Multi$$^3$$: Optimizing Multimodal Single-Objective Continuous Problems in the Multi-objective Space by Means of Multiobjectivization

2021 ◽  
pp. 311-322
Author(s):  
Pelin Aspar ◽  
Pascal Kerschke ◽  
Vera Steinhoff ◽  
Heike Trautmann ◽  
Christian Grimme
Keyword(s):  
Multi Objective ◽  
Objective Space ◽  
Continuous Problems ◽  
Single Objective

Multi-objective waveform inversion of shallow seismic wavefields

2019 ◽  
Vol 220 (3) ◽  
pp. 1619-1631 ◽  
Author(s):  
Yudi Pan ◽  
Lingli Gao ◽  
Renat Shigapov
Keyword(s):  
Objective Function ◽  
Waveform Inversion ◽  
Model Space ◽  
Earth Model ◽  
Near Surface ◽  
Multi Objective ◽  
Shallow Seismic ◽  
L2 Norm ◽  
Objective Space ◽  
Single Objective

SUMMARY It has been increasingly popular to use shallow-seismic full-waveform inversion (FWI) to reconstruct near-surface structures. Conventional FWI tries to resolve the earth model by minimizing the difference between observed and synthetic seismic data using a certain criterion (conventionally, l2-norm of waveform difference). In this paper, we propose a multi-objective waveform inversion (MOWI) in which the similarity of data is quantified and minimized using multiple criteria simultaneously. By doing so, we expand the dimensionality of objective space as well as the mapping from data space to objective space, which provides MOWI higher freedom in exploring the model space compared to single-objective FWI. We combine three different scalar-valued objective functions into a vector-valued multi-objective function which measures the similarity of the waveform, the waveform envelope, and the amplitude spectra of the data, respectively. This multi-objective function takes not only trace-based waveform and wave packet similarity but also the dispersion characteristics of surface waves into account. Furthermore, the uncertainty in the inversion result could be estimated and analysed quantitatively by the variance of the optimal models. We propose a modified ϵ-constraint algorithm to solve the multi-objective optimization problem. Two synthetic examples are used to show the advantages of using MOWI compared to single-objective FWI. We also test the efficiency of MOWI by using two synthetic shallow-seismic examples, which confirm that MOWI can converge to a better result compared to the conventional single-objective FWI.

Multi-Objective Optimization Based on Brain Storm Optimization Algorithm

2013 ◽  
Vol 4 (3) ◽  
pp. 1-21 ◽  
Author(s):  
Yuhui Shi ◽  
Jingqian Xue ◽  
Yali Wu
Keyword(s):  
Optimization Algorithm ◽  
Optimization Problems ◽  
Solution Space ◽  
Population Based ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Brain Storm Optimization ◽  
Objective Space ◽  
Different Characteristics ◽  
Single Objective

In recent years, many evolutionary algorithms and population-based algorithms have been developed for solving multi-objective optimization problems. In this paper, the authors propose a new multi-objective brain storm optimization algorithm in which the clustering strategy is applied in the objective space instead of in the solution space in the original brain storm optimization algorithm for solving single objective optimization problems. Two versions of multi-objective brain storm optimization algorithm with different characteristics of diverging operation were tested to validate the usefulness and effectiveness of the proposed algorithm. Experimental results show that the proposed multi-objective brain storm optimization algorithm is a very promising algorithm, at least for solving these tested multi-objective optimization problems.

scholarly journals Search Acceleration of Evolutionary Multi-Objective Optimization Using an Estimated Convergence Point

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 129 ◽  
Author(s):  
Yan Pei ◽  
Jun Yu ◽  
Hideyuki Takagi
Keyword(s):  
Parameter Space ◽  
Statistical Tests ◽  
Distribution Characteristic ◽  
Multi Objective Optimization ◽  
Pareto Improvement ◽  
Pareto Solutions ◽  
Pareto Solution ◽  
Multi Objective ◽  
Objective Space ◽  
Convergence Point

We propose a method to accelerate evolutionary multi-objective optimization (EMO) search using an estimated convergence point. Pareto improvement from the last generation to the current generation supports information of promising Pareto solution areas in both an objective space and a parameter space. We use this information to construct a set of moving vectors and estimate a non-dominated Pareto point from these moving vectors. In this work, we attempt to use different methods for constructing moving vectors, and use the convergence point estimated by using the moving vectors to accelerate EMO search. From our evaluation results, we found that the landscape of Pareto improvement has a uni-modal distribution characteristic in an objective space, and has a multi-modal distribution characteristic in a parameter space. Our proposed method can enhance EMO search when the landscape of Pareto improvement has a uni-modal distribution characteristic in a parameter space, and by chance also does that when landscape of Pareto improvement has a multi-modal distribution characteristic in a parameter space. The proposed methods can not only obtain more Pareto solutions compared with the conventional non-dominant sorting genetic algorithm (NSGA)-II algorithm, but can also increase the diversity of Pareto solutions. This indicates that our proposed method can enhance the search capability of EMO in both Pareto dominance and solution diversity. We also found that the method of constructing moving vectors is a primary issue for the success of our proposed method. We analyze and discuss this method with several evaluation metrics and statistical tests. The proposed method has potential to enhance EMO embedding deterministic learning methods in stochastic optimization algorithms.

