Large-scale Multi-objective Optimization Research Articles

Optimization of Water-Alternating-CO2 Injection Field Operations Using a Machine-Learning-Assisted Workflow

Summary This paper will present a robust workflow to address multiobjective optimization (MOO) of carbon dioxide (CO2)-enhanced oil recovery (EOR)-sequestration projects with a large number of operational control parameters. Farnsworth unit (FWU) field, a mature oil reservoir undergoing CO2 alternating water injection (CO2-WAG) EOR, will be used as a field case to validate the proposed optimization protocol. The expected outcome of this work would be a repository of Pareto-optimal solutions of multiple objective functions, including oil recovery, carbon storage volume, and project economics. FWU’s numerical model is used to demonstrate the proposed optimization workflow. Because using MOO requires computationally intensive procedures, machine-learning-based proxies are introduced to substitute for the high-fidelity model, thus reducing the total computation overhead. The vector machine regression combined with the Gaussian kernel (Gaussian-SVR) is used to construct proxies. An iterative self-adjusting process prepares the training knowledge base to develop robust proxies and minimizes computational time. The proxies’ hyperparameters will be optimally designed using Bayesian optimization to achieve better generalization performance. Trained proxies will be coupled with multiobjective particle swarm Optimization (MOPSO) protocol to construct the Pareto-front solution repository. The outcomes of this workflow will be a repository containing Pareto-optimal solutions of multiple objectives considered in the CO2-WAG project. The proposed optimization workflow will be compared with another established methodology using a multilayer neural network (MLNN) to validate its feasibility in handling MOO with a large number of parameters to control. Optimization parameters used include operational variables that might be used to control the CO2-WAG process, such as the duration of the water/gas injection period, producer bottomhole pressure (BHP) control, and water injection rate of each well included in the numerical model. It is proved that the workflow coupling Gaussian-SVR proxies and the iterative self-adjusting protocol is more computationally efficient. The MOO process is made more rapid by squeezing the size of the required training knowledge base while maintaining the high accuracy of the optimized results. The outcomes of the optimization study show promising results in successfully establishing the solution repository considering multiple objective functions. Results are also verified by validating the Pareto fronts with simulation results using obtained optimized control parameters. The outcome from this work could provide field operators an opportunity to design a CO2-WAG project using as many inputs as possible from the reservoir models. The proposed work introduces a novel concept that couples Gaussian-SVR proxies with a self-adjusting protocol to increase the computational efficiency of the proposed workflow and to guarantee the high accuracy of the obtained optimized results. More importantly, the workflow can optimize a large number of control parameters used in a complex CO2-WAG process, which greatly extends its utility in solving large-scale MOO problems in various projects with similar desired outcomes.

Research on improved artificial bee colony algorithm based on large-scale multi-objective group combination optimization

Large power system contains many generating units, and many factors need to be considered during operation. The unit combination optimization is a nonlinear large-scale optimization problem with multi-objective and multi-constraints, and the existing methods have many shortcomings. Artificial bee colony algorithm has good performance in solving nonlinear optimization problems, but it has some disadvantages such as low optimization efficiency and local extremum. To solve these problems, an improved artificial bee colony algorithm is proposed. The algorithm introduces variable field of vision, adjusts the initial solution and selection strategy, and combines with mutation operation in genetic algorithm. A multi - objective optimization model considering economy and environmental protection is constructed. In order to solve the problem that the calculation time is too long due to the expansion of the unit scale, a phased optimization method is adopted, and the improved algorithm is applied to the start-stop scheduling stage. After determining the start-stop state of the unit, the mixed integer programming method is used for load distribution. For unit contains up to 1000 units of large power grid optimization examples are simulated experiment, the experimental results show that the improved optimization algorithm convergence and global search ability is improved, greatly reduces the computation time of the mass unit combination, multiple objective conditions have also made the ideal results, verify the effectiveness of the proposed method.

A Robust Translational Motion Compensation Method Based on Weighted Optimization Framework—Second-Order Drift Particle Swarm Optimization

Accurate translational motion compensation is critical for ISAR imaging, especially for datasets with low signal-to-noise ratio (SNR) or sparse aperture. Among the existing translational motion compensation methods, the methods that based on the polynomial model have profound noise robustness but are easily affected by the variation of the reference distance. The methods that based on the range profile alignment have good versatility but are far from ideal under low SNR and sparse aperture environment. Therefore, we propose a novel and robust translational motion compensation method to overcome the shortcoming of the existing methods. Specifically, we estimate the translational phase error sequence by maximizing Laplacian average gray level and peak value. It can improve the robustness of translational motion compensation for noise and sparse aperture. Since such principle creates a large-scale multi-objective optimization problem, we design weighted optimization framework - second-order drift particle swarm optimization (WOF - SDPSO) to solve it accurately. WOF-SDPSO achieves full exploration of high-dimensional variable space by variable dimension reducing, random drift update, and second-order oscillation convergence. These ensure the global optimal solution easier to be found. Experimental results of the measured dataset prove that the proposed method is effective and accurate under the conditions of low SNR and sparse aperture. Moreover, the proposed method is noise robust for polynomial translational motion model with sparse aperture.

