Diagnostic Assessment of Search Controls and Failure Modes in Many-Objective Evolutionary Optimization

2012 ◽  
Vol 20 (3) ◽  
pp. 423-452 ◽  
Author(s):  
David Hadka ◽  
Patrick Reed
Keyword(s):  
Failure Modes ◽  
Variance Decomposition ◽  
Diagnostic Assessment ◽  
Test Problems ◽  
Multiobjective Evolutionary Algorithms ◽  
Assessment Framework ◽  
Nsga Ii ◽  
Diagnostic Framework ◽  
Careful Investigation ◽  
Test Suites

The growing popularity of multiobjective evolutionary algorithms (MOEAs) for solving many-objective problems warrants the careful investigation of their search controls and failure modes. This study contributes a new diagnostic assessment framework for rigorously evaluating the effectiveness, reliability, efficiency, and controllability of MOEAs as well as identifying their search controls and failure modes. The framework is demonstrated using the recently introduced Borg MOEA, [Formula: see text]-NSGA-II, [Formula: see text]-MOEA, IBEA, OMOPSO, GDE3, MOEA/D, SPEA2, and NSGA-II on 33 instances of 18 test problems from the DTLZ, WFG, and CEC 2009 test suites. The diagnostic framework exploits Sobol's variance decomposition to provide guidance on the algorithms’ non-separable, multi-parameter controls when performing a many-objective search. This study represents one of the most comprehensive empirical assessments of MOEAs ever completed.

scholarly journals Elite Exploitation: A Combination of Mathematical Concept and EMO Approach for Multi-Objective Decision Making

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 136
Author(s):  
Wenxiao Li ◽  
Yushui Geng ◽  
Jing Zhao ◽  
Kang Zhang ◽  
Jianxin Liu
Keyword(s):  
Decision Making ◽  
Optimization Problems ◽  
Hybrid Genetic Algorithm ◽  
Decision Makers ◽  
Superior Performance ◽  
Test Problems ◽  
Mathematical Function ◽  
Hyperbolic Tangent ◽  
Nsga Ii ◽  
Multi Objective

This paper explores the combination of a classic mathematical function named “hyperbolic tangent” with a metaheuristic algorithm, and proposes a novel hybrid genetic algorithm called NSGA-II-BnF for multi-objective decision making. Recently, many metaheuristic evolutionary algorithms have been proposed for tackling multi-objective optimization problems (MOPs). These algorithms demonstrate excellent capabilities and offer available solutions to decision makers. However, their convergence performance may be challenged by some MOPs with elaborate Pareto fronts such as CFs, WFGs, and UFs, primarily due to the neglect of diversity. We solve this problem by proposing an algorithm with elite exploitation strategy, which contains two parts: first, we design a biased elite allocation strategy, which allocates computation resources appropriately to elites of the population by crowding distance-based roulette. Second, we propose a self-guided fast individual exploitation approach, which guides elites to generate neighbors by a symmetry exploitation operator, which is based on mathematical hyperbolic tangent function. Furthermore, we designed a mechanism to emphasize the algorithm’s applicability, which allows decision makers to adjust the exploitation intensity with their preferences. We compare our proposed NSGA-II-BnF with four other improved versions of NSGA-II (NSGA-IIconflict, rNSGA-II, RPDNSGA-II, and NSGA-II-SDR) and four competitive and widely-used algorithms (MOEA/D-DE, dMOPSO, SPEA-II, and SMPSO) on 36 test problems (DTLZ1–DTLZ7, WGF1–WFG9, UF1–UF10, and CF1–CF10), and measured using two widely used indicators—inverted generational distance (IGD) and hypervolume (HV). Experiment results demonstrate that NSGA-II-BnF exhibits superior performance to most of the algorithms on all test problems.

Evaluating the ε-Domination Based Multi-Objective Evolutionary Algorithm for a Quick Computation of Pareto-Optimal Solutions

2005 ◽  
Vol 13 (4) ◽  
pp. 501-525 ◽  
Author(s):  
Kalyanmoy Deb ◽  
Manikanth Mohan ◽  
Shikhar Mishra
Keyword(s):  
Steady State ◽  
Evolutionary Algorithm ◽  
Optimization Problems ◽  
Computational Time ◽  
Test Problems ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Nsga Ii ◽  
Multi Objective

Since the suggestion of a computing procedure of multiple Pareto-optimal solutions in multi-objective optimization problems in the early Nineties, researchers have been on the look out for a procedure which is computationally fast and simultaneously capable of finding a well-converged and well-distributed set of solutions. Most multi-objective evolutionary algorithms (MOEAs) developed in the past decade are either good for achieving a well-distributed solutions at the expense of a large computational effort or computationally fast at the expense of achieving a not-so-good distribution of solutions. For example, although the Strength Pareto Evolutionary Algorithm or SPEA (Zitzler and Thiele, 1999) produces a much better distribution compared to the elitist non-dominated sorting GA or NSGA-II (Deb et al., 2002a), the computational time needed to run SPEA is much greater. In this paper, we evaluate a recently-proposed steady-state MOEA (Deb et al., 2003) which was developed based on the ε-dominance concept introduced earlier (Laumanns et al., 2002) and using efficient parent and archive update strategies for achieving a well-distributed and well-converged set of solutions quickly. Based on an extensive comparative study with four other state-of-the-art MOEAs on a number of two, three, and four objective test problems, it is observed that the steady-state MOEA is a good compromise in terms of convergence near to the Pareto-optimal front, diversity of solutions, and computational time. Moreover, the ε-MOEA is a step closer towards making MOEAs pragmatic, particularly allowing a decision-maker to control the achievable accuracy in the obtained Pareto-optimal solutions.

