On the Effect of the Cooperation of Indicator-Based Multiobjective Evolutionary Algorithms

Abstract

For almost 20 years, quality indicators (QIs) have promoted the design of new selection mechanisms of multiobjective evolutionary algorithms (MOEAs). Each indicatorbased MOEA (IB-MOEA) has specific search preferences related to its baseline QI, producing Pareto front approximations with different properties. In consequence, an IB-MOEA based on a single QI has a limited scope of multi-objective optimization problems (MOPs) in which it is expected to have a good performance. This issue is emphasized when the associated Pareto front geometries are highly irregular. In order to overcome these issues, we propose here an island-based multi-indicator algorithm (IMIA) that takes advantage of the search biases of multiple IB-MOEAs through a cooperative scheme. Our experimental results show that the cooperation of multiple IB-MOEAs allows IMIA to perform more robustly (considering several QIs) than the panmictic versions of its baseline IB-MOEAs as well as several stateof-the-art MOEAs. Additionally, IMIA shows a Pareto-frontshape invariance property which makes it a remarkable optimizer when tackling MOPs with complex Pareto front geometries.

Evolutionary Many‐objective Optimization: Difficulties, Approaches, and Discussions

“…Thus, different solutions can be highly ranked by different indicators. To exploit the advantages of each indicator, a cooperative multi‐indicator‐based MOEA (cMIB‐MOEA) [43] and an island‐based multi‐indicator algorithm (IMIA) [44] employ multiple indicator‐based algorithms simultaneously. cMIB‐MOEA is based on a sequential island model, and IMIA is based on a parallel model.…”

On the utilization of pair-potential energy functions in multi-objective optimization

“…Although niching and crowding/clustering boosted the development of MOEAs, the resulting Pareto front approximations presented poor diversity in some cases. To overcome this issue, decomposition-based [40,41], reference point-based [42,43], and indicator-based MOEAs (IB-MOEAs) [44,45] are able to generate Pareto front approximations with better diversity 4 . Regarding decomposition-based MOEAs, the aim is to search for the intersection points between the Pareto front and a set of weight vectors 5 , using a scalarizing function which in turn defines a single-objective optimization problem (SOP).…”

“…Last but not least, IB-MOEAs exploit the preferences of their baseline QIs to generate Pareto front approximations with specific diversity properties. For example, the S-Metric Selection Evolutionary Multi-Objective Algorithm (SMS-EMOA) [47] produces solutions emphasizing the 4 It is worth noting that the main focus of these MOEAs is to increase the convergence ability when solving MOPs with four or more objective functions (i.e., the so-called many-objective optimization problems) but they also improve the diversity as a collateral effect. 5 Given ⃗ w ∈ R m , we say that ⃗ w is a weight vector if m i=1 w i = 1 and w i ≥ 0 for all i ∈ {1, .…”

“…In EMO, 20 the discrete Riesz α-energy function (K RSE ) [2] has been the most popularly used PPF. K RSE has been used to design a density estimator [3] and an archiving strategy [4], to measure the diversity of an approximation to the Pareto front, i.e., as a quality indicator (QI 2 ) [4], to define a combined QI [8], to man-25 age a set of weight vectors [9][10][11], and to construct a reference point set [12,13]. In addition to K RSE , other PPFs have been empirically analyzed in the EMO field [14]: Gaussian α-energy (K GAE ), Pöschl-Teller potential (K PTP ), Modified Pöschl-Teller potential K MPT ), Kratzer potential (K KRA ), and Coulomb's law 30 (K COU ).…”

Learning-Aided Evolution for Optimization

“…More significantly, EC algorithms have also made the great pace in research and applications [8]- [13]. EC algorithms were born in the 1960s, when computer scientists designed EC algorithms such as the genetic algorithm (GA) [14] [15], evolution strategy [16], and evolutionary programming [17]- [19] for solving optimization problems. Since then, EC algorithms have attracted great attention and interest in the global optimization community.…”