Large-scale Optimization Research Articles

Research on the Strategy of Educational Management and Resource Optimization Based on Big Data Technology in the Mode of Industry-Education Integration

Abstract In order to build an education information platform to support “industry-education dialogue” and at the same time serve the teaching and research of industry-education integration. In this paper, we use big data technology to construct a system of education management and resource optimization, supporting education construction in the context of industrial transformation and upgrading. For larger-scale WSNs, an energy-efficient data collection algorithm based on non-uniform clustering is proposed. To deal with large-scale optimization problems, a hybrid algorithm of genetic algorithms and particle optimization hierarchical collaboration is introduced. Then, the algorithm is applied to cluster WSNs, an adaptation function is constructed with the goal of equalizing energy consumption, and a data collection algorithm based on non-uniform clustering is proposed. The Apriori algorithm, which is based on the interest degree model, is used to mine the course evaluation data for the system design in the university industry-teaching fusion model. This system design does both course evaluation and resource optimization. The system’s total evaluation score is high, at 90.84 points. It also improves the efficiency of cooperation between the education industry and schools. It proves that the system’s design is effective and high-level and has a positive effect on teaching management and resource optimization in education.

An Efficient Greedy Search Algorithm for High-dimensional Linear Discriminant Analysis.

High-dimensional classification is an important statistical problem that has applications in many areas. One widely used classifier is the Linear Discriminant Analysis (LDA). In recent years, many regularized LDA classifiers have been proposed to solve the problem of high-dimensional classification. However, these methods rely on inverting a large matrix or solving large-scale optimization problems to render classification rules-methods that are computationally prohibitive when the dimension is ultra-high. With the emergence of big data, it is increasingly important to develop more efficient algorithms to solve the high-dimensional LDA problem. In this paper, we propose an efficient greedy search algorithm that depends solely on closed-form formulae to learn a high-dimensional LDA rule. We establish theoretical guarantee of its statistical properties in terms of variable selection and error rate consistency; in addition, we provide an explicit interpretation of the extra information brought by an additional feature in a LDA problem under some mild distributional assumptions. We demonstrate that this new algorithm drastically improves computational speed compared with other high-dimensional LDA methods, while maintaining comparable or even better classification performance.

Swarm intelligence technique for solving optimal power flow problem in the Nigeria power system

This paper deals on the implementation of the particle swarm optimization method for solving power flow problems in the Nigeria power system. The difficulty of solving optimal power flow (OPF) problems increases significantly with increasing network size and complexity. Some of the weakness of the conventional methods include: limited ability in solving real-world large scale optimization problems, weakness in handling constraints, poor convergence and slow computational time. The results gotten by implementing the Particle Swarm Optimization (PSO) algorithm in Nigeria 330kV 52-Bus network show that the total active power and reactive power losses were substantially reduced to 0.03MW and 0.05MVAR. The system time of convergence was faster at 0.5seconds. Also, the maximum line active and reactive power losses on line 1 to 2 were reduced greatly to 0.00MW and 0.01MVAR respectively. These show that the system was better optimized with the PSO algorithm than the conventional method.

A fast interpolation-based multi-objective evolutionary algorithm for large-scale multi-objective optimization problems

A fast interpolation-based multi-objective evolutionary algorithm for large-scale multi-objective optimization problems

A Sufficient Descent 3-Term Conjugate Gradient Method for Unconstrained Optimization Algorithm

In recent years, 3-term conjugate gradient algorithms (TT-CG) have sparked interest for large scale unconstrained optimization algorithms due to appealing practical factors, such as simple computation, low memory requirement, better sufficient descent property, and strong global convergence property. In this study, minor changes were made to the BRB-CG method used for addressing the optimization algorithms discussed. Then, a new 3-term BRB-CG (MTTBRB) was presented. This new method solved large-scale unconstrained optimization problems. Despite the fact that the BRB algorithm achieved global convergence by employing a modified strong Wolfe line search, in this new MTTBRB-CG method the researchers employed the classical strong Wolfe-Powell condition (SWPC). This study also attempted to quantify how much better 3-term efficiency is than 2-term efficiency. As a result, in the numerical analysis, the new modification was compared to an effective 2-term CG- method. The numerical analysis demonstrated the effectiveness of the proposed method in solving optimization problems.

