability model of photovoltaic power generation, wind power generation and load, as well as the charging and discharging model of battery and super capacitor are established accordingly. On this basis, the optimization objective function is set, the constraints are determined, and the large-scale wind-solar hybrid grid energy storage capacity big data configuration optimization model is constructed. And the PSO algorithm is used to solve the model to realize the big data configuration optimization of large-scale wind-solar hybrid grid energy storage capacity. The research results show that the proposed method of large-scale wind-solar hybrid grid energy storage system has good power supply reliability and economy, and can effectively improve the utilization rate of renewable energy.

Large-scale parallel topology optimization of three-dimensional incompressible fluid flows in a level set, anisotropic mesh adaptation framework

This papers considers the topology optimization of duct flows governed by the three-dimensional steady state Navier–Stokes equations, using anisotropic mesh adaptation to achieve a high-fidelity description of all fluid–solid interfaces. The numerical framework combines an immersed volume method solving stabilized, linear equal-order finite element formulations cast in the Variational Multiscale (VMS) framework, and level set representations of the interface, used as a posteriori anisotropic error estimator to minimize the interpolation error under the constraint of a prescribed number of nodes in the mesh. Both the resolution and remeshing steps are performed in a massively parallel framework allowing for the optimization of large-scale systems. In particular, an original parallelization strategy is used for mesh adaptation, that combines local remeshing performed sequentially and independently on each subdomain with blocked interfaces, and constrained repartitioning to optimally move the interfaces between subdomains in an optimal way, both iterated until a satisfying mesh and partition are obtained. The proposed approach reduces the computational burden related to the call of the finite element solver, compared to classical optimization schemes working on uniform grids with similar mesh refinement. For a given number of nodes, it improves the accuracy in the geometric description of all layouts. Finally, it has the potential to alleviates the end user from most of the post-processing step aiming at extracting the final layout, due to ability of anisotropic adapted meshes to generate intrinsically smooth designs. Numerical results are provided for several three-dimensional problems of power dissipation minimization involving several dozen million state degrees of freedom, for which the optimal designs agree well with reference results from the literature, while providing superior accuracy over prior studies solved on isotropic meshes (in the sense that the flow is better resolved, especially in the near-wall regions, and the layouts are more smooth). The potential of the method for engineering problems of practical interest is eventually exposed by optimizing the distributor section conveying the cold fluid within the plates of a plate fin heat exchanger.

A resource allocation-based multi-objective evolutionary algorithm for large-scale multi-objective optimization

A resource allocation-based multi-objective evolutionary algorithm for large-scale multi-objective optimization

Multi-objective multidisciplinary design optimization of liquid-propellant engines thrust chamber based on a surrogate model

The design of liquid-propellant engines (LPEs) has several challenges in setting the performance parameters. Accordingly, optimizing the design of a thrust chamber is of considerable importance that has been considered in several research projects. Previous research has focused on multidisciplinary design optimization (MDO). However, despite these efforts, the main issues remain. The present paper proposes a multi-objective multidisciplinary design optimization based on an efficient adaptive surrogate model of the thrust chamber to address these issues. The proposed method introduces a practical multidisciplinary optimization method based on an adaptive surrogate model that uses the moving least squares methodology, CCM, sensitivity analysis, and the elite multi-objective genetic algorithm (NSGAII). Due to the high importance of specific impulse and thrust-to-weight ratio, these two functions were used as target functions and in the NSGAII framework, the Pareto frontier was drawn for them. The proposed method is applied to a thrust-chamber engine test case. The results show that the target performance of the engine is improved, the specific impulse value is increased by 3.4 s, and the thrust-to-weight ratio is increased by 4%. These values represent significant advances in LPE engine design. The results obtained in this study indicate the potential of the proposed method in solving large-scale thrust-chamber design optimization problems.

An accelerated exact distributed first-order algorithm for optimization over directed networks

Distributed optimization over networked agents has emerged as an advanced paradigm to address large-scale control, optimization, and signal-processing problems. In the last few years, the distributed first-order gradient methods have witnessed significant progress and enrichment due to the simplicity of using only the first derivatives of local functions. An exact first-order algorithm is developed in this work for distributed optimization over general directed networks with only row-stochastic weighted matrices. It employs the rescaling gradient method to address unbalanced information diffusion among agents, where the weights on the received information can be arbitrarily assigned. Moreover, uncoordinated step-sizes are employed to magnify the autonomy of agents, and an error compensation term and a heavy-ball momentum are incorporated to accelerate convergency. A linear convergence rate is rigorously proven for strongly-convex objective functions with Lipschitz continuous gradients. Explicit upper bounds of step-size and momentum parameter are provided. Finally, simulations illustrate the performance of the proposed algorithm.

Dynamic Data-Driven Application System for Flow Field Prediction with Autonomous Marine Vehicles

Efficiently predicting high-resolution and accurate flow fields through networked autonomous marine vehicles (AMVs) is crucial for diverse applications. Nonetheless, a research gap exists in the seamless integration of data-driven flow modeling, real-time data assimilation from flow sensing, and the optimization of AMVs’ sensing strategies, culminating in a closed-loop dynamic data-driven application system (DDDAS). This article presents a novel DDDAS that systematically integrates flow modeling, data assimilation, and adaptive flow sensing using networked AMVs. It features a hybrid data-driven flow model, uniting a neural network for trend prediction and a Gaussian process model for residual fitting. The neural network architecture is designed using knowledge extracted from historic flow data through tidal harmonic analysis, enhancing its capability in flow prediction. The Kriged ensemble transform Kalman filter is introduced to assimilate spatially correlated flow-sensing data from AMVs, enabling effective model learning and accurate spatiotemporal flow prediction, while forming the basis for optimizing AMVs’ flow-sensing paths. A receding horizon strategy is proposed to implement non-myopic optimal path planning, and a distributed strategy of implementing Monte Carlo tree search is proposed to solve the resulting large-scale tree searching-based optimization problem. Computer simulations, employing underwater gliders as sensing networks, demonstrate the effectiveness of the proposed DDDAS in predicting depth-averaged flow in nearshore ocean environments.

A Population Cooperation based Particle Swarm Optimization algorithm for large-scale multi-objective optimization

There are many multi-objective optimization problems (MOPs) in real life that contain a large number of decision variables, such as auto body parts design, financial investment, engineering design, adversarial textual attack and so on. These problems are known as large-scale multi-objective optimization problems (LSMOPs). Due to the curse of dimensionality, existing multi-objective evolutionary algorithm encounter difficulties in balancing convergence and diversity on LSMOPs. In this paper, a Population Cooperation based Particle Swarm Optimization algorithm (PCPSO) is proposed for tackling LSMOPs. To be specific, PCPSO is a two-stage optimizer with two key components: (1) In the first stage, an inter-population collaboration component named Auxiliary Population Cooperation (APC) is used to improve the convergence speed. (2) In the second stage, an intra-subpopulation collaboration component called SubPopulation Cooperation (SPC) is applied to balance convergence and diversity. Experimental results on benchmark problems with up to 5000 decision variables and 2, 3, 5, 10 objectives demonstrate that the proposed PCPSO achieves better performance than several state-of-the-art large-scale multi-objective evolutionary algorithms (LSMOEAs) on most test problems.

A parallel hub-and-spoke system for large-scale scenario-based optimization under uncertainty

A parallel hub-and-spoke system for large-scale scenario-based optimization under uncertainty