scholarly journals A Decomposition-Based Multiobjective Optimization Evolutionary Algorithm with Adaptive Weight Generation Strategy

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Guo-Zhong Fu ◽  
Tianda Yu ◽  
Wei Li ◽  
Qiang Deng ◽  
Bo Yang
Keyword(s):  
Evolutionary Algorithms ◽  
Multiobjective Optimization ◽  
Evolutionary Algorithm ◽  
Multiobjective Evolutionary Algorithms ◽  
Optimal Solutions ◽  
Optimal Weight ◽  
Vector Generation ◽  
Adaptive Weight ◽  
Fixed Set ◽  
Distributed Solutions

Multiobjective evolutionary algorithm based on decomposition (MOEA/D) is the seminal framework of multiobjective evolutionary algorithms (MOEAs). To alleviate the nonuniformly distributed solutions generated by a fixed set of evenly distributed weight vectors in the presence of nonconvex and disconnected problems, an adaptive vector generation mechanism is proposed. A coevolution strategy and a vector generator are synergistically cooperated to remedy the weight vectors. Optimal weight vectors are generated to replace the useless weight vectors to assure that optimal solutions are distributed evenly. Experiment results indicate that this mechanism is efficient in improving the diversity of MOEA/D.

scholarly journals Comparison of Multiobjective Evolutionary Algorithms: Empirical Results

2000 ◽  
Vol 8 (2) ◽  
pp. 173-195 ◽  
Author(s):  
Eckart Zitzler ◽  
Kalyanmoy Deb ◽  
Lothar Thiele
Keyword(s):  
Evolutionary Algorithms ◽  
Multiobjective Optimization ◽  
Experimental Results ◽  
Pareto Optimal ◽  
Multiobjective Evolutionary Algorithms ◽  
Test Functions ◽  
Test Function ◽  
Pareto Optimal Front ◽  
Systematic Comparison ◽  
Empirical Results

In this paper, we provide a systematic comparison of various evolutionary approaches to multiobjective optimization using six carefully chosen test functions. Each test function involves a particular feature that is known to cause difficulty in the evolutionary optimization process, mainly in converging to the Pareto-optimal front (e.g., multimodality and deception). By investigating these different problem features separately, it is possible to predict the kind of problems to which a certain technique is or is not well suited. However, in contrast to what was suspected beforehand, the experimental results indicate a hierarchy of the algorithms under consideration. Furthermore, the emerging effects are evidence that the suggested test functions provide sufficient complexity to compare multiobjective optimizers. Finally, elitism is shown to be an important factor for improving evolutionary multiobjective search.

Combining Convergence and Diversity in Evolutionary Multiobjective Optimization

2002 ◽  
Vol 10 (3) ◽  
pp. 263-282 ◽  
Author(s):  
Marco Laumanns ◽  
Lothar Thiele ◽  
Kalyanmoy Deb ◽  
Eckart Zitzler
Keyword(s):  
Evolutionary Algorithms ◽  
Multiobjective Optimization ◽  
Optimization Problems ◽  
Fundamental Problem ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Pareto Optimal Set ◽  
Multiobjective Optimization Problems ◽  
Baseline Algorithm

Over the past few years, the research on evolutionary algorithms has demonstrated their niche in solving multiobjective optimization problems, where the goal is to find a number of Pareto-optimal solutions in a single simulation run. Many studies have depicted different ways evolutionary algorithms can progress towards the Pareto-optimal set with a widely spread distribution of solutions. However, none of the multiobjective evolutionary algorithms (MOEAs) has a proof of convergence to the true Pareto-optimal solutions with a wide diversity among the solutions. In this paper, we discuss why a number of earlier MOEAs do not have such properties. Based on the concept of ɛ-dominance, new archiving strategies are proposed that overcome this fundamental problem and provably lead to MOEAs that have both the desired convergence and distribution properties. A number of modifications to the baseline algorithm are also suggested. The concept of ɛ-dominance introduced in this paper is practical and should make the proposed algorithms useful to researchers and practitioners alike.

Pareto-adaptive ε-dominance

2007 ◽  
Vol 15 (4) ◽  
pp. 493-517 ◽  
Author(s):  
Alfredo G. Hernández-Díaz ◽  
Luis V. Santana-Quintero ◽  
Carlos A. Coello Coello ◽  
Julián Molina
Keyword(s):  
Evolutionary Algorithms ◽  
Multiobjective Optimization ◽  
Pareto Front ◽  
Multiobjective Evolutionary Algorithms ◽  
Pareto Dominance ◽  
Nondominated Solutions ◽  
Evolutionary Multiobjective Optimization ◽  
The Way

Efficiency has become one of the main concerns in evolutionary multiobjective optimization during recent years. One of the possible alternatives to achieve a faster convergence is to use a relaxed form of Pareto dominance that allows us to regulate the granularity of the approximation of the Pareto front that we wish to achieve. One such relaxed forms of Pareto dominance that has become popular in the last few years is ε-dominance, which has been mainly used as an archiving strategy in some multiobjective evolutionary algorithms. Despite its advantages, ε-dominance has some limitations. In this paper, we propose a mechanism that can be seen as a variant of ε-dominance, which we call Pareto-adaptive ε-dominance (paε-dominance). Our proposed approach tries to overcome the main limitation of ε-dominance: the loss of several nondominated solutions from the hypergrid adopted in the archive because of the way in which solutions are selected within each box.

