A sparse optimization approach to supervised NMF based on convex analytic method

2013 ◽  
Author(s):  
Yu Morikawa ◽  
Masahiro Yukawa
Keyword(s):  
Sparse Optimization ◽  
Analytic Method ◽  
Optimization Approach

scholarly journals A Sparse Optimization Approach for Energy-Efficient Timetabling in Metro Railway Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-19 ◽  
Author(s):  
Ziyan Luo ◽  
Xiaoyu Li ◽  
Naihua Xiu
Keyword(s):  
Optimization Model ◽  
Energy Efficient ◽  
Convex Relaxation ◽  
Sparse Optimization ◽  
Computational Time ◽  
Optimization Approach ◽  
Railway Systems ◽  
Alternating Direction ◽  
Np Hard Problem ◽  
Regenerative Energy

In this paper, we propose a sparse optimization approach to maximize the utilization of regenerative energy produced by braking trains for energy-efficient timetabling in metro railway systems. By introducing the cardinality function and the square of the Euclidean norm function as the objective function, the resulting sparse optimization model can characterize the utilization of the regenerative energy appropriately. A two-stage alternating direction method of multipliers is designed to efficiently solve the convex relaxation counterpart of the original NP-hard problem and then to produce an energy-efficient timetable of trains. The resulting approach is applied to Beijing Metro Yizhuang Line with different instances of service for case study. Comparison with the existing two-step linear program approach is also conducted which illustrates the effectiveness of our proposed sparse optimization model in terms of the energy saving rate and the efficiency of our numerical optimization algorithm in terms of computational time.

Interactive multiobjective DEA target setting using lexicographic DDF

2020 ◽  
Vol 54 (6) ◽  
pp. 1703-1722 ◽  
Author(s):  
Narges Soltani ◽  
Sebastián Lozano
Keyword(s):  
Efficient Frontier ◽  
Directional Distance Function ◽  
Fixed Number ◽  
Optimization Approach ◽  
Target Setting ◽  
Interactive Process ◽  
Decision Making Unit ◽  
Setting Approach ◽  
Promising Area ◽  
Current Region

In this paper, a new interactive multiobjective target setting approach based on lexicographic directional distance function (DDF) method is proposed. Lexicographic DDF computes efficient targets along a specified directional vector. The interactive multiobjective optimization approach consists in several iteration cycles in each of which the Decision Making Unit (DMU) is presented a fixed number of efficient targets computed corresponding to different directional vectors. If the DMU finds one of them promising, the directional vectors tried in the next iteration are generated close to the promising one, thus focusing the exploration of the efficient frontier on the promising area. In any iteration the DMU may choose to finish the exploration of the current region and restart the process to probe a new region. The interactive process ends when the DMU finds its most preferred solution (MPS).

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