scholarly journals Study on coloring method of airport flight-gate allocation problem

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Hongyan Li ◽  
Xianfeng Ding ◽  
Jiang Lin ◽  
Jingyu Zhou
Keyword(s):  
Graph Coloring ◽  
Programming Model ◽  
Weight Vector ◽  
Multi Objective ◽  
Average Value ◽  
Two Factors ◽  
Minimum Number ◽  
First Come First Serve ◽  
Airport Terminals ◽  
Single Objective

Abstract With the development of economy, more and more people travel by plane. Many airports have added satellite halls to relieve the pressure of insufficient boarding gates in airport terminals. However, the addition of satellite halls will have a certain impact on connecting flights of transit passengers and increase the difficulty of reasonable allocation of flight and gate in airports. Based on the requirements and data of question F of the 2018 postgraduate mathematical contest in modeling, this paper studies the flight-gate allocation of additional satellite halls at airports. Firstly, match the seven types of flights with the ten types of gates. Secondly, considering the number of gates used and the least number of flights not allocated to the gate, and adding the two factors of the overall tension of passengers and the minimum number of passengers who failed to transfer, the multi-objective 0–1 programming model was established. Determine the weight vector $w=(0.112,0.097,0.496,0.395)$ w = ( 0.112 , 0.097 , 0.496 , 0.395 ) of objective function by entropy value method based on personal preference, then the multi-objective 0–1 programming model is transformed into single-objective 0–1 programming model. Finally, a graph coloring algorithm based on parameter adjustment is used to solve the transformed model. The concept of time slice was used to determine the set of time conflicts of flight slots, and the vertex sequences were colored by applying the principle of “first come first serve”. Applying the model and algorithm proposed in this paper, it can be obtained that the average value of the overall tension degree of passengers minimized in question F is 35.179%, the number of flights successfully allocated to the gate maximized is 262, and the number of gates used is minimized to be 60. The corresponding flight-gate difficulty allocation weight is $\alpha =0.32$ α = 0.32 and $\beta =0.40$ β = 0.40 , and the proportion of flights successfully assigned to the gate is 86.469%. The number of passengers who failed to transfer was 642, with a failure rate of 23.337%.

A two-sided matching decision-making approach based on regret theory under intuitionistic fuzzy environment

2021 ◽  
pp. 1-18
Author(s):  
Xiang Jia ◽  
Xinfan Wang ◽  
Yuanfang Zhu ◽  
Lang Zhou ◽  
Huan Zhou
Keyword(s):  
Decision Making ◽  
Hamming Distance ◽  
Optimal Solution ◽  
Intuitionistic Fuzzy Sets ◽  
Regret Theory ◽  
Multi Objective ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Objective Model ◽  
Single Objective

This study proposes a two-sided matching decision-making (TSMDM) approach by combining the regret theory under the intuitionistic fuzzy environment. At first, according to the Hamming distance of intuitionistic fuzzy sets and regret theory, superior and inferior flows are defined to describe the comparative preference of subjects. Hereafter, the satisfaction degrees are obtained by integrating the superior and inferior flows of the subjects. The comprehensive satisfaction degrees are calculated by aggregating the satisfaction degrees, based on which, a multi-objective TSMDM model is built. Furthermore, the multi-objective TSMDM model is converted to a single-objective model, the optimal solution of the latter is derived. Finally, an illustrative example and several analyses are provided to verify the feasibility and the effectiveness of the proposed approach.

The Position of ADME Predictions in Multi-Objective QSAR

2021 ◽  
Vol 6 (1) ◽  
pp. 1-8
Author(s):  
Anna Tsantili-Kakoulidou
Keyword(s):  
Drug Efficacy ◽  
Clinical Development ◽  
Efficacy And Safety ◽  
Huge Amount ◽  
Multi Objective ◽  
Drug Candidates ◽  
Drug Molecules ◽  
Qsar Models ◽  
Adme Properties ◽  
Single Objective

ADME properties and toxicity predictions play an essential role in prioritization and optimization of drug molecules. According to recent statistics, drug efficacy and safety are principal reasons for drug failure. In this perspective, the position of ADME predictions in the evolution of traditional QSAR from the single objective of biological activity to a multi-task concept is discussed. The essential features of ADME and toxicity QSAR models are highlighted. Since such models are applied to prioritize existing or virtual project compounds with already established or predicted target affinity, a mechanistic interpretation, although desirable, is not a primary goal. However, a broad applicability domain is crucial. A future challenge with multi-objective QSAR is to adapt to the realm of big data by integrating techniques for the exploitation of the continuously increasing number of ADME data and the huge amount of clinical development endpoints for the sake of efficacy and safety of new drug candidates.

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