Adaptive Weighted Optimization Framework for Multiobjective Long-Term Planning of Concentrate Ingredients in Copper Industry

The multi-objective long-term concentrate ingredients planning (MLCIP) plays an important role in modern smelting production measurement systems. MLCIP is a constrained multi-objective optimization problem which comprises a series of continuous ingredient stages and with numerous decision variables under dynamic environments. The existing on-site ingredient planning methods primarily focus on satisfying short-term production constraints, while neglecting the resulting global impact on long-term objectives. Consequently, the overall duration of ingredient lists and the interest arising from concentrate hoarding cannot be estimated manually. Thus, we formulated MLCIP into a multistage constrained large-scale multiobjective optimization problem, where the multiple objectives and constraints are formulated by the safety production rules from the smelting system. Furthermore, an adaptive weighted optimization framework (AWOF) is constructed to reduce the dimensions of searching space in grouping strategy while adaptively determining the termination of weight optimization process. Specifically, a two-stage stochastic coding simulation method is proposed for the handling of dynamic constraints of the MLICP. Extensive experiments on various benchmark problems and the MLCIP of actual inventory concentration data acquired from a copper industry were comprehensively used to validate the effectiveness of the designed AWOF.

Evolutionary Algorithm with Tri-Population Based Reproduction Strategy for Large-Scale Multi-Objective Optimization

Evolutionary Algorithm with Tri-Population Based Reproduction Strategy for Large-Scale Multi-Objective Optimization

A Reference Point Selection and Direction Guidance-Based Algorithm for Large-Scale Multi-Objective Optimization

Designing efficient algorithms for the large-scale multi-objective problems (LSMOPs) is a very challenging problem currently. To tackle LSMOPs, we first design a new reference points selection strategy to enhance the diversity of algorithms and avoid the algorithm falling into local minima. The strategy selects not only a part of nondominated solutions with the largest crowding distance, but also a part of relatively uniformly distributed solutions as the reference points. In this way, much better diversity and convergence can be obtained. Second, we propose a direction-guided offspring generation strategy, where a type of potential directions is designed to generate the promising solutions which can balance the convergence and diversity of the obtained solutions and improve the effectiveness of the algorithm significantly. Based on the two proposed strategies, we propose a new effective algorithm for LSMOPs. Numerical experiments are executed on two widely used large-scale multi-objective benchmark problem sets with 200, 500 and 1000 decision variables and a comparison with five state-of-the-art algorithms is made. The experimental results show that our proposed algorithm is effective and can obtain significantly better solutions than the compared algorithms.

Improved SparseEA for sparse large-scale multi-objective optimization problems

Sparse large-scale multi-objective optimization problems (LSMOPs) widely exist in real-world applications, which have the properties of involving a large number of decision variables and sparse Pareto optimal solutions, i.e., most decision variables of these solutions are zero. In recent years, sparse LSMOPs have attracted increasing attentions in the evolutionary computation community. However, all the recently tailored algorithms for sparse LSMOPs put the sparsity detection and maintenance in the first place, where the nonzero variables can hardly be optimized sufficiently within a limited budget of function evaluations. To address this issue, this paper proposes to enhance the connection between real variables and binary variables within the two-layer encoding scheme with the assistance of variable grouping techniques. In this way, more efforts can be devoted to the real part of nonzero variables, achieving the balance between sparsity maintenance and variable optimization. According to the experimental results on eight benchmark problems and three real-world applications, the proposed algorithm is superior over existing state-of-the-art evolutionary algorithms for sparse LSMOPs.

Evolutionary Large-Scale Multi-Objective Optimization: A Survey

Multi-objective evolutionary algorithms (MOEAs) have shown promising performance in solving various optimization problems, but their performance may deteriorate drastically when tackling problems containing a large number of decision variables. In recent years, much effort been devoted to addressing the challenges brought by large-scale multi-objective optimization problems. This article presents a comprehensive survey of stat-of-the-art MOEAs for solving large-scale multi-objective optimization problems. We start with a categorization of these MOEAs into decision variable grouping based, decision space reduction based, and novel search strategy based MOEAs, discussing their strengths and weaknesses. Then, we review the benchmark problems for performance assessment and a few important and emerging applications of MOEAs for large-scale multi-objective optimization. Last, we discuss some remaining challenges and future research directions of evolutionary large-scale multi-objective optimization.