scholarly journals A Review of Surrogate Assisted Multiobjective Evolutionary Algorithms

2016 ◽  
Vol 2016 ◽  
pp. 1-14 ◽  
Author(s):  
Alan Díaz-Manríquez ◽  
Gregorio Toscano ◽  
Jose Hugo Barron-Zambrano ◽  
Edgar Tello-Leal
Keyword(s):  
Evolutionary Algorithms ◽  
Multiobjective Optimization ◽  
Pareto Front ◽  
Optimization Problems ◽  
State Of The Art ◽  
Surrogate Models ◽  
Multiobjective Evolutionary Algorithms ◽  
Advantages And Disadvantages ◽  
Multiobjective Optimization Problems ◽  
Computationally Expensive

Multiobjective evolutionary algorithms have incorporated surrogate models in order to reduce the number of required evaluations to approximate the Pareto front of computationally expensive multiobjective optimization problems. Currently, few works have reviewed the state of the art in this topic. However, the existing reviews have focused on classifying the evolutionary multiobjective optimization algorithms with respect to the type of underlying surrogate model. In this paper, we center our focus on classifying multiobjective evolutionary algorithms with respect to their integration with surrogate models. This interaction has led us to classify similar approaches and identify advantages and disadvantages of each class.

scholarly journals A Constrained Solution Update Strategy for Multiobjective Evolutionary Algorithm Based on Decomposition

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Yuchao Su ◽  
Qiuzhen Lin ◽  
Jia Wang ◽  
Jianqiang Li ◽  
Jianyong Chen ◽  
...  
Keyword(s):  
Evolutionary Algorithms ◽  
Evolutionary Algorithm ◽  
Population Size ◽  
Test Problems ◽  
Multiobjective Evolutionary Algorithms ◽  
Number Of Solutions ◽  
Multiobjective Evolutionary Algorithm ◽  
Population Selection ◽  
Update Strategy

This paper proposes a constrained solution update strategy for multiobjective evolutionary algorithm based on decomposition, in which each agent aims to optimize one decomposed subproblem. Different from the existing approaches that assign one solution to each agent, our approach allocates the closest solutions to each agent and thus the number of solutions in an agent may be zero and no less than one. Regarding the agent with no solution, it will be assigned one solution in priority, once offspring are generated closest to its subproblem. To keep the same population size, the agent with the largest number of solutions will remove one solution showing the worst convergence. This improves diversity for one agent, while the convergence of other agents is not lowered. On the agent with no less than one solution, offspring assigned to this agent are only allowed to update its original solutions. Thus, the convergence of this agent is enhanced, while the diversity of other agents will not be affected. After a period of evolution, our approach may gradually reach a stable status for solution assignment; i.e., each agent is only assigned with one solution. When compared to six competitive multiobjective evolutionary algorithms with different population selection or update strategies, the experiments validated the advantages of our approach on tackling two sets of test problems.

scholarly journals Multichannel optimization for electromyogram signals with complex features in a decomposition-based multi-objective evolution framework with adaptive angle selection

2020 ◽  
Vol 17 (2) ◽  
pp. 172988142091701
Author(s):  
Zheng Wang ◽  
Guoqi Chen ◽  
Weikun Li ◽  
Honghai Liu ◽  
Wanliang Wang
Keyword(s):  
Evolutionary Algorithms ◽  
Evolutionary Algorithm ◽  
Real Time ◽  
Ant Colony Algorithm ◽  
Support Vector ◽  
Signal Recognition ◽  
Multiobjective Evolutionary Algorithms ◽  
Real Time Control ◽  
Recognition Method ◽  
Multi Objective

Intelligent manufacturing is a focus of current manufacturing research, and, in combination with the Internet, it enables accurate real-time control of intelligent equipment. Highly accurate real-time prosthesis control has very important applications in therapeutics, intelligent prosthesis, and other fields. However, the applicability of the current electromyogram signal recognition method is not strong because of multiple factors. These include considering one objective (correctness) only and the inability to consider differences of recognition accuracy between actions, to recognize the number of channels, or to recognize computational complexity. In this article, we propose a multi-objective evolutionary algorithm based on a decomposition-based multi-objective differential evolution framework to construct a multi-objective model for electromyogram signals with multiple features and channels. Such channels and features are balanced and selected by using a support vector machine as an electromyogram signal classifier. Results of substantial experiment analyses indicate that the multi-objective electromyogram signal recognition method is superior to the single-objective ant colony algorithm and that the decomposition-based multiobjective evolutionary algorithms with Angle-based updating and global margin ranking is better than the decomposition-based multi-objective evolutionary algorithm and decomposition-based multiobjective evolutionary algorithms with angle-based updating strategy in handling multi-objective models for electromyogram signals.

