scholarly journals High-Dimensional Robust Multi-Objective Optimization for Order Scheduling: A Decision Variable Classification Approach

2019 ◽  
Vol 15 (1) ◽  
pp. 293-304 ◽  
Author(s):  
Wei Du ◽  
Weimin Zhong ◽  
Yang Tang ◽  
Wenli Du ◽  
Yaochu Jin
Keyword(s):  
High Dimensional ◽  
Decision Variable ◽  
Multi Objective Optimization ◽  
Order Scheduling ◽  
Classification Approach ◽  
Multi Objective

Multiobjective Optimization for High Dimensional Expensively Constrained Black-Box Problems

2021 ◽  
pp. 1-59
Author(s):  
George Cheng ◽  
G. Gary Wang ◽  
Yeong-Maw Hwang
Keyword(s):  
Multiobjective Optimization ◽  
Trust Region ◽  
Adaptive Strategy ◽  
Black Box ◽  
Superior Performance ◽  
High Dimensional ◽  
Multi Objective Optimization ◽  
Semiconductor Substrate ◽  
Multi Objective ◽  
Computationally Expensive

Abstract Multi-objective optimization (MOO) problems with computationally expensive constraints are commonly seen in real-world engineering design. However, metamodel based design optimization (MBDO) approaches for MOO are often not suitable for high-dimensional problems and often do not support expensive constraints. In this work, the Situational Adaptive Kreisselmeier and Steinhauser (SAKS) method was combined with a new multi-objective trust region optimizer (MTRO) strategy to form the SAKS-MTRO method for MOO problems with expensive black-box constraint functions. The SAKS method is an approach that hybridizes the modeling and aggregation of expensive constraints and adds an adaptive strategy to control the level of hybridization. The MTRO strategy uses a combination of objective decomposition and K-means clustering to handle MOO problems. SAKS-MTRO was benchmarked against four popular multi-objective optimizers and demonstrated superior performance on average. SAKS-MTRO was also applied to optimize the design of a semiconductor substrate and the design of an industrial recessed impeller.

scholarly journals Bézier Simplex Fitting: Describing Pareto Fronts of´ Simplicial Problems with Small Samples in Multi-Objective Optimization

2019 ◽  
Vol 33 ◽  
pp. 2304-2313 ◽  
Author(s):  
Ken Kobayashi ◽  
Naoki Hamada ◽  
Akiyoshi Sannai ◽  
Akinori Tanaka ◽  
Kenichi Bannai ◽  
...  
Keyword(s):  
Sample Size ◽  
Optimization Problems ◽  
Solution Set ◽  
Small Samples ◽  
High Dimensional ◽  
Large Sample Size ◽  
Multi Objective Optimization ◽  
Dimensional Solution ◽  
Multi Objective ◽  
Simplex Model

Multi-objective optimization problems require simultaneously optimizing two or more objective functions. Many studies have reported that the solution set of an M-objective optimization problem often forms an (M − 1)-dimensional topological simplex (a curved line for M = 2, a curved triangle for M = 3, a curved tetrahedron for M = 4, etc.). Since the dimensionality of the solution set increases as the number of objectives grows, an exponentially large sample size is needed to cover the solution set. To reduce the required sample size, this paper proposes a Bézier simplex model and its fitting algorithm. These techniques can exploit the simplex structure of the solution set and decompose a high-dimensional surface fitting task into a sequence of low-dimensional ones. An approximation theorem of Bézier simplices is proven. Numerical experiments with synthetic and real-world optimization problems demonstrate that the proposed method achieves an accurate approximation of high-dimensional solution sets with small samples. In practice, such an approximation will be conducted in the postoptimization process and enable a better trade-off analysis.

scholarly journals Energy efficient route planning for electric vehicles with special consideration of the topography and battery lifetime

2020 ◽  
Vol 13 (8) ◽  
pp. 1705-1726
Author(s):  
Theresia Perger ◽  
Hans Auer
Keyword(s):  
Energy Consumption ◽  
San Francisco ◽  
Electric Vehicles ◽  
Optimization Problem ◽  
Route Planning ◽  
Planning System ◽  
Decision Variable ◽  
Multi Objective Optimization ◽  
Battery Lifetime ◽  
Multi Objective