Crashworthiness design and optimization of nested structures with a circumferentially corrugated circular outer wall and inner ribs

Twenty-six nested structures with a circumferentially corrugated circular outer wall and inner ribs are investigated under quasi-static axial compression using the finite element method. The finite element model is validated by literature. Also, theoretical predictions for the nested structures are derived and compared with finite element analyses. Among the structures whose crashworthiness performances are examined, CO1D and CSIN2D are selected as the best ones. The comparisons have shown that the ribs attached to the closest points of the corrugated outer wall provide stable collapse modes and better crash performance. Also, the crashworthiness performance of the nested structures with octagon inner structures is higher than other alternative structures because the number of corner members and the cross-section lengths are more efficient. Finally, the objective functions developed by the surrogate modeling method are optimized by non-dominated sorting genetic algorithm II (NSGA-II), multi-objective particle swarm optimization (MOPSO), paired offspring generation for constrained large-scale multiobjective optimization (POCEA) and an evolutionary algorithm for large-scale many-objective optimization (LMEA). Optimum CO1D and CSIN2D designs obtained by the NSGAII method have 37.00% and 26.68% higher SEA values, respectively than ‘Cribs’ structure at the same PCF value.

Large-Scale Evolutionary Multiobjective Optimization Assisted by Directed Sampling

It is particularly challenging for evolutionary algorithms to quickly converge to the Pareto front in large-scale multiobjective optimization. To tackle this problem, this article proposes a large-scale multiobjective evolutionary algorithm assisted by some selected individuals generated by directed sampling (DS). At each generation, a set of individuals closer to the ideal point is chosen for performing a DS in the decision space, and those nondominated ones of the sampled solutions are used to assist the reproduction to improve the convergence in evolutionary large-scale multiobjective optimization. In addition, elitist nondominated sorting is adopted complementarily for environmental selection with a reference vector-based method in order to maintain diversity of the population. Our experimental results show that the proposed algorithm is highly competitive on large-scale multiobjective optimization test problems with up to 5000 decision variables compared to five state-of-the-art multiobjective evolutionary algorithms.

A multi-objective scheduling method for operational coordination time using improved triangular fuzzy number representation.

In modern warfare, the comprehensiveness of combat domain and the complexity of tasks pose great challenges to operational coordination.To address this challenge, we use the improved triangular fuzzy number to express the combat mission time, first present a new multi-objective operational cooperative time scheduling model that takes the fluctuation of combat coordinative time and the time flexibility between each task into account. The resulting model is essentially a large-scale multi-objective combinatorial optimization problem, intractably complicated to solve optimally. We next propose multi-objective improved Bat algorithm based on angle decomposition (MOIBA/AD) to quickly identify high-quality solutions to the model. Our proposed algorithm improves the decomposition strategy by replacing the planar space with the angle space, which helps greatly reduce the difficulty of processing evolutionary individuals and hence the time complexity of the multi-objective evolutionary algorithm based on decomposition (MOEA/D). Moreover, the population replacement strategy is enhanced utilizing the improved bat algorithm, which helps evolutionary individuals avoid getting trapped in local optima. Computational experiments on multi-objective operational cooperative time scheduling (MOOCTS) problems of different scales demonstrate the superiority of our proposed method over four state-of-the-art multi-objective evolutionary algorithms (MOEAs), including multi-objective bat Algorithm (MOBA), MOEA/D, non-dominated sorting genetic algorithm version II (NSGA-II) and multi-objective particle swarm optimization algorithm (MOPSO). Our proposed method performs better in terms of four performance criteria, producing solutions of higher quality while keeping a better distribution of the Pareto solution set.

Solving Large-Scale Multiobjective Optimization Problems With Sparse Optimal Solutions via Unsupervised Neural Networks.

