A Self-adaptive Response Strategy for Dynamic Multi-objective Evolutionary Optimization based on Objective Space Decomposition

2021 ◽  
pp. 1-26
Author(s):  
Ruochen Liu ◽  
Jianxia Li ◽  
Yaochu Jin ◽  
Licheng Jiao
Keyword(s):  
Adaptive Response ◽  
Environmental Changes ◽  
Fitness Function ◽  
Response Strategy ◽  
Multi Objective ◽  
Response Strategies ◽  
Space Decomposition ◽  
Conflicting Objectives ◽  
Objective Space ◽  
Self Adaptive

Dynamic multi-objective optimization deals with simultaneous optimization of multiple conflicting objectives that change over time. Several response strategies for dynamic optimization have been proposed, which do not work well for all types of environmental changes. In this paper, we propose a new dynamic multi-objective evolutionary algorithm based on objective space decomposition, in which the maxi-min fitness function is adopted for selection and a self-adaptive response strategy integrating a number of different response strategies is designed to handle unknown environmental changes. The self-adaptive response strategy can adaptively select one of the strategies according to their contributions to the tracking performance in the previous environments. Experimental results indicate that the proposed algorithm is competitive and promising for solving different DMOPs in the presence of unknown environmental changes. Meanwhile, the proposed algorithm is applied to solve the parameter tuning problem of a proportional integral derivative (PID) controller of a dynamic system, obtaining better control effect.

MULTI-OBJECTIVE GA-OPTIMIZED INTERPOLATION KERNELS FOR RECONSTRUCTION OF HIGH RESOLUTION EMR IMAGES FROM LOW-SAMPLED K-SPACE DATA

2009 ◽  
Vol 08 (02) ◽  
pp. 127-140 ◽  
Author(s):  
D. BALASUBRAMANIAN ◽  
MURALI C. KRISHNA ◽  
R. MURUGESAN
Keyword(s):  
Image Reconstruction ◽  
Signal To Noise Ratio ◽  
Fitness Function ◽  
Computing Time ◽  
Reference Image ◽  
Signal To Noise ◽  
Multi Objective ◽  
Conflicting Objectives ◽  
Noise Ratio ◽  
Space Data

The low-frequency instrumentation and imaging capabilities facilitate electron magnetic resonance imaging (EMRI) as an emerging non-invasive imaging technology for mapping free radicals in biological systems. Unlike MRI, EMRI is implemented as a pure phase–phase encoding technique. The fast bio-clearance of the imaging agent and the requirement to reduce radio frequency power deposition dictate collection of reduced k-space samples, compromising the quality and resolution of the EMR images. The present work evaluates various interpolation kernels to generate larger k-space samples for image reconstruction, from the acquired reduced k-space samples. Using k-space EMR data sets, acquired for phantom as well as live mice, the proposed technique is critically evaluated by computing quality metrics viz. signal-to-noise ratio (SNR), standard deviation error (SDE), root mean square error (RMSE), peak signal-to-noise ratio (PSNR), contrast-to-noise ratio (CNR) and Lui's error function (F(I)). The quantitative evaluation of 24 different interpolation functions (including piecewise polynomial functions and many windowed sinc functions) to upsample the k-space data for the Fourier EMR image reconstruction shows that at the expense of a slight increase in computing time, the reconstructed images from upsampled data, produced using Spline-sinc, Welch-sinc, and Gaussian-sinc kernels, are closer to reference image with minimal distortion. Support of the interpolating kernel is a characteristic parameter deciding the quality of the reconstructed image and the time complexity. In this paper, a method to optimize the kernel support using genetic algorithm (GA) is also explored. Maximization of the fitness function has two conflicting objectives and it is approached as a multi-objective optimization problem.

On the Use of Problem-Specific Candidate Generators for the Hybrid Optimization of Multi-Objective Production Engineering Problems

2009 ◽  
Vol 17 (4) ◽  
pp. 527-544 ◽  
Author(s):  
K. Weinert ◽  
A. Zabel ◽  
P. Kersting ◽  
T. Michelitsch ◽  
T. Wagner
Keyword(s):  
Pareto Front ◽  
Mold Temperature ◽  
Milling Process ◽  
Production Engineering ◽  
General Applicability ◽  
Multi Objective ◽  
Conflicting Objectives ◽  
Objective Space ◽  
Engineering Problems ◽  
Five Axis