On Benchmark Problems and Metrics for Decision Space Performance Analysis in Multi-Objective Optimization

2017 ◽  
Vol 16 (01) ◽  
pp. 1750006 ◽  
Author(s):  
Bin Zhang ◽  
Kamran Shafi ◽  
Hussein Abbass
Keyword(s):  
Performance Analysis ◽  
Fitness Landscape ◽  
Benchmark Problems ◽  
Test Problems ◽  
Multi Objective Optimization ◽  
Decision Space ◽  
Nsga Ii ◽  
Multi Objective ◽  
Objective Space ◽  
Problem Instances

A number of benchmark problems exist for evaluating multi-objective evolutionary algorithms (MOEAs) in the objective space. However, the decision space performance analysis is a recent and relatively less explored topic in evolutionary multi-objective optimization research. Among other implications, such analysis can lead to designing more realistic test problems, gaining better understanding about optimal and robust design areas, and design and evaluation of knowledge-based optimization algorithms. This paper complements the existing research in this area and proposes a new method to generate multi-objective optimization test problems with clustered Pareto sets in hyper-rectangular defined areas of decision space. The test problem is parametrized to control number of decision variables, number and position of optimal areas in the decision space and modality of fitness landscape. Three leading MOEAs, including NSGA-II, NSGA-III, and MOEA/D, are evaluated on a number of problem instances with varying characteristics. A new metric is proposed that measures the performance of algorithms in terms of their coverage of the optimal areas in the decision space. The empirical analysis presented in this research shows that the decision space performance may not necessarily be reflective of the objective space performance and that all algorithms are sensitive to population size parameter for the new test problems.

scholarly journals Data-Driven Bayesian Network Learning: A Bi-Objective Approach to Address the Bias-Variance Decomposition

2020 ◽  
Vol 25 (2) ◽  
pp. 37 ◽  
Author(s):  
Vicente-Josué Aguilera-Rueda ◽  
Nicandro Cruz-Ramírez ◽  
Efrén Mezura-Montes
Keyword(s):  
Bayesian Networks ◽  
Bayesian Network ◽  
Variance Decomposition ◽  
Data Driven ◽  
End User ◽  
Learning Problem ◽  
Nsga Ii ◽  
Bias Variance ◽  
Core Idea ◽  
Nondominated Sorting

We present a novel bi-objective approach to address the data-driven learning problem of Bayesian networks. Both the log-likelihood and the complexity of each candidate Bayesian network are considered as objectives to be optimized by our proposed algorithm named Nondominated Sorting Genetic Algorithm for learning Bayesian networks (NS2BN) which is based on the well-known NSGA-II algorithm. The core idea is to reduce the implicit selection bias-variance decomposition while identifying a set of competitive models using both objectives. Numerical results suggest that, in stark contrast to the single-objective approach, our bi-objective approach is useful to find competitive Bayesian networks especially in the complexity. Furthermore, our approach presents the end user with a set of solutions by showing different Bayesian network and their respective MDL and classification accuracy results.

scholarly journals Evolutionary Search with Multiple Utopian Reference Points in Decomposition-Based Multiobjective Optimization

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-22 ◽  
Author(s):  
Wu Lin ◽  
Qiuzhen Lin ◽  
Zexuan Zhu ◽  
Jianqiang Li ◽  
Jianyong Chen ◽  
...  
Keyword(s):  
Evolutionary Algorithms ◽  
Reference Point ◽  
Ideal Point ◽  
Search Space ◽  
Weight Vector ◽  
Reference Points ◽  
Test Problems ◽  
Evolutionary Search ◽  
Multiobjective Evolutionary Algorithms ◽  
Nadir Point

Decomposition-based multiobjective evolutionary algorithms (MOEA/Ds) have become increasingly popular in recent years. In these MOEA/Ds, evolutionary search is guided by the used weight vectors in decomposition function to approximate the Pareto front (PF). Generally, the decomposition function will be constructed by the weight vectors and the reference point, which play an important role to balance convergence and diversity during the evolutionary search. However, in most existing MOEA/Ds, only one ideal point is used as the reference point for all the evolutionary search, which is harmful to search the entire PF when tackling the problems with difficult-to-approximate PF boundaries. To address the above problem, this paper proposes an evolutionary search method with multiple utopian reference points in MOEA/Ds. Similar to the existing MOEA/Ds, each solution is associated with one weight vector, which provides an evolutionary search direction, while the novelty of our approach is to use multiple utopian reference points, which can provide evolutionary search directions for different weight vectors. Corner solutions are used to approximate the nadir point and then multiple utopian reference points for evolutionary search can be constructed based on the ideal point and the nadir point, which are uniformly distributed on the coordinate axis or planes. The use of these utopian points can prevent solutions to gather in the same region of PF and helps to strike a good balance of exploration and exploitation in the search space. The performance of our proposed algorithm is validated on tackling 16 recently proposed test problems with difficult-to-approximate PF boundaries and empirically compared to eight state-of-the-art multiobjective evolutionary algorithms. The experimental results demonstrate the superiority of the proposed algorithm on solving most of the test problems adopted.

