scholarly journals Two-stage multi-tasking transform framework for large-scale many-objective optimization problems

2021 ◽  
Author(s):  
Lu Chen ◽  
Handing Wang ◽  
Wenping Ma
Keyword(s):  
Large Scale ◽  
Original Problem ◽  
Optimization Problems ◽  
Reference Points ◽  
Optimization Strategy ◽  
Two Stage ◽  
Decision Space ◽  
Second Stage ◽  
Decision Variables ◽  
Objective Space

AbstractReal-world optimization applications in complex systems always contain multiple factors to be optimized, which can be formulated as multi-objective optimization problems. These problems have been solved by many evolutionary algorithms like MOEA/D, NSGA-III, and KnEA. However, when the numbers of decision variables and objectives increase, the computation costs of those mentioned algorithms will be unaffordable. To reduce such high computation cost on large-scale many-objective optimization problems, we proposed a two-stage framework. The first stage of the proposed algorithm combines with a multi-tasking optimization strategy and a bi-directional search strategy, where the original problem is reformulated as a multi-tasking optimization problem in the decision space to enhance the convergence. To improve the diversity, in the second stage, the proposed algorithm applies multi-tasking optimization to a number of sub-problems based on reference points in the objective space. In this paper, to show the effectiveness of the proposed algorithm, we test the algorithm on the DTLZ and LSMOP problems and compare it with existing algorithms, and it outperforms other compared algorithms in most cases and shows disadvantage on both convergence and diversity.

A Memetic Optimization Strategy Based on Dimension Reduction in Decision Space

2015 ◽  
Vol 23 (1) ◽  
pp. 69-100 ◽  
Author(s):  
Handing Wang ◽  
Licheng Jiao ◽  
Ronghua Shang ◽  
Shan He ◽  
Fang Liu
Keyword(s):  
Dimension Reduction ◽  
Optimization Problems ◽  
State Of The Art ◽  
Search Space ◽  
Optimization Strategy ◽  
Objective Functions ◽  
Multi Objective Optimization ◽  
Decision Space ◽  
Multi Objective ◽  
Decision Variables

There can be a complicated mapping relation between decision variables and objective functions in multi-objective optimization problems (MOPs). It is uncommon that decision variables influence objective functions equally. Decision variables act differently in different objective functions. Hence, often, the mapping relation is unbalanced, which causes some redundancy during the search in a decision space. In response to this scenario, we propose a novel memetic (multi-objective) optimization strategy based on dimension reduction in decision space (DRMOS). DRMOS firstly analyzes the mapping relation between decision variables and objective functions. Then, it reduces the dimension of the search space by dividing the decision space into several subspaces according to the obtained relation. Finally, it improves the population by the memetic local search strategies in these decision subspaces separately. Further, DRMOS has good portability to other multi-objective evolutionary algorithms (MOEAs); that is, it is easily compatible with existing MOEAs. In order to evaluate its performance, we embed DRMOS in several state of the art MOEAs to facilitate our experiments. The results show that DRMOS has the advantage in terms of convergence speed, diversity maintenance, and portability when solving MOPs with an unbalanced mapping relation between decision variables and objective functions.

A Novel Approach for Two-Stage UAV Path Planning in Pipeline Network Inspection

2020 ◽  
Author(s):  
Rui Qiu ◽  
Yongtu Liang
Keyword(s):  
Path Planning ◽  
Large Scale ◽  
Flight Path ◽  
Mixed Integer ◽  
Optimization Approach ◽  
Two Stage ◽  
Calculation Time ◽  
Pipeline Network ◽  
Second Stage ◽  
Computational Performance

