Is Our Archiving Reliable? Multiobjective Archiving Methods on “Simple” Artificial Input Sequences

2021 ◽  
Vol 1 (3) ◽  
pp. 1-19
Author(s):  
Miqing Li
Keyword(s):  
Pareto Front ◽  
Search Process ◽  
Good Representation ◽  
Optimal Solutions ◽  
Fixed Size ◽  
Multiobjective Optimisation ◽  
Common Component ◽  
Front Shape ◽  
Internal Set ◽  
Pareto Fronts

In evolutionary multiobjective optimisation ( EMO ), archiving is a common component that maintains an (external or internal) set during the search process, typically with a fixed size, in order to provide a good representation of high-quality solutions produced. Such an archive set can be used solely to store the final results shown to the decision maker, but in many cases may participate in the process of producing solutions (e.g., as a solution pool where the parental solutions are selected). Over the last three decades, archiving stands as an important issue in EMO, leading to the emergence of various methods such as those based on Pareto, indicator, or decomposition criteria. Such methods have demonstrated their effectiveness in literature and have been believed to be good options to many problems, particularly those having a regular Pareto front shape, e.g., a simplex shape. In this article, we challenge this belief. We do this through artificially constructing several sequences with extremely simple shapes, i.e., 1D/2D simplex Pareto front. We show the struggle of predominantly used archiving methods which have been deemed to well handle such shapes. This reveals that the order of solutions entering the archive matters, and that current EMO algorithms may not be fully capable of maintaining a representative population on problems with linear Pareto fronts even in the case that all of their optimal solutions can be found.

scholarly journals What Weights Work for You? Adapting Weights for Any Pareto Front Shape in Decomposition-Based Evolutionary Multiobjective Optimisation

2020 ◽  
Vol 28 (2) ◽  
pp. 227-253 ◽  
Author(s):  
Miqing Li ◽  
Xin Yao
Keyword(s):  
Pareto Front ◽  
Evolutionary Process ◽  
Highly Nonlinear ◽  
Distributed Solutions ◽  
Front Shape ◽  
Different Shapes ◽  
Pareto Fronts ◽  
The Given ◽  
Update Frequency

The quality of solution sets generated by decomposition-based evolutionary multi-objective optimisation (EMO) algorithms depends heavily on the consistency between a given problem's Pareto front shape and the specified weights' distribution. A set of weights distributed uniformly in a simplex often leads to a set of well-distributed solutions on a Pareto front with a simplex-like shape, but may fail on other Pareto front shapes. It is an open problem on how to specify a set of appropriate weights without the information of the problem's Pareto front beforehand. In this article, we propose an approach to adapt weights during the evolutionary process (called AdaW). AdaW progressively seeks a suitable distribution of weights for the given problem by elaborating several key parts in weight adaptation—weight generation, weight addition, weight deletion, and weight update frequency. Experimental results have shown the effectiveness of the proposed approach. AdaW works well for Pareto fronts with very different shapes: 1) the simplex-like, 2) the inverted simplex-like, 3) the highly nonlinear, 4) the disconnect, 5) the degenerate, 6) the scaled, and 7) the high-dimensional.

scholarly journals Improving Vector Evaluated Particle Swarm Optimisation Using Multiple Nondominated Leaders

2014 ◽  
Vol 2014 ◽  
pp. 1-21 ◽  
Author(s):  
Kian Sheng Lim ◽  
Salinda Buyamin ◽  
Anita Ahmad ◽  
Mohd Ibrahim Shapiai ◽  
Faradila Naim ◽  
...  
Keyword(s):  
Objective Function ◽  
Pareto Front ◽  
Particle Swarm ◽  
Particle Swarm Optimisation ◽  
Optimal Solutions ◽  
Multiobjective Optimisation ◽  
Nondominated Solutions