Due to the curse of dimensionality of search space, it is extremely difficult for evolutionary algorithms to approximate the optimal solutions of large-scale multiobjective optimization problems (LMOPs) by using a limited budget of evaluations. If the Pareto-optimal subspace is approximated during the evolutionary process, the search space can be reduced and the difficulty encountered by evolutionary algorithms can be highly alleviated. Following the above idea, this article proposes an evolutionary algorithm to solve sparse LMOPs by learning the Pareto-optimal subspace. The proposed algorithm uses two unsupervised neural networks, a restricted Boltzmann machine, and a denoising autoencoder to learn a sparse distribution and a compact representation of the decision variables, where the combination of the learnt sparse distribution and compact representation is regarded as an approximation of the Pareto-optimal subspace. The genetic operators are conducted in the learnt subspace, and the resultant offspring solutions then can be mapped back to the original search space by the two neural networks. According to the experimental results on eight benchmark problems and eight real-world problems, the proposed algorithm can effectively solve sparse LMOPs with 10000 decision variables by only 100000 evaluations.

A comparative study of many-objective optimizers on large-scale many-objective software clustering problems

Over the past 2 decades, several multi-objective optimizers (MOOs) have been proposed to address the different aspects of multi-objective optimization problems (MOPs). Unfortunately, it has been observed that many of MOOs experiences performance degradation when applied over MOPs having a large number of decision variables and objective functions. Specially, the performance of MOOs rapidly decreases when the number of decision variables and objective functions increases by more than a hundred and three, respectively. To address the challenges caused by such special case of MOPs, some large-scale multi-objective optimization optimizers (L-MuOOs) and large-scale many-objective optimization optimizers (L-MaOOs) have been developed in the literature. Even after vast development in the direction of L-MuOOs and L-MaOOs, the supremacy of these optimizers has not been tested on real-world optimization problems containing a large number of decision variables and objectives such as large-scale many-objective software clustering problems (L-MaSCPs). In this study, the performance of nine L-MuOOs and L-MaOOs (i.e., S3-CMA-ES, LMOSCO, LSMOF, LMEA, IDMOPSO, ADC-MaOO, NSGA-III, H-RVEA, and DREA) is evaluated and compared over five L-MaSCPs in terms of IGD, Hypervolume, and MQ metrics. The experimentation results show that the S3-CMA-ES and LMOSCO perform better compared to the LSMOF, LMEA, IDMOPSO, ADC-MaOO, NSGA-III, H-RVEA, and DREA in most of the cases. The LSMOF, LMEA, IDMOPSO, ADC-MaOO, NSGA-III, and DREA, are the average performer, and H-RVEA is the worst performer.

An Adaptive Localized Decision Variable Analysis Approach to Large-Scale Multiobjective and Many-Objective Optimization.

This article proposes an adaptive localized decision variable analysis approach under the decomposition-based framework to solve the large-scale multiobjective and many-objective optimization problems (MaOPs). Its main idea is to incorporate the guidance of reference vectors into the control variable analysis and optimize the decision variables using an adaptive strategy. Especially, in the control variable analysis, for each search direction, the convergence relevance degree of each decision variable is measured by a projection-based detection method. In the decision variable optimization, the grouped decision variables are optimized with an adaptive scalarization strategy, which is able to adaptively balance the convergence and diversity of the solutions in the objective space. The proposed algorithm is evaluated with a suite of test problems with 2-10 objectives and 200-1000 variables. Experimental results validate the effectiveness and efficiency of the proposed algorithm on the large-scale multiobjective and MaOPs.

Paired Offspring Generation for Constrained Large-Scale Multiobjective Optimization

Constrained multiobjective optimization problems (CMOPs) widely exist in real-world applications, and they are challenging for conventional evolutionary algorithms (EAs) due to the existence of multiple constraints and objectives. When the number of objectives or decision variables is scaled up in CMOPs, the performance of EAs may degenerate dramatically and may fail to obtain any feasible solutions. To address this issue, we propose a paired offspring generation-based multiobjective EA for constrained large-scale optimization. The general idea is to emphasize the role of offspring generation in reproducing some promising feasible or useful infeasible offspring solutions. We first adopt a small set of reference vectors for constructing several subpopulations with a fixed number of neighborhood solutions. Then, a pairing strategy is adopted to determine some pairwise parent solutions for offspring generation. Consequently, the pairwise parent solutions, which could be infeasible, may guide the generation of well-converged solutions to cross the infeasible region(s) effectively. The proposed algorithm is evaluated on CMOPs with up to 1000 decision variables and ten objectives. Moreover, each component in the proposed algorithm is examined in terms of its effect on the overall algorithmic performance. Experimental results on a variety of existing and our tailored test problems demonstrate the effectiveness of the proposed algorithm in constrained large-scale multiobjective optimization.