Abstract Currently, unmanned aerial vehicle (UAV) provides the possibility of comprehensive coverage and multi-dimensional visualization of pipeline monitoring. Encouraged by industry policy, research on UAV path planning in pipeline network inspection has emerged. The difficulties of this issue lie in strict operational requirements, variable flight missions, as well as unified optimization for UAV deployment and real-time path planning. Meanwhile, the intricate structure and large scale of the pipeline network further complicate this issue. At present, there is still room to improve the practicality and applicability of the mathematical model and solution strategy. Aiming at this problem, this paper proposes a novel two-stage optimization approach for UAV path planning in pipeline network inspection. The first stage is conventional pre-flight planning, where the requirement for optimality is higher than calculation time. Therefore, a mixed integer linear programming (MILP) model is established and solved by the commercial solver to obtain the optimal UAV number, take-off location and detailed flight path. The second stage is re-planning during the flight, taking into account frequent pipeline accidents (e.g. leaks and cracks). In this stage, the flight path must be timely rescheduled to identify specific hazardous locations. Thus, the requirement for calculation time is higher than optimality and the genetic algorithm is used for solution to satisfy the timeliness of decision-making. Finally, the proposed method is applied to the UAV inspection of a branched oil and gas transmission pipeline network with 36 nodes and the results are analyzed in detail in terms of computational performance. In the first stage, compared to manpower inspection, the total cost and time of UAV inspection is decreased by 54% and 56% respectively. In the second stage, it takes less than 1 minute to obtain a suboptimal solution, verifying the applicability and superiority of the method.

scholarly journals A Hybrid Predictive Strategy Carried through Simultaneously from Decision Space and Objective Space for Evolutionary Dynamic Multiobjective Optimization

2019 ◽  
Vol 2019 ◽  
pp. 1-17
Author(s):  
Peng Xu ◽  
Xiaoming Wu ◽  
Man Guo ◽  
Shuai Wang ◽  
Qingya Li ◽  
...  
Keyword(s):  
Multiobjective Optimization ◽  
Optimization Problems ◽  
Ideal Point ◽  
Dynamic Environment ◽  
Decision Space ◽  
Center Point ◽  
Multiobjective Optimization Problems ◽  
Objective Space ◽  
Adaptive Diversity ◽  
Dynamic Multiobjective Optimization

There are many issues to consider when integrating 5G networks and the Internet of things to build a future smart city, such as how to schedule resources and how to reduce costs. This has a lot to do with dynamic multiobjective optimization. In order to deal with this kind of problem, it is necessary to design a good processing strategy. Evolutionary algorithm can handle this problem well. The prediction in the dynamic environment has been the very challenging work. In the previous literature, the location and distribution of PF or PS are mostly predicted by the center point. The center point generally refers to the center point of the population in the decision space. However, the center point of the decision space cannot meet the needs of various problems. In fact, there are many points with special meanings in objective space, such as ideal point and CTI. In this paper, a hybrid prediction strategy carried through from both decision space and objective space (DOPS) is proposed to handle all kinds of optimization problems. The prediction in decision space is based on the center point. And the prediction in objective space is based on CTI. In addition, for handling the problems with periodic changes, a kind of memory method is added. Finally, to compensate for the inaccuracy of the prediction in particularly complex problems, a self-adaptive diversity maintenance method is adopted. The proposed strategy was compared with other four state-of-the-art strategies on 13 classic dynamic multiobjective optimization problems (DMOPs). The experimental results show that DOPS is effective in dynamic multiobjective optimization.

scholarly journals Managing randomization in the multi-block alternating direction method of multipliers for quadratic optimization

2020 ◽  
Author(s):  
Krešimir Mihić ◽  
Mingxi Zhu ◽  
Yinyu Ye
Keyword(s):  
Quadratic Programming ◽  
Large Scale ◽  
Optimization Problems ◽  
Quadratic Optimization ◽  
Alternating Direction Method ◽  
Convex Quadratic Programming ◽  
Method Of Multipliers ◽  
Numerical Tests ◽  
Alternating Direction ◽  
Decision Variables

Abstract The Alternating Direction Method of Multipliers (ADMM) has gained a lot of attention for solving large-scale and objective-separable constrained optimization. However, the two-block variable structure of the ADMM still limits the practical computational efficiency of the method, because one big matrix factorization is needed at least once even for linear and convex quadratic programming. This drawback may be overcome by enforcing a multi-block structure of the decision variables in the original optimization problem. Unfortunately, the multi-block ADMM, with more than two blocks, is not guaranteed to be convergent. On the other hand, two positive developments have been made: first, if in each cyclic loop one randomly permutes the updating order of the multiple blocks, then the method converges in expectation for solving any system of linear equations with any number of blocks. Secondly, such a randomly permuted ADMM also works for equality-constrained convex quadratic programming even when the objective function is not separable. The goal of this paper is twofold. First, we add more randomness into the ADMM by developing a randomly assembled cyclic ADMM (RAC-ADMM) where the decision variables in each block are randomly assembled. We discuss the theoretical properties of RAC-ADMM and show when random assembling helps and when it hurts, and develop a criterion to guarantee that it converges almost surely. Secondly, using the theoretical guidance on RAC-ADMM, we conduct multiple numerical tests on solving both randomly generated and large-scale benchmark quadratic optimization problems, which include continuous, and binary graph-partition and quadratic assignment, and selected machine learning problems. Our numerical tests show that the RAC-ADMM, with a variable-grouping strategy, could significantly improve the computation efficiency on solving most quadratic optimization problems.