The vector evaluated particle swarm optimisation (VEPSO) algorithm was previously improved by incorporating nondominated solutions for solving multiobjective optimisation problems. However, the obtained solutions did not converge close to the Pareto front and also did not distribute evenly over the Pareto front. Therefore, in this study, the concept of multiple nondominated leaders is incorporated to further improve the VEPSO algorithm. Hence, multiple nondominated solutions that are best at a respective objective function are used to guide particles in finding optimal solutions. The improved VEPSO is measured by the number of nondominated solutions found, generational distance, spread, and hypervolume. The results from the conducted experiments show that the proposed VEPSO significantly improved the existing VEPSO algorithms.

scholarly journals The dilemma between eliminating dominance-resistant solutions and preserving boundary solutions of extremely convex Pareto fronts

2021 ◽  
Author(s):  
Zhenkun Wang ◽  
Qingyan Li ◽  
Qite Yang ◽  
Hisao Ishibuchi
Keyword(s):  
Evolutionary Algorithms ◽  
Coping Strategies ◽  
Test Problem ◽  
Pareto Front ◽  
Optimization Problems ◽  
Feasible Region ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Pareto Fronts ◽  
Boundary Solutions

AbstractIt has been acknowledged that dominance-resistant solutions (DRSs) extensively exist in the feasible region of multi-objective optimization problems. Recent studies show that DRSs can cause serious performance degradation of many multi-objective evolutionary algorithms (MOEAs). Thereafter, various strategies (e.g., the $$\epsilon $$ ϵ -dominance and the modified objective calculation) to eliminate DRSs have been proposed. However, these strategies may in turn cause algorithm inefficiency in other aspects. We argue that these coping strategies prevent the algorithm from obtaining some boundary solutions of an extremely convex Pareto front (ECPF). That is, there is a dilemma between eliminating DRSs and preserving boundary solutions of the ECPF. To illustrate such a dilemma, we propose a new multi-objective optimization test problem with the ECPF as well as DRSs. Using this test problem, we investigate the performance of six representative MOEAs in terms of boundary solutions preservation and DRS elimination. The results reveal that it is quite challenging to distinguish between DRSs and boundary solutions of the ECPF.

Efficient Gradient-Based Algorithms for the Construction of Pareto Fronts

2011 ◽  
Author(s):  
Sriram Shankaran ◽  
Brian Barr
Keyword(s):  
Pareto Front ◽  
Computational Cost ◽  
High Fidelity ◽  
Simulation Tools ◽  
Pareto Points ◽  
Uniform Spacing ◽  
Design Variables ◽  
Gradient Based ◽  
Pareto Fronts ◽  
Sampling Approach

The objective of this study is to develop and assess a gradient-based algorithm that efficiently traverses the Pareto front for multi-objective problems. We use high-fidelity, computationally intensive simulation tools (for eg: Computational Fluid Dynamics (CFD) and Finite Element (FE) structural analysis) for function and gradient evaluations. The use of evolutionary algorithms with these high-fidelity simulation tools results in prohibitive computational costs. Hence, in this study we use an alternate gradient-based approach. We first outline an algorithm that can be proven to recover Pareto fronts. The performance of this algorithm is then tested on three academic problems: a convex front with uniform spacing of Pareto points, a convex front with non-uniform spacing and a concave front. The algorithm is shown to be able to retrieve the Pareto front in all three cases hence overcoming a common deficiency in gradient-based methods that use the idea of scalarization. Then the algorithm is applied to a practical problem in concurrent design for aerodynamic and structural performance of an axial turbine blade. For this problem, with 5 design variables, and for 10 points to approximate the front, the computational cost of the gradient-based method was roughly the same as that of a method that builds the front from a sampling approach. However, as the sampling approach involves building a surrogate model to identify the Pareto front, there is the possibility that validation of this predicted front with CFD and FE analysis results in a different location of the “Pareto” points. This can be avoided with the gradient-based method. Additionally, as the number of design variables increases and/or the number of required points on the Pareto front is reduced, the computational cost favors the gradient-based approach.

scholarly journals A Multiobjective Genetic Algorithm for the Localization of Optimal and Nearly Optimal Solutions Which Are Potentially Useful: nevMOGA