scholarly journals A Comparative Analysis of NSGA-II and NSGA-III for Autoscaling Parameter Sweep Experiments in the Cloud

2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Virginia Yannibelli ◽  
Elina Pacini ◽  
David Monge ◽  
Cristian Mateos ◽  
Guillermo Rodriguez
Keyword(s):  
Cloud Computing ◽  
Optimization Algorithm ◽  
Virtual Machines ◽  
State Of The Art ◽  
Multiobjective Evolutionary Algorithms ◽  
Nsga Ii ◽  
Trade Off ◽  
Computing Paradigm ◽  
Virtual Infrastructure ◽  
And Storage

The Cloud Computing paradigm is focused on the provisioning of reliable and scalable virtual infrastructures that deliver execution and storage services. This paradigm is particularly suitable to solve resource-greedy scientific computing applications such as parameter sweep experiments (PSEs). Through the implementation of autoscalers, the virtual infrastructure can be scaled up and down by acquiring or terminating instances of virtual machines (VMs) at the time that application tasks are being scheduled. In this paper, we extend an existing study centered in a state-of-the-art autoscaler called multiobjective evolutionary autoscaler (MOEA). MOEA uses a multiobjective optimization algorithm to determine the set of possible virtual infrastructure settings. In this context, the performance of MOEA is greatly influenced by the underlying optimization algorithm used and its tuning. Therefore, we analyze two well-known multiobjective evolutionary algorithms (NSGA-II and NSGA-III) and how they impact on the performance of the MOEA autoscaler. Simulated experiments with three real-world PSEs show that MOEA gets significantly improved when using NSGA-III instead of NSGA-II due to the former provides a better exploitation versus exploration trade-off.

Optimization of Anti-Spam Systems with Multiobjective Evolutionary Algorithms

2013 ◽  
Vol 26 (1) ◽  
pp. 54-67 ◽  
Author(s):  
Vitor Basto-Fernandes ◽  
Iryna Yevseyeva ◽  
José R. Méndez
Keyword(s):  
Evolutionary Algorithms ◽  
Open Source Software ◽  
Research Area ◽  
Multiobjective Evolutionary Algorithms ◽  
Spam Filtering ◽  
Nsga Ii ◽  
Software Product ◽  
Spam Filters ◽  
Problem Description ◽  
Human Effort

In this paper anti-spam filtering is presented as a cumbersome service, as opposed to a software product perspective. The huge human effort for setting up, adaptation, maintenance, and tuning of filters for spam detection in anti-spam systems is explained. Choosing the best importance scores for the spam filters is essential for the accuracy of any rules based anti-spam system, and is also one of the biggest challenges in this research area. Optimal filters score settings for Apache SpamAssassin project (the most widely adopted anti-spam open-source software) is addressed. In addition to a survey done on single/multi-objective optimization research in this area, we also present a study for filters score setting using multiobjective optimization based on two most representative evolutionary algorithms, NSGA II and SPEA2. Problem description, simulation and results analysis is done for SpamAssassin public mail corpus which is widely used for benchmarking purposes.

Comprehensive Survey of the Hybrid Evolutionary Algorithms

2013 ◽  
Vol 4 (2) ◽  
pp. 1-19 ◽  
Author(s):  
Wali Khan Mashwani
Keyword(s):  
Evolutionary Algorithms ◽  
Pareto Front ◽  
Optimization Problems ◽  
Mathematical Formulation ◽  
Multiobjective Evolutionary Algorithms ◽  
Nsga Ii ◽  
Pareto Optimal Set ◽  
Multiobjective Optimization Problems ◽  
Comprehensive Survey ◽  
Optimal Set

Multiobjective evolutionary algorithm based on decomposition (MOEA/D) and an improved non-dominating sorting multiobjective genetic algorithm (NSGA-II) is two well known multiobjective evolutionary algorithms (MOEAs) in the field of evolutionary computation. This paper mainly reviews their hybrid versions and some other algorithms which are developed for solving multiobjective optimization problems (MOPs. The mathematical formulation of a MOP and some basic definitions for tackling MOPs, including Pareto optimality, Pareto optimal set (PS), Pareto front (PF) are provided in Section 1. Section 2 presents a brief introduction to hybrid MOEAs. The authors present literature review in subsections. Subsection 2.1 provides memetic multiobjective evolutionary algorithms. Subsection 2.2 presents the hybrid versions of well-known Pareto dominance based MOEAs. Subsection 2.4 summarizes some enhanced Versions of MOEA/D paradigm. Subsection 2.5 reviews some multimethod search approaches dealing optimization problems.

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