An Adaptive Low Computational Cost Alternating Direction Method of Multiplier for RELM Large-Scale Distributed Optimization

In a class of large-scale distributed optimization, the calculation of RELM based on the Moore–Penrose inverse matrix is prohibitively expensive, which hinders the formulation of a computationally efficient optimization model. Attempting to improve the model’s convergence performance, this paper proposes a low computing cost Alternating Direction Method of Multipliers (ADMM), where the original update in ADMM is solved inexactly with approximate curvature information. Based on quasi-Newton techniques, the ADMM approach allows us to solve convex optimization with reasonable accuracy and computational effort. By introducing this algorithm into the RELM model, the model fitting problem can be decomposed into a set of subproblems that can be executed in parallel to achieve efficient classification performance. To avoid the storage of expensive Hessian for large problems, BFGS with limited memory is proposed with computational efficiency. And the optimal parameter values of the step-size search method are obtained through Wolfe line search strategy. To demonstrate the superiority of our methods, numerical experiments are conducted on eight real-world datasets. Results on problems arising in machine learning suggest that the proposed method is competitive with other similar methods, both in terms of better computational efficiency as well as accuracy.

A survey of meta-heuristic algorithms in optimization of space scale expansion

Optimization problem of space scale expansion widely exists in practical applications, such as transportation, logistics, scheduling, social networks, etc. According to different expansion directions, the problem of space scale expansion can be divided into three categories: expansion of decision space, expansion of objective space and simultaneous expansion of decision space and objective space. These three types of problems correspond to large-scale global optimization problem, multi/many-objective optimization problem, and large-scale multi/many-objective optimization problem, respectively. Driven by the above problems, meta-heuristic algorithms (MHAs) with scalable characteristics have received extensive attention in this field. This paper summarizes the research progress of MHAs for space scale expansion optimization from three perspectives. Starting from the key difficulties of the optimization problem, the challenges brought by the expansion of the space scale to the existing MHAs are emphatically analyzed. From the perspective of methodology, the optimization methods of MHAs are divided into three modules: simplify problem structure, improve algorithm performance and expand application fields. Based on the review of performance evaluation benchmark problems, the simulation degree of various test suites for different practical application problems is summarized. In addition, some remaining challenges and future research directions on optimization of space scale expansion are discussed and analyzed.

A Quasi-Newton Matrix Factorization-Based Model for Recommendation

Solving large-scale non-convex optimization problems is the fundamental challenge in the development of matrix factorization (MF)-based recommender systems. Unfortunately, employing conventional first-order optimization approaches proves to be an arduous endeavor since their curves are very complex. The exploration of second-order optimization methods holds great promise. They are more powerful because they consider the curvature of the optimization problem, which is captured by the second-order derivatives of the objective function. However, a significant obstacle arises when directly applying Hessian-based approaches: their computational demands are often prohibitively high. Therefore, the authors propose AdaGO, a novel quasi-Newton method-based optimizer to meet the specific requirements of large-scale non-convex optimization problems. AdaGO can strike a balance between computational efficiency and optimization performance. In the comparative studies with state-of-the-art MF-based models, AdaGO demonstrates its superiority by achieving higher prediction accuracy.

Deep Q-Learning-Based Mud Ring Optimization Approach for Optimal Power Flow in Islanded DC Microgrid

Microgrid (MG) is the basic element that recreates a significant role in integrating renewable energy sources (RES). Direct current (DC) MG has advantages over alternating current (AC) for many applications. A DC-MG is connected to the islanded mode through power electronic converters, which are also an important component for RES integration. Due to environmental factors, RES will struggle to load the conditions. Branches of DC-MG have battery energy storage systems (BESSs) installed for compensating the supply–load imbalance. Even though BESS are installed, accurate maintenance is still required to maintain a balanced power flow. This work proposes an adaptive deep Q-learning (DQL) based mud ring optimization technique (DQMR) for optimal power flow in islanded DC-MG. DQL is effective for the task with discrete and low-dimensional action spaces, and mud ring algorithm (MRA) is to clear up large-scale optimization problems and power flow problems. The implementation is done through MATLAB/Simulink model. The error is minimized to 6% by this method, and the losses are also reduced. IEEE-9 bus system and IEEE-30 bus system are used in the proposed work to validate the performance.