In the field of production engineering, various complex multi-objective problems are known. In this paper we focus on the design of mold temperature control systems, the reconstruction of digitized surfaces, and the optimization of NC paths for the five-axis milling process. For all these applications, efficient problem-specific algorithms exist that only consider a subset of the desirable objectives. In contrast, modern multi-objective evolutionary algorithms are able to cope with many conflicting objectives, but they require a long runtime due to their general applicability. Therefore, we propose hybrid algorithms for the three applications mentioned. In each case, the problem-specific algorithms are used to determine promising initial solutions for the multi-objective evolutionary approach, whose variation concepts are used to generate diversity in the objective space. We show that the combination of these techniques provides great benefits. Since the final solution is chosen by a decision maker based on this Pareto front approximation, appropriate visualizations of the high-dimensional solutions are presented.

A Multi-Objective Robust Preference Genetic Algorithm Based on Decision Variable Perturbation

2011 ◽  
Vol 211-212 ◽  
pp. 818-822 ◽  
Author(s):  
Bing Kun Zhu ◽  
Li Hong Xu ◽  
Hai Gen Hu
Keyword(s):  
Fitness Function ◽  
Latin Hypercube Sampling ◽  
Simultaneous Optimization ◽  
Function Parameter ◽  
Decision Variable ◽  
Multi Objective Optimization ◽  
Robust Solution ◽  
Robust Solutions ◽  
Multi Objective ◽  
Conflicting Objectives

Multi-objective optimization is a challenging research topic because it involves the simultaneous optimization of several complex and conflicting objectives. However multi-objectivity is only one aspect of real-world applications and there is a growing interest in the optimization of solutions that are insensitive to parametric variations as well. A new robust preference multi-objective optimization algorithm is proposed in this paper, and the robust measurement of solution is designed based on Latin Hypercube Sampling, which is embedded in the optimization process to guide the optimization direction and help the better robust solution have more chance to survive. In order to obtain different preference of the robust solutions, a new fitness scheme is also presented. Through the adjustment of fitness function parameter preference, robust solutions can be obtained. Results suggest that the proposed algorithm has a bias towards the region where the preference robust solutions lie.

Security Constrained Stochastic Multi-objective Optimal Power Dispatch

2007 ◽  
Vol 8 (1) ◽  
Author(s):  
Sarbjeet Kaur Bath ◽  
Jaspreet Singh Dhillon ◽  
D P Kothari
Keyword(s):  
Power Generation ◽  
Reactive Power ◽  
Fitness Function ◽  
Thermal Power ◽  
Operating Cost ◽  
Active Power ◽  
Weighting Method ◽  
Gaseous Emission ◽  
Multi Objective ◽  
Conflicting Objectives

A stochastic multi-objective line security constrained problem is formulated to minimize non-commensurable objectives viz. operating cost, polluting gaseous emission and variance of active power generation and reactive power generation, with explicit recognition of statistical uncertainties in the thermal power generation cost coefficients, gaseous emission coefficients, power demands and hence power generations and bus voltages, which are considered random variables. Specific technique is put forth to convert the stochastic models into their respective deterministic equivalents. Fuzzy set theory has been exploited to evaluate the different objectives that are quantified by defining their membership functions. Security of transmission lines with respect to expected active power flow is considered in the form of fuzzy objective function. The solution set of such formulated problems is non-inferior due to contradictions among the objectives undertaken. The weighting method is used to simulate the trade-off relationship between the conflicting objectives in the non-inferior domain. Generally, the weights are either simulated or searched in the non-inferior domain. In the paper Evolutionary search technique is implemented to search the ‘preferred’ weightage pattern in the non-inferior domain, which corresponds to the ‘best’ compromised solution. Among the non-inferior solutions, the system operator selects the ‘preferred’ optimal operating point that provides maximum satisfaction level of the most under achieved objective in terms of membership function and is termed as fitness function. The validity of the proposed method has been demonstrated on an IEEE system comprising of 11-nodes, 17-lines and 5-generators.

scholarly journals DPb-MOPSO: A Novel Dynamic Pareto bi-level Multi-Objective Particle Swarm Optimization Algorithm

