Over the last decade, a variety of evolutionary algorithms (EAs) have been proposed for solving multi-objective optimization problems. Especially more recent multi-objective evolutionary algorithms (MOEAs) have been shown to be efficient and superior to earlier approaches. In the development of new MOEAs, the strive is to obtain increasingly better performing MOEAs. An important question however is whether we can expect such improvements to converge onto a specific efficient MOEA that behaves best on a large variety of problems. The best MOEAs to date behave similarly or are individually preferable with respect to different performance indicators. In this paper, we argue that the development of new MOEAs cannot converge onto a single new most efficient MOEA because the performance of MOEAs shows characteristics of multi-objective problems. While we will point out the most important aspects for designing competent MOEAs in this paper, we will also indicate the inherent multi-objective trade-off in multi-objective optimization between proximity and diversity preservation. We will discuss the impact of this trade-off on the concepts and design of exploration and exploitation operators. We also present a general framework for competent MOEAs and show how current state-of-the-art MOEAs can be obtained by making choices within this framework. Furthermore, we show an example of how we can separate non-domination selection pressure from diversity preservation selection pressure and discuss the impact of changing the ratio between these components.

No abstract

High-Dose-Rate (HDR) brachytherapy (BT) treatment planning involves determining an appropriate schedule of a radiation source moving through a patient's body such that target volumes are irradiated with the planning-aim dose as much as possible while healthy tissues (i.e., organs at risk) should not be irradiated more than certain thresholds. Such movement of a radiation source can be defined by so-called dwell times at hundreds of potential dwell positions, which must be configured to satisfy a clinical protocol of multiple different treatment criteria within a strictly-limited time frame of not more than one hour. In this article, we propose a bi-objective optimization model that intuitively encapsulates in two objectives the complicated high-dimensional multi-criteria nature of the BT treatment planning problem. The resulting Pareto-optimal fronts exhibit possible trade-offs between the coverage of target volumes and the sparing of organs at risk, thereby intuitively facilitating the decision-making process of treatment planners when creating a clinically-acceptable plan. We employ real medical data for conducting experiments and benchmark four different Multi-Objective Evolutionary Algorithms (MOEAs) on solving our problem: the Non-dominated Sorting Genetic Algorithm II (NSGA-II), the Multi-Objective Evolutionary Algorithm based on Decomposition (MOEA/D), the Multi-objective Adapted Maximum-Likelihood Gaussian Model Iterated Density-Estimation Evolutionary Algorithm (MAMaLGaM), and the recently-introduced Multi-Objective Real-Valued Gene-pool Optimal Mixing Evolutionary Algorithm (MO-RV-GOMEA). The variation operator that is specific to MO-RV-GOMEA enables performing partial evaluations to efficiently calculate objective values of offspring solutions without incurring the cost of fully recomputing the radiation dose distributions for new treatment plans. Experimental results show that MO-RV-GOMEA is the best performing MOEA that effectively exploits dependencies between decision variables to efficiently solve the multi-objective BT treatment planning problem.

No abstract

It is known that in real-valued Single-Objective (SO) optimization with Gaussian Estimation-of-Distribution Algorithms (EDAs), it is important to take into account how distribution parameters change in subsequent generations to prevent inefficient convergence as a result of overfitting, especially if dependencies are modelled. We illustrate that in Multi-Objective (MO) optimization the risk of overfitting is even larger and only further increased if clustered variation is used, a technique often employed in Multi-Objective EDAs (MOEDAs) in the form of mixture modelling via clustering selected solutions in objective space. We point out that a technique previously used in EDAs to remove the risk of overfitting for SO optimization, the anticipated mean shift (AMS), can also be used in MO optimization if clusters in subsequent generations are registered. We propose to compute this registration explicitly. Although computationally more intensive than existing approaches, the effectiveness of AMS is thereby increased. We further propose a new clustering technique to improve mixture modelling in EDAs by 1) allowing clusters to overlap substantially and 2) assigning each cluster the same number of solutions. This allows any existing EDA to be transformed into a mixture-based version straightforwardly. Finally, we point out the benefit of injecting solutions obtained from running equal-capacity SO optimizers in synchronous parallel and investigate experimentally, using 9 well-known benchmark problems, the advantages of each of the techniques.