Evolutionary Multi-Objective Optimization: Basic Concepts and Some Applications in Pattern Recognition

Abstract

Abstract. This paper provides a brief introduction to the so-called multi-objective evolutionary algorithms, which are bio-inspired metaheuristics designed to deal with problems having two or more (normally conflicting) objectives. First, we provide some basic concepts related to multi-objective optimization and a brief review of approaches available in the specialized literature. Then, we provide a short review of applications of multi-objective evolutionary algorithms in pattern recognition. In the final part of the paper, we provide some possible paths for future research in this area, which are promising, from the author's perspective.

A Parallel Technique for Multi-objective Bayesian Global Optimization: Using a Batch Selection of Probability of Improvement

“…Pareto dominance, or briefly dominance, is an ordering relationship on a set of potential solutions. Dominance is defined as follows: Definition 3.1 (Dominance -≺ [36]) Given two decision vectors x (1) , x (2) ∈ R d and their corresponding objective values y (1) = f (x (1) ), y (2) = f (x (2) ) in a minimization problem, it is said that y (1) dominates y (2) , being represented by y (1) ≺ y (2) , iff ∀i ∈ {1, 2, • • • , m} : f i (x (1) ) ≤ f i (x (2) ) and ∃j ∈ {1, 2, • • • , m} : f j (x (1) ) < f j (x (2) ). Definition 3.2 (Non-Dominated Space of a Set [37]) Let PF be a subset of R m and let a reference point r ∈ R m be such that ∀p ∈ PF : p ≺ r. The non-dominated space of PF with respect to r, denoted as ndom(PF), is then defined as:…”

Efficient computation of expected hypervolume improvement using box decomposition algorithms

“…Definition 1 (Dominance [4]) Given two decision vectors x (1) , x (2) ∈ R m and their corresponding objective values y (1) = y(x (1) ), y (2) = y(x (2) ) in a maximization problem, it is said that y (1) dominates y (2) , being represented by y (1) ≺ y (2) , iff ∀i ∈ {1, 2, · · · , d} : y i (x (1) ) ≥ y i (x (2) ) and ∃j ∈ {1, 2, · · · , d} : y j (x (1) ) > y j (x (2) ).…”

“…3 Initialize the number of integration slices n b = 1; 4 Initialize EHV I = 0; 5 for i = 2 to n + 1 do / * Main loop * / 6 Retrieve the following information from tree T: .…”

“…(2) = (4, 2, 3) , y (3) = (2, 4, 2) and y(4) =(3, 5, 1) ), and this Pareto front is shown in the upper left figure. The upper right figure represents the partitioned integration slices of P. The lower center figure illustrates the projection of the upper right figure onto the y 1 y 2 -plane with rectangle slices and l, u.…”