2021 ◽  
Author(s):  
Ahlem Aboud ◽  
Nizar Rokbani ◽  
Raja Fdhila ◽  
Abdulrahman M. Qahtani ◽  
Omar Almutiry ◽  
...  
Keyword(s):  
Particle Swarm Optimization ◽  
Environmental Changes ◽  
Dynamic Change ◽  
Particle Swarm ◽  
Search Space ◽  
Response Strategy ◽  
Parallel Optimization ◽  
Pareto Optimal ◽  
Swarm Optimization ◽  
Multi Objective

Particle swarm optimization system based on the distributed architecture has shown its efficiency for static optimization and has not been studied to solve dynamic multiobjective problems (DMOPs). When solving DMOP, tracking the best solutions over time and ensuring good exploitation and exploration are the main challenging tasks. This study proposes a novel Dynamic Pareto bi-level Multi-Objective Particle Swarm Optimization (DPb-MOPSO) algorithm including two parallel optimization levels. At the first level, all solutions are managed in a single search space. When a dynamic change is successfully detected, the Pareto ranking operator is used to enable a multiswarm subdivisions and processing which drives the second level of enhanced exploitation. A dynamic handling strategy based on random detectors is used to track the changes of the objective function due to time-varying parameters. A response strategy consisting in re-evaluate all unimproved solutions and replacing them with newly generated ones is also implemented. Inverted generational distance, mean inverted generational distance, and hypervolume difference metrics are used to assess the DPb-MOPSO performances. All quantitative results are analyzed using Friedman's analysis while the Lyapunov theorem is used for stability analysis. Compared with several multi-objective evolutionary algorithms, the DPb-MOPSO is robust in solving 21 complex problems over a range of changes in both the Pareto optimal set and Pareto optimal front. For 13 UDF and ZJZ functions, DPb-MOPSO can solve 8/13 and 7/13 on IGD and HVD with moderate changes. For the 8 FDA and dMOP benchmarks, DPb-MOPSO was able to resolve 4/8 with severe change on MIGD, and 5/8 for moderate and slight changes. However, for the 3 kind of environmental changes, DPb-MOPSO assumes 4/8 of the solving function on IGD and HVD. <br>

Multi-Objective Optimal Design of a PID Sliding Mode Controller With Three Different Reaching Laws

2019 ◽  
Author(s):  
Xiaotian Xu ◽  
Yousef Sardahi ◽  
Almuatazbellah Boker
Keyword(s):  
Optimal Design ◽  
Optimization Problems ◽  
Sliding Mode ◽  
Sliding Mode Controller ◽  
Reaching Law ◽  
Multi Objective ◽  
Conflicting Objectives ◽  
Objective Space ◽  
Pareto Fronts ◽  
Selection Of

Abstract Sliding mode controllers (SMCs) are well-known nonlinear control techniques. The design of a SMC involves the selection of a sliding mode surface and reaching law. The constant, exponential, and power rate reaching laws are the most widely used. Selecting a reaching law is often based on the desired reaching time; that is how fast the state trajectory approaches the switching manifold. However, the selection of a reaching law does not only affect the reaching time (tr) but also other design specifications such as the settling time (ts), overshoot (Mp), and tracking error (JIAE). Indeed, the design of a closed-loop system usually involves multiple and often conflicting objectives. Therefore, a multi-objective optimal design approach that takes into consideration all the design requirements should be adopted. Furthermore, a systematic study is needed to evaluate and compare the performance of a SMC controller under these reaching laws in multi-objective settings. To this end, the problems of designing a PID (Proportional-Integral-Derivative) sliding mode controller applied to linear and nonlinear dynamic systems using the three reaching laws are formulated as multi-objective optimization problems (MOPs). The objective space includes tr, Mp, ts, and JIAE and the parameter space consists of the design gains of the reaching laws and the sliding mode surface. The non-dominated sorting genetic algorithm (NSGA – II) is used to solve the optimization problem. The solution of the MOP is a Pareto front of optimal design points. Therefore, comparing three Pareto fronts is not a straightforward task. As a result, sections of the Pareto fronts that satisfy some legitimate constraints on the objective space are extracted. Then, a comparison among these sections is conducted graphically. The results show that the exponential rate reaching law outperforms the other two laws in most of the objectives under investigation.

scholarly journals DPb-MOPSO: A Novel Dynamic Pareto bi-level Multi-Objective Particle Swarm Optimization Algorithm