Optimization of Communication Base Station Battery Configuration Considering Demand Transfer and Sleep Mechanism under Uncertain Interruption Duration

In the communication power supply field, base station interruptions may occur due to sudden natural disasters or unstable power supplies. This work studies the optimization of battery resource configurations to cope with the duration uncertainty of base station interruption. We mainly consider the demand transfer and sleep mechanism of the base station and establish a two-stage stochastic programming model to minimize battery configuration costs and operational costs. To transform the uncertainty expression in the first stage into a deterministic model, we design the K-Means-SAA algorithm to accelerate problem-solving and to compare it with the SAA algorithm. The case study results indicate that the proposed two-stage stochastic programming model can save 17.02% of the total cost compared to the expected value model. The proposed demand transfer and sleep mechanism can reduce the total cost by 41.92% compared to no mechanism. The results of numerical experiments and sensitivity analysis also verify the superiority of the designed algorithm in terms of running efficiency and solving time. Therefore, the model and algorithm proposed in this work provide valuable application guidance for large-scale base station configuration optimization of battery resources to cope with interruptions in practical scenarios.

Optimal cyclic scheduling of ethylene plants in backup furnace mode with separation capacity constraints

Ethylene plants (EPs) are a critical output source of ethylene. The cyclic scheduling optimization is crucial to increase the profitability of an EP. The EP comprises the ethylene cracking furnace system (ECFS), quenching, compression, separation sections, etc., which culminates in a large-scale optimization problem. In addition, the performance-decaying and semi-continuous characteristics of the ECFS inevitably lead to fluctuations in product throughput, resulting in an unstable production process and product quality decline. To address this issue, we propose a mixed-integer quadratic programming (MIQP) model for the cyclic scheduling of the EP in backup furnace mode with separation capacity constraints. This novel model can reduce fluctuations in product throughput by running a backup furnace when one furnace is shut down for decoking. Besides, the separation capacity constraints ensure that high-quality products can be separated from the cracked gas downstream. Moreover, the reformulated normalized multiparametric disaggregation technique (RNMDT), which relies on convex envelopes, is employed to relax the proposed MIQP model into a mixed-integer linear programming (MILP) model by partitioning the domain of the variables in the quadratic terms. Subsequently, an optimization framework based on the RNMDT is established to enhance the solution efficiency of the original problem. Finally, a case study from the real world reveals the effectiveness of the proposed method, which can provide instructive optimal cyclic scheduling for the EP.

Multiobjective visual evolutionary neural network and related convolutional neural network optimization

Biological visual systems intrinsically include a variety of direction-selective neurons capable of detecting changes in visual motion. Some of the neurons have been used to construct computational models for problem-specific engineering applications. However, it remains unclear how these neurons' visual response mechanisms can serve an interdisciplinary topic - visual evolutionary neural networks. In this study, we draw inspiration from swarm evolution and the fly's visual response and attention mechanisms to develop a fast multiobjective visual evolutionary neural network for solving multiobjective optimization problems, specifically focusing on convolutional neural network optimization. Our approach involves designing a multi-channel input visual neural network that outputs global and local learning rates for state transition, proposing a new population-like state update strategy to move current states toward the Pareto front as quickly as possible, and exploiting a point-to-plane distance model to control the size of the external archive set. The computational complexity of the evolutionary neural network mainly depends on the size of the external archive set and the number of fitness evaluations. Comparative experiments demonstrate that our network is an extremely competitive optimizer, effectively solving multiple kinds of benchmark examples. Especially, when optimizing the 8,248 parameters of a conventional convolutional neural network, our approach quickly achieves large-scale optimization.

Surrogate-Assisted Differential Evolution With Adaptive Multisubspace Search for Large-Scale Expensive Optimization

Real-world industrial engineering optimization problems often have a large number of decision variables. Most existing large-scale evolutionary algorithms need a large number of function evaluations to achieve high-quality solutions. However, the function evaluations can be computationally intensive for many of these problems, particularly, which makes large-scale expensive optimization challenging. To address this challenge, surrogate-assisted evolutionary algorithms based on the divide-and-conquer strategy have been proposed and shown to be promising. Following this line of research, we propose a surrogate-assisted differential evolution algorithm with adaptive multi-subspace search for large-scale expensive optimization to take full advantage of the population and the surrogate mechanism. The proposed algorithm constructs multi-subspace based on principal component analysis and random decision variable selection, and searches adaptively in the constructed subspaces with three search strategies. The experimental results on a set of large-scale expensive test problems have demonstrated its superiority over three state-of-the-art algorithms on the optimization problems with up to 1000 decision variables.