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-22 ◽  
Author(s):  
Alberto Pajares ◽  
Xavier Blasco ◽  
Juan M. Herrero ◽  
Gilberto Reynoso-Meza
Keyword(s):  
Genetic Algorithm ◽  
Decision Making ◽  
Decision Maker ◽  
Pareto Front ◽  
Optimization Problem ◽  
Engineering Problem ◽  
Multiobjective Optimization Problem ◽  
Optimal Solutions ◽  
Multiobjective Genetic Algorithm ◽  
Pi Controllers

Traditionally, in a multiobjective optimization problem, the aim is to find the set of optimal solutions, the Pareto front, which provides the decision-maker with a better understanding of the problem. This results in a more knowledgeable decision. However, multimodal solutions and nearly optimal solutions are ignored, although their consideration may be useful for the decision-maker. In particular, there are some of these solutions which we consider specially interesting, namely, the ones that have distinct characteristics from those which dominate them (i.e., the solutions that are not dominated in their neighborhood). We call these solutions potentially useful solutions. In this work, a new genetic algorithm called nevMOGA is presented, which provides not only the optimal solutions but also the multimodal and nearly optimal solutions nondominated in their neighborhood. This means that nevMOGA is able to supply additional and potentially useful solutions for the decision-making stage. This is its main advantage. In order to assess its performance, nevMOGA is tested on two benchmarks and compared with two other optimization algorithms (random and exhaustive searches). Finally, as an example of application, nevMOGA is used in an engineering problem to optimally adjust the parameters of two PI controllers that operate a plant.

Quantifying the Shape of Pareto Fronts During Multi-Objective Trade Space Exploration

2017 ◽  
Vol 140 (2) ◽  
Author(s):  
Mehmet Unal ◽  
Gordon P. Warn ◽  
Timothy W. Simpson
Keyword(s):  
Pareto Front ◽  
Space Exploration ◽  
Problem Formulation ◽  
Shape Index ◽  
Multi Objective ◽  
Conflicting Objectives ◽  
Complex Engineering ◽  
Trade Space Exploration ◽  
Pareto Fronts ◽  
Future Work

Recent advances in simulation and computation capabilities have enabled designers to model increasingly complex engineering problems, taking into account many dimensions, or objectives, in the problem formulation. Increasing the dimensionality often results in a large trade space, where decision-makers (DM) must identify and negotiate conflicting objectives to select the best designs. Trade space exploration often involves the projection of nondominated solutions, that is, the Pareto front, onto two-objective trade spaces to help identify and negotiate tradeoffs between conflicting objectives. However, as the number of objectives increases, an exhaustive exploration of all of the two-dimensional (2D) Pareto fronts can be inefficient due to a combinatorial increase in objective pairs. Recently, an index was introduced to quantify the shape of a Pareto front without having to visualize the solution set. In this paper, a formal derivation of the Pareto Shape Index is presented and used to support multi-objective trade space exploration. Two approaches for trade space exploration are presented and their advantages are discussed, specifically: (1) using the Pareto shape index for weighting objectives and (2) using the Pareto shape index to rank objective pairs for visualization. By applying the two approaches to two multi-objective problems, the efficiency of using the Pareto shape index for weighting objectives to identify solutions is demonstrated. We also show that using the index to rank objective pairs provides DM with the flexibility to form preferences throughout the process without closely investigating all objective pairs. The limitations and future work are also discussed.

New Dynamic Multi-Objective Constrained Optimization Evolutionary Algorithm

2015 ◽  
Vol 32 (05) ◽  
pp. 1550036 ◽  
Author(s):  
Chun-An Liu ◽  
Yuping Wang ◽  
Aihong Ren
Keyword(s):  
Constrained Optimization ◽  
Evolutionary Algorithm ◽  
Optimization Problem ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Constrained Optimization Problem ◽  
Multi Objective ◽  
Time Period ◽  
Pareto Fronts

For dynamic multi-objective constrained optimization problem (DMCOP), it is important to find a sufficient number of uniformly distributed and representative dynamic Pareto optimal solutions. In this paper, the time period of the DMCOP is first divided into several random subperiods. In each random subperiod, the DMCOP is approximately regarded as a static optimization problem by taking the time subperiod fixed. Then, in order to decrease the amount of computation and improve the effectiveness of the algorithm, the dynamic multi-objective constrained optimization problem is further transformed into a dynamic bi-objective constrained optimization problem based on the dynamic mean rank variance and dynamic mean density variance of the evolution population. The evolution operators and a self-check operator which can automatically checkout the change of time parameter are introduced to solve the optimization problem efficiently. And finally, a dynamic multi-objective constrained optimization evolutionary algorithm is proposed. Also, the convergence analysis for the proposed algorithm is given. The computer simulations are made on four dynamic multi-objective optimization test functions and the results demonstrate that the proposed algorithm can effectively track and find the varying Pareto optimal solutions or the varying Pareto fronts with the change of time.