2022 ◽  
Author(s):  
Ahlem Aboud ◽  
Nizar Rokbani ◽  
Raja Fdhila ◽  
Abdulrahman M. Qahtani ◽  
Omar Almutiry ◽  
...  
Keyword(s):  
Particle Swarm Optimization ◽  
Environmental Changes ◽  
Dynamic Change ◽  
Particle Swarm ◽  
Search Space ◽  
Response Strategy ◽  
Parallel Optimization ◽  
Pareto Optimal ◽  
Swarm Optimization ◽  
Multi Objective

Particle swarm optimization system based on the distributed architecture over multiple sub-swarms has shown its efficiency for static optimization and has not been studied to solve dynamic multi-objective problems (DMOPs). When solving DMOP, tracking the best solutions over time and ensuring good exploitation and exploration are the main challenging tasks. This study proposes a novel Dynamic Pareto bi-level Multi-Objective Particle Swarm Optimization (DPb-MOPSO) algorithm including two parallel optimization levels. At the first level, all solutions are managed in a single search space. When a dynamic change is successfully detected in the objective values, the Pareto ranking operator is used to enable a multiple sub-swarm’ subdivisions and processing which drives the second level of enhanced exploitation. A dynamic handling strategy based on random detectors is used to track the changes of the objective function due to time-varying parameters. A response strategy consisting in re-evaluate all unimproved solutions and replacing them with newly generated ones is also implemented. Inverted generational distance, mean inverted generational distance, and hypervolume difference metrics are used to assess the DPb-MOPSO performances. All quantitative results are analyzed using Friedman's analysis of variance while the Lyapunov theorem is used for stability analysis. Compared with several multi-objective evolutionary algorithms, the DPb-MOPSO is robust in solving 21 complex problems over a range of changes in both the Pareto optimal set and Pareto optimal front. For 13 UDF and ZJZ functions, DPb-MOPSO can solve 8/13 and 7/13 on IGD and HVD with moderate changes. For the 8 FDA and dMOP benchmarks, DPb-MOPSO was able to resolve 4/8 with severe change on MIGD, and 5/8 for moderate and slight changes. However, for the 3 kind of environmental changes, DPb-MOPSO assumes 4/8 of the solving function on IGD and HVD metrics.<br>

scholarly journals DPb-MOPSO: A Novel Dynamic Pareto bi-level Multi-Objective Particle Swarm Optimization Algorithm

2021 ◽  
Author(s):  
Ahlem Aboud ◽  
Nizar Rokbani ◽  
Raja Fdhila ◽  
Abdulrahman M. Qahtani ◽  
Omar Almutiry ◽  
...  
Keyword(s):  
Particle Swarm Optimization ◽  
Environmental Changes ◽  
Dynamic Change ◽  
Particle Swarm ◽  
Search Space ◽  
Response Strategy ◽  
Parallel Optimization ◽  
Pareto Optimal ◽  
Swarm Optimization ◽  
Multi Objective

Particle swarm optimization system based on the distributed architecture has shown its efficiency for static optimization and has not been studied to solve dynamic multiobjective problems (DMOPs). When solving DMOP, tracking the best solutions over time and ensuring good exploitation and exploration are the main challenging tasks. This study proposes a novel Dynamic Pareto bi-level Multi-Objective Particle Swarm Optimization (DPb-MOPSO) algorithm including two parallel optimization levels. At the first level, all solutions are managed in a single search space. When a dynamic change is successfully detected, the Pareto ranking operator is used to enable a multiswarm subdivisions and processing which drives the second level of enhanced exploitation. A dynamic handling strategy based on random detectors is used to track the changes of the objective function due to time-varying parameters. A response strategy consisting in re-evaluate all unimproved solutions and replacing them with newly generated ones is also implemented. Inverted generational distance, mean inverted generational distance, and hypervolume difference metrics are used to assess the DPb-MOPSO performances. All quantitative results are analyzed using Friedman's analysis while the Lyapunov theorem is used for stability analysis. Compared with several multi-objective evolutionary algorithms, the DPb-MOPSO is robust in solving 21 complex problems over a range of changes in both the Pareto optimal set and Pareto optimal front. For 13 UDF and ZJZ functions, DPb-MOPSO can solve 8/13 and 7/13 on IGD and HVD with moderate changes. For the 8 FDA and dMOP benchmarks, DPb-MOPSO was able to resolve 4/8 with severe change on MIGD, and 5/8 for moderate and slight changes. However, for the 3 kind of environmental changes, DPb-MOPSO assumes 4/8 of the solving function on IGD and HVD. <br>

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