Multipopulation-Based Differential Evolution for Large-Scale Many-Objective Optimization.

In recent years, numerous efficient many-objective optimization evolutionary algorithms have been proposed to find well-converged and well-distributed nondominated optimal solutions. However, their scalability performance may deteriorate drastically to solve large-scale many-objective optimization problems (LSMaOPs). Encountering high-dimensional solution space with more than 100 decision variables, some of them may lose diversity and trap into local optima, while others may achieve poor convergence performance. This article proposes a multipopulation-based differential evolution algorithm, called LSMaODE, which can solve LSMaOPs efficiently and effectively. In order to exploit and explore the exponential decision space, the proposed algorithm divides the population into two groups of subpopulations, which are optimized with different strategies. First, the randomized coordinate descent technique is applied to 10% of individuals to exploit the decision variables independently. This subpopulation maintains diversity in the decision space to avoid premature convergence into local optimum. Second, the remaining 90% of individuals are optimized with the nondominated guided random interpolation strategy, which interpolates individual among three nondominated solutions randomly. The strategy can guide the population convergent toward the nondominated solutions quickly, meanwhile, maintain good distribution in objective space. Finally, the proposed LSMaODE is evaluated on the LSMOP test suites from the scalability in both decision and objective dimensions. The performance is compared against five state-of-the-art large-scale many-objective evolutionary algorithms. The experimental results show that LSMaODE provides highly competitive performance.

A Decomposition Method for Both Additively and Nonadditively Separable Problems

Problem decomposition is crucial for coping with large-scale global optimization problems, which relies heavily on highly precise variable grouping methods. The state-of-the-art decomposition methods identify separability based on the finite differences principle, which is valid only for additively separable functions but not applicable to non-additively separable functions. Therefore, we need to investigate separability in more depth in order to propose a more general principle and design more universal decomposition methods. In this paper, we conduct a comprehensive theoretical investigation on separability, the core of which is proposing an innovative separability identification principle: the minimum points shift principle. By utilizing the new principle, we develop a general separability grouping (GSG) method that can handle both additively and non-additively separable functions with high accuracy. In addition, we design a new set of benchmark functions based on non-additive separability, which compensates for the lack of non-additively separable functions in the previous test suites. Extensive experiments demonstrate that the proposed GSG achieves high grouping accuracy on both new and CEC series benchmark problems, especially on non-additively separable problems Finally, we verify that the proposed GSG can effectively improve the optimization performance of non-additively separable problems through optimization experiments.

Solving Large-Scale Routing Optimization Problems with Networks and Only Networks

Solving Large-Scale Routing Optimization Problems with Networks and Only Networks

A problem transformation-based and decomposition-based evolutionary algorithm for large-scale multiobjective optimization

For large-scale multi-objective optimization problems, the search space becomes exceptionally vast, resulting in increased complexity in the search process. The search space usually contains several local optimal individuals, and the difficulty of finding the global optimal individuals increases greatly. A problem transformation-based and decomposition-based large-scale multi-objective evolutionary algorithm is proposed to solve the problem of reducing the dimensionality of the search space and the optimization of populations. Reducing the number of optimization problems in the decision space through problem transformation has lowered the complexity of multi-objective optimization problems and enhanced computational efficiency. In the decision space, employing two direction vectors adaptively guides the generation of promising individuals, thereby preventing the population from falling into local optima. Due to the dimensionality reduction of the decision space and the optimization of the individuals in the objective space, a set of optimal solutions are effectively obtained and uniformly distributed on the approximate Pareto optimal front. Experimental results show that the algorithm is highly competitive with five large-scale multi-objective evolutionary algorithms for large-scale multi-objective optimization test problems with up to 2000 decision variables.