Abstract In contrast to conventional routing systems, which determine the shortest distance or the fastest path to a destination, this work designs a route planning specifically for electric vehicles by finding an energy-optimal solution while simultaneously considering stress on the battery. After finding a physical model of the energy consumption of the electric vehicle including heating, air conditioning, and other additional loads, the street network is modeled as a network with nodes and weighted edges in order to apply a shortest path algorithm that finds the route with the smallest edge costs. A variation of the Bellman-Ford algorithm, the Yen algorithm, is modified such that battery constraints can be included. Thus, the modified Yen algorithm helps solving a multi-objective optimization problem with three optimization variables representing the energy consumption with (vehicle reaching the destination with the highest state of charge possible), the journey time, and the cyclic lifetime of the battery (minimizing the number of charging/discharging cycles by minimizing the amount of energy consumed or regenerated). For the optimization problem, weights are assigned to each variable in order to put emphasis on one or the other. The route planning system is tested for a suburban area in Austria and for the city of San Francisco, CA. Topography has a strong influence on energy consumption and battery operation and therefore the choice of route. The algorithm finds different results considering different preferences, putting weights on the decision variable of the multi-objective optimization. Also, the tests are conducted for different outside temperatures and weather conditions, as well as for different vehicle types.

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.

Aerodynamic optimization to tandem stators by using sweep and dihedral

2020 ◽  
Vol 234 (6) ◽  
pp. 1225-1236
Author(s):  
Jinouwen Zhang ◽  
Haowan Zhuang ◽  
Jinfang Teng ◽  
Mingmin Zhu ◽  
Xiaoqing Qiang
Keyword(s):  
Gaussian Process ◽  
Surrogate Model ◽  
Aerodynamic Performance ◽  
High Dimensional ◽  
Two Dimensional ◽  
Multi Objective Optimization ◽  
Optimization Scheme ◽  
Multi Objective ◽  
Design Variables ◽  
Dimensional Optimization

In the modern aerodynamic design of turbomachinery blades, the geometries of blades often need to be reshaped to achieve better aerodynamic performance by introducing extra parametric design variables. A higher variable dimension will lead to a larger sampling range as well as a sparser sample distribution, which challenges the effectiveness and stability of optimization schemes based on surrogate model by making the model prediction quality even poorer. In this paper, a multi-objective optimization based on Gaussian process model was carried out for a high dimensional design space. Based on the previous two-dimensional optimization, tandem stators of a modern compressor were optimized by the design of sweep and dihedral. The purpose of the study is to improve the aerodynamic performance of the compressor tandem stators as well as to provide an effective optimization scheme for high dimensional multi-objective optimization problems. The design of sweep and dihedral for reshaping the tandem stators consists of a total of 18 design variables. An improvement in total pressure recovery coefficient of at least 0.7% at positive incidence and at least 0.3% at negative incidence was obtained, much larger than that in the previous two-dimensional optimization. The optimization process shows that, by using Gaussian process as the surrogate model and a special sampling strategy, this optimization scheme is effective and efficient to handle this high dimensional space. The aerodynamic influences of design parameters of tandem blades were analyzed in detail and the superiority of sweep and dihedral in reducing aerodynamic loss was confirmed.

Multi-Objective Optimization with Estimation of Distribution Algorithm in a Noisy Environment

2013 ◽  
Vol 21 (1) ◽  
pp. 149-177 ◽  
Author(s):  
Vui Ann Shim ◽  
Kay Chen Tan ◽  
Jun Yong Chia ◽  
Abdullah Al Mamun
Keyword(s):  
Optimization Problems ◽  
Estimation Of Distribution Algorithm ◽  
Computational Time ◽  
Decision Variable ◽  
Objective Functions ◽  
Multi Objective Optimization ◽  
Noisy Environment ◽  
Multi Objective ◽  
Noisy Information ◽  
Estimation Of Distribution

Many real-world optimization problems are subjected to uncertainties that may be characterized by the presence of noise in the objective functions. The estimation of distribution algorithm (EDA), which models the global distribution of the population for searching tasks, is one of the evolutionary computation techniques that deals with noisy information. This paper studies the potential of EDAs; particularly an EDA based on restricted Boltzmann machines that handles multi-objective optimization problems in a noisy environment. Noise is introduced to the objective functions in the form of a Gaussian distribution. In order to reduce the detrimental effect of noise, a likelihood correction feature is proposed to tune the marginal probability distribution of each decision variable. The EDA is subsequently hybridized with a particle swarm optimization algorithm in a discrete domain to improve its search ability. The effectiveness of the proposed algorithm is examined via eight benchmark instances with different characteristics and shapes of the Pareto optimal front. The scalability, hybridization, and computational time are rigorously studied. Comparative studies show that the proposed approach outperforms other state of the art algorithms.

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