Cooperative multiobjective optimization with bounds on objective functions

When solving large-scale multiobjective optimization problems, solvers can get stuck because of memory and/or time limitations. In such cases, one is left with no information on the distance to the best feasible solution, found before the optimization process has stopped, to the true Pareto optimal solution. In this work, we show how to provide such information. To this aim we make use of the concept of lower shells and upper shells, developed in our earlier works. No specific assumptions about the problems to be solved are made. We illustrate the proposed approach on biobjective multidimensional knapsack problems derived from single-objective multidimensional knapsack problems in the Beasley OR Library. We address cases when a top-class commercial mixed-integer linear solver fails to provide Pareto optimal solutions attempted to be derived by scalarization.

A SATELLITE IMAGING MISSION PLANNING METHOD FOR FAST ANTARCTICA COVERAGE

Abstract. Global warming has become one of the most prominent global issues, and Antarctic ice sheet is one of the indicator of global climate change. Satellite imagery has become an important means of monitoring the changes in Antarctic ice sheet. Due to the high overlap of satellite imaging swaths, the existing Antarctica images have the disadvantages of long period of imagery acquisition, large temporal difference among the mosaic images, and low utilization of satellite resource. This paper proposes a satellite imaging mission planning method for fast Antarctica coverage. First, the imaging time window is forecasted within the specified imaging time range to obtain all the visible time windows of the imaging satellite to Antarctica. Then, taking the selection of each time window and the satellite swing angle in each time window as decision variables, and the satellite attitude maneuver ability as constraint, an imaging mission model including two objective functions with minimum number of imaging time windows and the maximum coverage rate is established. To solving the proposed multi-objective optimization model, an improved real-binary hybrid LMOCSO (large-scale multi-objective optimization based on a competitive swarm optimizer) is proposed in this paper. Finally, a simulation experiment was performed using Gaofen-3 satellite to verify the effectiveness of the proposed method.

Adaptive Offspring Generation for Evolutionary Large-Scale Multiobjective Optimization

Offspring generation plays an important role in evolutionary multiobjective optimization. However, generating promising candidate solutions effectively in high-dimensional spaces is particularly challenging. To address this issue, we propose an adaptive offspring generation method for large-scale multiobjective optimization. First, a preselection strategy is proposed to select a balanced parent population, and then these parent solutions are used to construct direction vectors in the decision spaces for reproducing promising offspring solutions. Specifically, two kinds of direction vectors are adaptively used to generate offspring solutions. The first kind takes advantage of the dominated solutions to generate offspring solutions toward the Pareto optimal set (PS) for convergence enhancement, while the other kind uses those nondominated solutions to spread the solutions over the PS for diversity maintenance. The proposed offspring generation method can be embedded in many existing multiobjective evolutionary algorithms (EAs) for large-scale multiobjective optimization. Experiments are conducted to reveal the mechanism of our proposed adaptive reproduction strategy and validate its effectiveness. Experimental results on some large-scale multiobjective optimization problems have demonstrated the competitive performance of our proposed algorithm in comparison with five state-of-the-art large-scale EAs.

Random Matrix Generators for Optimizing a Fuzzy Biofuel Supply Chain System

Complex industrial systems often contain various uncertainties. Hence sophisticated fuzzy optimization (metaheuristics) techniques have become commonplace; and are currently indispensable for effective design, maintenance and operations of such systems. Unfortunately, such state-of-the-art techniques suffer several drawbacks when applied to largescale problems. In line of improving the performance of metaheuristics in those, this work proposes the fuzzy random matrix theory (RMT) as an add-on to the cuckoo search (CS) technique for solving the fuzzy large-scale multiobjective (MO) optimization problem; biofuel supply chain. The fuzzy biofuel supply chain problem accounts for uncertainties resulting from fluctuations in the annual electricity generation output of the biomass power plant [kWh/year]. The details of these investigations are presented and analyzed.This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium provided the original work is properly cited.

A random dynamic grouping based weight optimization framework for large-scale multi-objective optimization problems

Abstract For large-scale multi-objective problems (LSMOPs), it is necessary to get a good grouping strategy or another way to reduce dimensions because of “the curse of dimensions”. In this paper, a weighted optimization framework with random dynamic grouping is proposed for large-scale problems. A weight optimization framework utilizes a problem transformation scheme in which weights are chosen to be optimized instead of the decision variables in order to reduce the dimensionality of the search space. Random dynamic grouping is used to determine sizes of each group adaptively. And multi-objective particle swarm optimization with multiple search strategies (MMOPSO) is employed as an optimizer for both original variables and weight variables. The proposed algorithm is performed on 28 benchmark test problems with 1000 dimensions, and the experimental results show that it can get better performance than some the-state-of-art algorithms in fewer function evaluations. In addition, it can be extended to solve LSMOPs with 5000 dimensions.