Presorting as a method of acceleration of algorithms in multi-objective optimization problems

2016 ◽  
Vol 0 (0) ◽  
pp. 5-11
Author(s):  
Andrzej Ameljańczyk
Keyword(s):  
Distance Function ◽  
Pareto Front ◽  
Optimization Problems ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Multi Objective Optimization ◽  
Minkowski Distance ◽  
Finite Set ◽  
Feasible Solutions

The paper presents a method of algorithms acceleration for determining Pareto-optimal solutions (Pareto Front) multi-criteria optimization tasks, consisting of pre-ordering (presorting) set of feasible solutions. It is proposed to use the generalized Minkowski distance function as a presorting tool that allows build a very simple and fast algorithm Pareto Front for the task with a finite set of feasible solutions.

scholarly journals An Automated Structural Optimisation Methodology for Scissor Structures Using a Genetic Algorithm

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
Aushim Koumar ◽  
Tine Tysmans ◽  
Rajan Filomeno Coelho ◽  
Niels De Temmerman
Keyword(s):  
Genetic Algorithms ◽  
Search Space ◽  
Optimal Solutions ◽  
Multiobjective Optimisation ◽  
Nsga Ii ◽  
Design Variables ◽  
Depth Analysis ◽  
Making Choices ◽  
Optimisation Methods ◽  
Number Of Individuals

We developed a fully automated multiobjective optimisation framework using genetic algorithms to generate a range of optimal barrel vault scissor structures. Compared to other optimisation methods, genetic algorithms are more robust and efficient when dealing with multiobjective optimisation problems and provide a better view of the search space while reducing the chance to be stuck in a local minimum. The novelty of this work is the application and validation (using metrics) of genetic algorithms for the shape and size optimisation of scissor structures, which has not been done so far for two objectives. We tested the feasibility and capacity of the methodology by optimising a 6 m span barrel vault to weight and compactness and by obtaining optimal solutions in an efficient way using NSGA-II. This paper presents the framework and the results of the case study. The in-depth analysis of the influence of the optimisation variables on the results yields new insights which can help in making choices with regard to the design variables, the constraints, and the number of individuals and generations in order to obtain efficiently a trade-off of optimal solutions.

scholarly journals Evolutionary Algorithm for Multiobjective Optimization Based on Density Estimation Ranking

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Lin Li ◽  
Hengfei Wu ◽  
Xiujian Hu ◽  
Guanglei Sheng
Keyword(s):  
Evolutionary Algorithms ◽  
Multiobjective Optimization ◽  
Density Estimation ◽  
Pareto Front ◽  
Selection Criterion ◽  
Pareto Dominance ◽  
Environmental Selection ◽  
Different Shapes ◽  
Pareto Fronts ◽  
Optimal Candidate

In the past few decades, a number of multiobjective evolutionary algorithms (MOEAs) have been proposed in the continue study. As pointed out in some recent studies, the performance of the most existing MOEAs is not promising when solving different shapes of Pareto fronts. To address this issue, this paper proposes an MOEA based on density estimation ranking. The algorithm includes density estimation ranking to shift the reference solution position, calculating the density of candidate solutions and ranking by the estimated density value, to modify the Pareto dominance relation and for handling complicated Pareto front. The result of this ranking can be used as the second selection criterion for environmental selection, and the optimal candidate individual with distribution and diversity information is selected. Experimental results show that the proposed algorithm can solve various types of Pareto fronts, outperformance several state-of-the-art evolutionary algorithms in multiobjective optimization.

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