A two-stage approach for assessment of distributional impacts in model-based delta planning: exploration of plausible inequality patterns and justice-based evaluation of policies

2020 ◽  
Author(s):  
Bramka Arga Jafino ◽  
Jan Kwakkel
Keyword(s):  
Large Scale ◽  
Mekong Delta ◽  
Adaptation Planning ◽  
Small Scale ◽  
Two Stage ◽  
Second Stage ◽  
Adaptation Policies ◽  
Small Scale Farmers ◽  
New Policies ◽  
Distributional Impacts

<p>Climate-related inequality can arise from the implementation of adaptation policies. As an example, the dike expansion policy for protecting rice farmers in the Vietnam Mekong Delta in the long run backfires to the small-scale farmers. The prevention of annual flooding reduces the supply of natural sediments, forcing farmers to apply more and more fertilizers to achieve the same yield. While large-scale farmers can afford this, small-scale farmers do not possess the required economics of scale and are thus harmed eventually. Together with climatic and socioeconomic uncertainties, the implementation of new policies can not only exacerbate existing inequalities, but also induce new inequalities. Hence, distributional impacts to affected stakeholders should be assessed in climate change adaptation planning.</p><p>In this study, we propose a two-stage approach to assess the distributional impacts of policies in model-based support for adaptation planning. The first stage is intended to explore potential inequality patterns that may emerge due to combination of new policies and the realization of exogenous scenarios. This stage comprises four steps: (i) disaggregation of performance indicators in the model in order to observe distributional impacts, (ii) performance of large-scale simulation experimentation to account for deep uncertainties, (iii) clustering of simulation results to identify distinctive inequality patterns, and (iv) application of scenario discovery tools, in particular classification and regression trees, to identify combinations of policies and uncertainties that lead to a specific inequality pattern.</p><p>In the second stage we attempt to asses which policies are morally preferable with respect to the inequality patterns they generate, rather than only descriptively explore the patterns which is the case in the previous stage. To perform a normative evaluation of the distributional impacts, we operationalize five alternative principles of justice: improvement of total welfare (utilitarianism), prioritization of worse-off actors (prioritarianism), reduction of welfare differences across actors (two derivations: absolute inequality and envy measure), and improvement of worst-off actor (Rawlsian difference). The different operationalization of each of these principles forms the so-called social welfare function with which the distributional impacts can be aggregated.</p><p>To test this approach, we use an agricultural planning case study in the upper Vietnam Mekong Delta. Specifically, we assess the distributional impacts of alternative adaptation policies in the upper Vietnam Mekong Delta by using an integrated assessment model. We consider six alternative policies as well as uncertainties related to upstream discharge, sediment supply, and land-use change. Through the first stage, we identify six potential inequality patterns among the 23 districts in the study area, as well as the combinations of policies and uncertainties that result in these types of patterns. From applying the second stage we obtain complete rankings of alternative policies, based on their performance with respect to distributional impacts, under different realizations of scenarios. The explorative stage allows policy-makers to identify potential actions to compensate worse-off actors while the normative stage helps them to easily rank alternative policies based on a preferred moral principle.</p>

scholarly journals A Two-Stage PV Accommodation Optimization in Jinzhai County, Anhui Province with Hydropower as Stand-By Unit

2021 ◽  
Vol 252 ◽  
pp. 01017
Author(s):  
Tianyi Liu ◽  
Hai Bao
Keyword(s):  
Renewable Energy ◽  
Poverty Alleviation ◽  
Power Loss ◽  
Thermal Power ◽  
Anhui Province ◽  
Reserve Capacity ◽  
Optimization Strategy ◽  
Two Stage ◽  
Second Stage ◽  
Grid Operation

