Indicator-based Multi-objective Evolutionary Algorithms

Abstract

For over 25 years, most multi-objective evolutionary algorithms (MOEAs) have adopted selection criteria based on Pareto dominance. However, the performance of Pareto-based MOEAs quickly degrades when solving multi-objective optimization problems (MOPs) having four or more objective functions (the so-called many-objective optimization problems), mainly because of the loss of selection pressure. Consequently, in recent years, MOEAs have been coupled with indicator-based selection mechanisms in furtherance of increasing the selection pressure so that they can properly solve many-objective optimization problems. Several research efforts have been conducted since 2003 regarding the design of the so-called indicator-based (IB) MOEAs. In this article, we present a comprehensive survey of IB-MOEAs for continuous search spaces since their origins up to the current state-of-the-art approaches. We propose a taxonomy that classifies IB-mechanisms into two main categories: (1) IB-Selection (which is divided into IB-Environmental Selection, IB-Density Estimation, and IB-Archiving) and (2) IB-Mating Selection. Each of these classes is discussed in detail in this article, emphasizing the advantages and drawbacks of the selection mechanisms. In the final part, we provide some possible paths for future research.

Optimizing viral genome subsampling by genetic diversity and temporal distribution (TARDiS) for Phylogenetics

“…To generate a novel individual, TARDiS uses three operators: selection, mutation, and crossover. The selection operator is based on deterministic tournament selection with k = 5 [3]. Briefly, two sets of k individuals are randomly chosen, and the individual with the highest fitness is selected from each set.…”

“…The crossover operator combines two tournament winners A and B into a new individual C by keeping the all the g genomes ∈ (A ∪ B), and randomly selecting n−g 2 genomes ∈ (A ∩ B) − (A ∪ B). To help avoid local maxima, each newly generated individual C has a 0.08 probability of mutating [9,3]. A mutation is defined as swapping a genome of individual C with one randomly chosen from the remaining, non-(A|B) genome pool.…”

Multi-Objective Ant Lion Optimizer Based on Time Weight

“…Multi-objective optimization problems widely exist in many real-world applications, such as job scheduling, route planning, wireless sensor deployment, virtual machine placement [1]. Multi-objective evolutionary algorithms (MOEAs) are approaches which simulate biological swarm behaviors and could resolve multi-objective optimization issues effectively.…”

An Ensemble Indicator-Based Density Estimator for Evolutionary Multi-objective Optimization

“…There exist four main design methodologies for MOEAs [1]: (1) MOEAs using the Pareto dominance relation or any of its relaxed forms, (2) decompositionbased MOEAs, (3) reference set-based MOEAs, and (4) indicator-based MOEAs (IB-MOEAs). In the last fifteen years, IB-MOEAs have attracted considerable attention due to their ability to solve MOPs having more than three objective functions (i.e., the so-called many-objective optimization problems) [2]. The underlying idea of IB-MOEAs is the use of a quality indicator (QI) [3], which is a set function that evaluates the quality of an approximation set based on specific preferences, in order to guide the evolutionary search process by focusing on the selection mechanisms.…”

“…The underlying idea of IB-MOEAs is the use of a quality indicator (QI) [3], which is a set function that evaluates the quality of an approximation set based on specific preferences, in order to guide the evolutionary search process by focusing on the selection mechanisms. Currently, there exist several QIs, such as the hypervolume indicator (HV) [4], R2 [5], the inverted generational distance plus (IGD + ) [6], the additive epsilon indicator (✏ + ) [7], and the averaged Hausdor↵ distance ( p ) [8], being these ones the most popular within the currently available IB-MOEAs [2].…”