Parallel-in-time multiple shooting for optimal control problems governed by the Navier–Stokes equations

In the past decades, multiple shooting methods have proven to be a promising direction to speed up the optimization process, especially in the context of ODE-based optimization. Very recently, Fang et al. (Journal of Computational Physics, vol. 452, 110926, 2022) proposed a multiple shooting algorithm for large-scale PDE-constrained optimization. The current paper continues this line of work and explores the potential of multiple shooting methods for optimal control problems governed by the three-dimensional Navier–Stokes equations. Similar to Fang et al., the augmented Lagrangian (AL) method is used to solve the resulting equality-constrained optimization problem, and we employ the classical limited-memory BFGS method for the unconstrained subproblems inside the AL loop. In the current work, we exploit the multiple shooting paradigm in full by processing the shooting windows parallel-in-time, allowing for significant parallel speed-ups compared to single shooting. The proposed method is validated on a velocity tracking case, using up to 100 windows. Our analysis shows that the multiple shooting algorithm allows for considerable algorithmic and parallel speed-ups. While algorithmic speed-up depends on the exact tracking case and initialization of the shooting windows, the multiple shooting algorithm always outperforms single shooting in terms of computational time (if the number of windows is sufficiently high) due to the parallel-in-time implementation. For a given amount of resources, we also show that the proposed parallel-in-time strategy can outperform spatial parallelization alone, especially when the spatial parallelization is saturated.

A heuristic method for production scheduling of an open pit mining operation

ABSTRACT A mathematical model for production scheduling of open pit mines maximises the net present value and satisfies the reserves, pit slope angle, and production capacity constraints. A solution to this model aims to deliver an extraction sequence and the movement of materials across various stages within the operation over a defined planning horizon. However, given that the mineral reserves delineated into thousands of mining blocks form the geological input, the model falls in the category of large-scale optimisation problems, i.e. it is computationally intractable, and exact methods cannot solve realistic scenarios of the problem. Therefore, this paper contributes an alternative to the conventional mathematical model along with a corresponding heuristic method to solve this proposed model. An implementation of the proposed method at various realistic instances reveals better performance in terms of net present value, computation time and optimality gap as compared to the traditional methods.

A cooperative resilience-oriented planning framework for integrated distribution energy systems and multi-carrier energy microgrids considering energy trading

Integrated distribution systems (IDSs) and multi-carrier energy microgrids (MCEMs) can play a crucial role in enhancing distribution energy systems’ overall efficiency and flexibility. By cascading energy usage and cooperating through energy trading, IDSs and MCEMs can reduce overall system costs and provide more flexibility for system operators. Adding resilience to the planning problem of IDSs can reduce planning costs in the long term, as proactive preparedness is key to coping with high-impact rare (HR) events. Adding resilience to the planning problem of IDSs can reduce the planning costs in the long term since proactive preparedness is a key necessity to cope with high-impact rare (HR) events. This paper proposes a resilience-oriented stochastic tri-level and two-stage cooperative expansion planning of IDSs and MCEMs, considering energy trading between IDSs and MCEMs. The first stage comprises two levels; the first level minimizes the investment and operation costs of IDSs and MCEMs, while the second level desires to maximize the energy exchange profit for MCEMs and thus reduce the overall costs. The second stage includes the third level problem involving two objective functions: resilience cost minimization and resilience index (RI) maximization. The multi-objective problem in the second stage is converted into a single-objective problem using the min–max regret method. The DC and AC configurations for the power distribution system (PDS) and power microgrids (PMGs) are studied to identify the optimal configuration of these networks in the expansion planning problem. A new framework is proposed based on an aggregator-agent splitting solution using the aggregator coupling coordinator unit (ACC) responsible for coordinating IDNs and MCEMs. The studied large-scale complex optimization problem is efficiently solved computationally by introducing a combined adaptive dynamic programming (ADP) and linearized alternating direction method of multipliers with parallel splitting (LADMMPSAP) algorithm. Three cases are studied to demonstrate the effectiveness of the proposed model and method. The results depict that MCEMs help reduce expansion planning costs and improve the system’s resilience. Adding resilience to the expansion planning problem enhances the resilience of the whole system and simultaneously reduces the costs by 2.7%. The expansion planning costs for the AC and DC configuration are close, and the AC is the optimal choice in all case studies. By increasing the planning horizon from 5 to 10 years, DC will be the optimal solution since network reinforcement costs and power losses are significantly lower.