scholarly journals Drift Analysis and Evolutionary Algorithms Revisited

2018 ◽  
Vol 27 (4) ◽  
pp. 643-666 ◽  
Author(s):  
J. LENGLER ◽  
A. STEGER
Keyword(s):  
Evolutionary Algorithms ◽  
Evolutionary Algorithm ◽  
Random Search ◽  
Optimization Algorithms ◽  
Simple Algorithm ◽  
Linear Functions ◽  
Search Point ◽  
Drift Analysis ◽  
Fixed Constant ◽  
Greedy Optimization

One of the easiest randomized greedy optimization algorithms is the following evolutionary algorithm which aims at maximizing a function f: {0,1}n → ℝ. The algorithm starts with a random search point ξ ∈ {0,1}n, and in each round it flips each bit of ξ with probability c/n independently at random, where c > 0 is a fixed constant. The thus created offspring ξ' replaces ξ if and only if f(ξ') ≥ f(ξ). The analysis of the runtime of this simple algorithm for monotone and for linear functions turned out to be highly non-trivial. In this paper we review known results and provide new and self-contained proofs of partly stronger results.

scholarly journals An automated system analysis and design tool for spacecrafts ceas space journal

2021 ◽  
Author(s):  
Manfred Ehresmann ◽  
Georg Herdrich ◽  
Stefanos Fasoulas
Keyword(s):  
Evolutionary Algorithms ◽  
Evolutionary Algorithm ◽  
Degrees Of Freedom ◽  
System Analysis ◽  
Propulsion System ◽  
Optimal System ◽  
Automated System ◽  
Processing Unit ◽  
Data Set ◽  
Analysis And Design

AbstractIn this paper, a generic full-system estimation software tool is introduced and applied to a data set of actual flight missions to derive a heuristic for system composition for mass and power ratios of considered sub-systems. The capability of evolutionary algorithms to analyse and effectively design spacecraft (sub-)systems is shown. After deriving top-level estimates for each spacecraft sub-system based on heuristic heritage data, a detailed component-based system analysis follows. Various degrees of freedom exist for a hardware-based sub-system design; these are to be resolved via an evolutionary algorithm to determine an optimal system configuration. A propulsion system implementation for a small satellite test case will serve as a reference example of the implemented algorithm application. The propulsion system includes thruster, power processing unit, tank, propellant and general power supply system masses and power consumptions. Relevant performance parameters such as desired thrust, effective exhaust velocity, utilised propellant, and the propulsion type are considered as degrees of freedom. An evolutionary algorithm is applied to the propulsion system scaling model to demonstrate that such evolutionary algorithms are capable of bypassing complex multidimensional design optimisation problems. An evolutionary algorithm is an algorithm that uses a heuristic to change input parameters and a defined selection criterion (e.g., mass fraction of the system) on an optimisation function to refine solutions successively. With sufficient generations and, thereby, iterations of design points, local optima are determined. Using mitigation methods and a sufficient number of seed points, a global optimal system configurations can be found.

scholarly journals Comparison of Searching Behaviour of Three Evolutionary Algorithms Applied to Water Distribution System Design Optimization

Water ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 695 ◽  
Author(s):  
Weiwei Bi ◽  
Yihui Xu ◽  
Hongyu Wang
Keyword(s):  
Evolutionary Algorithms ◽  
Real Time ◽  
Distribution System ◽  
Optimization Design ◽  
Distribution Systems ◽  
Water Distribution ◽  
Optimal Solutions ◽  
Great Ability ◽  
Searching Behaviour ◽  
Run Time

Over the past few decades, various evolutionary algorithms (EAs) have been applied to the optimization design of water distribution systems (WDSs). An important research area is to compare the performance of these EAs, thereby offering guidance for the selection of the appropriate EAs for practical implementations. Such comparisons are mainly based on the final solution statistics and, hence, are unable to provide knowledge on how different EAs reach the final optimal solutions and why different EAs performed differently in identifying optimal solutions. To this end, this paper aims to compare the real-time searching behaviour of three widely used EAs, which are genetic algorithms (GAs), the differential evolution (DE) algorithm and the ant colony optimization (ACO). These three EAs are applied to five WDS benchmarking case studies with different scales and complexities, and a set of five metrics are used to measure their run-time searching quality and convergence properties. Results show that the run-time metrics can effectively reveal the underlying searching mechanisms associated with each EA, which significantly goes beyond the knowledge from the traditional end-of-run solution statistics. It is observed that the DE is able to identify better solutions if moderate and large computational budgets are allowed due to its great ability in maintaining the balance between the exploration and exploitation. However, if the computational resources are rather limited or the decision has to be made in a very short time (e.g., real-time WDS operation), the GA can be a good choice as it can always identify better solutions than the DE and ACO at the early searching stages. Based on the results, the ACO performs the worst for the five case study considered. The outcome of this study is the offer of guidance for the algorithm selection based on the available computation resources, as well as knowledge into the EA’s underlying searching behaviours.

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