In respond to the national “Photovoltaic Poverty Alleviation” and renewable energy accommodation policy, this paper proposes a two-stage PV accommodation optimization strategy based on improved PSO, PV forecast, and hydropower dispatch to tackle with the instability caused by distributed PV, since Jinzhai County, Anhui Province has both sufficient hydropower and photovoltaic. In the first stage, the hydropower reserve capacity of each period of the next day is optimized according to the PV forecast. In the second stage, real-time online optimization is carried out using the operation data to determine the amount of power generated by each PV source during each period. Finally, the optimization strategy is verified by simulations using grid operation data in Jinzhai, and the comparison is made with the thermal power standby unit. The results show that the hydropower units which has higher climbing rate can immensely increase the photovoltaic consumption, reduce the power loss and enhance the voltage stability of the network.

Evolutionary Large-Scale Multi-Objective Optimization: A Survey

2022 ◽  
Vol 54 (8) ◽  
pp. 1-34
Author(s):  
Ye Tian ◽  
Langchun Si ◽  
Xingyi Zhang ◽  
Ran Cheng ◽  
Cheng He ◽  
...  
Keyword(s):  
Large Scale ◽  
Optimization Problems ◽  
Benchmark Problems ◽  
Future Research ◽  
Decision Variable ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Space Reduction ◽  
Decision Variables ◽  
Comprehensive 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.

scholarly journals Two-stage sector sampling for estimating small woodlot attributes

2011 ◽  
Vol 41 (9) ◽  
pp. 1819-1826 ◽  
Author(s):  
Piermaria Corona ◽  
Lorenzo Fattorini ◽  
Sara Franceschi
Keyword(s):  
Large Scale ◽  
Sampling Strategy ◽  
Sampling Variance ◽  
Sampling Strategies ◽  
Fixed Size ◽  
Two Stage ◽  
Sampling Schemes ◽  
Second Stage ◽  
Forest Inventories ◽  
Plot Sampling

A two-stage sampling strategy is proposed to assess small woodlots outside the forests scattered on extensive territories. The first stage is performed to select a sample of small woodlots using fixed-size sampling schemes, and the second stage is performed to sample trees within woodlots selected at first stage. Usually, fixed- or variable-area plots are adopted to sample trees. However, the use of plot sampling in small patches such as woodlots is likely to induce a relevant amount of bias owing to edge effects. In this framework, sector sampling proves to be particularly effective. The present paper investigates the statistical properties of two-stage sampling strategies for estimating forest attributes of woodlot populations when sector sampling is adopted at the second stage. A two-stage estimator of population totals is derived together with a conservative estimator of its sampling variance. By means of a simulation study, the performance of the proposed estimator is checked and compared with that achieved using traditional plot sampling with edge corrections. Simulation results prove the adequacy of sector sampling and provide some guidelines for the effective planning of the strategy. In some countries, the proposed strategy can be performed with few modifications within the framework of large-scale forest inventories.

scholarly journals An Efficient Two-Stage Sparse Representation Method

2015 ◽  
Vol 30 (01) ◽  
pp. 1651001 ◽  
Author(s):  
Chengyu Peng ◽  
Hong Cheng ◽  
Manchor Ko
Keyword(s):  
Sparse Representation ◽  
Large Scale ◽  
Optimization Problem ◽  
Two Stage ◽  
Linear Inverse Problems ◽  
Second Stage ◽  
Concrete Realization ◽  
Representation Method ◽  
Scale Optimization ◽  
Very High

There are a large number of methods for solving under-determined linear inverse problems. For large-scale optimization problem, many of them have very high time complexity. We propose a new method called two-stage sparse representation (TSSR) to tackle it. We decompose the representing space of signals into two parts”, the measurement dictionary and the sparsifying basis. The dictionary is designed to obey or nearly obey the sub-Gaussian distribution. The signals are then encoded on the dictionary to obtain the training and testing coefficients individually in the first stage. Then, we design the basis based on the training coefficients to approach an identity matrix, and we apply sparse coding to the testing coefficients over the basis in the second stage. We verify that the projection of testing coefficients onto the basis is a good approximation of the original signals onto the representing space. Since the projection is conducted on a much sparser space, the runtime is greatly reduced. For concrete realization, we provide an instance for the proposed TSSR. Experiments on four biometric databases show that TSSR is effective compared to several classical methods for solving linear inverse problem.

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