Many practical multiobjectiveoptimization problems have a nested bilevel structure in variables, which can be modeled as bilevel multiobjective optimization problems (BLMOPs). In this article, a cooperative coevoluti...
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Many practical multiobjectiveoptimization problems have a nested bilevel structure in variables, which can be modeled as bilevel multiobjective optimization problems (BLMOPs). In this article, a cooperative coevolution (CC) with knowledge-based variable decomposition, called bilevelmultiobjective CC (BLMOCC), is proposed for BLMOPs. In BLMOCC, the variable interactions are represented by an interaction matrix. The perturbation-based variable decomposition combined with the matrix completion approach has been designed for dynamically discovering the correlation among the bilevel variables, based on which the variables are divided into different groups. To further handle possible weak correlations among various groups of variables, a CC has been adopted for optimizing them in a collaborative way. In experimental studies, BLMOCC is compared with a nested method (NS) and a state-of-the-art algorithm (H-BLEMO) on a set of benchmark problems. The effects of each component in BLMOCC have also been verified by comparing it with its three variants. The experimental results demonstrate that BLMOCC has the best performance among all the compared algorithms. In addition, BLMOCC has also been applied to a real-world management decision-making problem, which further validates its efficiency and effectiveness.
An efficient solution strategy is proposed for bilevel multiobjective optimization problem (BLMOP) with multiple objectives at both levels when multiobjectiveoptimization problem (MOP) at the lower level satisfies th...
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An efficient solution strategy is proposed for bilevel multiobjective optimization problem (BLMOP) with multiple objectives at both levels when multiobjectiveoptimization problem (MOP) at the lower level satisfies the convexity and differentiability for the lower-level decision variables. In the proposed strategy, the MOP at the lower level is first converted into a single-objective optimization formulation through adopting adaptive weighted sum scalarization, in which the lower-level weight vector is adjusted adaptively while the iteration progressing. The Karush-Kuhn-Tucker optimality conditions are used to the lower-level single-objective scalarization problem, thus the original BLMOP can be converted into a single-level MOP with complementarity constraints. Then an effective smoothing technique is suggested to cope with the complementarity constraints. In such a way, the BLMOP is finally formalized as a single-level constrained nonlinear MOP. A decomposition-based constrained multiobjective differential evolution is developed to solve this transformed MOP and some instances are tested to illustrate the feasibility and effectiveness of the solution methodology. The experimental results show that the proposed solution method possesses favorite convergence and diversity.
Many practical optimization problems in the fields of transportation, business, engineering, environmental economics, etc., involve more than one level of decision making and can be modeled as a bileveloptimization p...
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Many practical optimization problems in the fields of transportation, business, engineering, environmental economics, etc., involve more than one level of decision making and can be modeled as a bileveloptimization problem with a nested structure of decision variables. Existing studies have made remarkable progress on bilevel single-objective problems. However, due to the increased complexities in terms of computation and decision making, few efforts have been devoted to bilevel multiobjective optimization problems (BLMOPs). This article proposes an evolutionary multiform optimization paradigm that explores alternative formulations of the target task to assist in the search with the original formulation, namely, BLMFO, for bilevel multiobjective optimization. First, in the proposed framework, alternative formulations of the original problem are derived to facilitate the problem solving and also alleviate computational overheads. Then, BLMFO performs the evolutionary search in the original problem space and the auxiliary task space simultaneously to combine searching for feasible solutions and exploring regions of promising solutions, thus ensuring the effectiveness of the proposed framework. Further, useful information is transferred across the original and auxiliary tasks via explicit knowledge transfer to enable complementary exploration for better optimization performance. To the best of our knowledge, this work serves as the first attempt to solve BLMOPs via multiform evolutionary optimization in the literature. The framework is verified using four instantiation groups with different underlying baseline solvers on various benchmarks and practical problems. The experimental results show the effectiveness and superiority of the proposed framework in terms of performance indicators and the quality of final optimized solutions.
Nanoscale crossbar architectures have received steadily growing interests as a result of their great potential to be main building blocks in nanoelectronic circuits. However, due to the extremely small size of nanodev...
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Nanoscale crossbar architectures have received steadily growing interests as a result of their great potential to be main building blocks in nanoelectronic circuits. However, due to the extremely small size of nanodevices and the bottom-up self-assembly nanofabrication process, considerable process variation will be an inherent vice for crossbar nanoarchitectures. In this paper, the variation tolerant logical mapping problem is treated as a bilevel multiobjective optimization problem. Since variation mapping is an NP-complete problem, a hybrid multiobjective evolutionary algorithm is designed to solve the problem adhering to a bileveloptimization framework. The lower level optimization problem, most frequently tackled, is modeled as the min-max-weight and min-weight-gap bipartite matching (MMBM) problem, and a Hungarian-based linear programming (HLP) method is proposed to solve MMBM in polynomial time. The upper level optimization problem is solved by evolutionary multiobjectiveoptimization algorithms, where a greedy reassignment local search operator, capable of exploiting the domain knowledge and information from problem instances, is introduced to improve the efficiency of the algorithm. The numerical experiment results show the effectiveness and efficiency of proposed techniques for the variation tolerant logical mapping problem. (C) 2015 Elsevier B.V. All rights reserved.
This study evaluates the tradeoff between agricultural production and water quality at both the watershed scale and the farm scale, using an integrated economic-biophysical hybrid genetic algorithm. We apply a multi-i...
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This study evaluates the tradeoff between agricultural production and water quality at both the watershed scale and the farm scale, using an integrated economic-biophysical hybrid genetic algorithm. We apply a multi-input, multi-output profit maximization model to detailed farm-level production data from the Oregon Willamette Valley to predict each producer's response to a targeted fertilizer tax policy. Their resulting production decisions are included in a biophysical model of basin-level soil and water quality. Building on a general regulation problem for nonpoint pollution, we use a hybrid genetic algorithm to integrate the economic and biophysical models into one bilevel multiobjective optimization problem, the joint maximization of farm profits and minimization of Nitrate runoff resulting from fertilizer usage. This approach allows us to more fully endogenize fertilizer reduction cost, rather than assume an average cost relationship. The solution set of tax rates generates the Pareto optimal frontier at the watershed level. We then measure the tradeoffs between maximum profit and Nitrogen loading for individual farms, subject to the solution fertilizer tax policy. We find considerable variation in tradeoff values across the basin, which could be used to target incentives for reducing Nitrogen loading to agricultural producers under non-uniform control strategies. (C) 2015 Elsevier B.V. All rights reserved.
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