A Hierachical Evolutionary Algorithm for Multiobjective Optimization in IMRT

Purpose: Current inverse planning methods for IMRT are limited because they are not designed to explore the trade-offs between the competing objectives between the tumor and normal tissues. Our goal was to develop an efficient multiobjective optimization algorithm that was flexible enough to handle any form of objective function and that resulted in a set of Pareto optimal plans. Methods: We developed a hierarchical evolutionary multiobjective algorithm designed to quickly generate a diverse Pareto optimal set of IMRT plans that meet all clinical constraints and reflect the trade-offs in the plans. The top level of the hierarchical algorithm is a multiobjective evolutionary algorithm (MOEA). The genes of the individuals generated in the MOEA are the parameters that define the penalty function minimized during an accelerated deterministic IMRT optimization that represents the bottom level of the hierarchy. The MOEA incorporates clinical criteria to restrict the search space through protocol objectives and then uses Pareto optimality among the fitness objectives to select individuals. Results: Acceleration techniques implemented on both levels of the hierarchical algorithm resulted in short, practical runtimes for optimizations. The MOEA improvements were evaluated for example prostate cases with one target and two OARs. The modified MOEA dominated 11.3% of plans using a standard genetic algorithm package. By implementing domination advantage and protocol objectives, small diverse populations of clinically acceptable plans that were only dominated 0.2% by the Pareto front could be generated in a fraction of an hour. Conclusions: Our MOEA produces a diverse Pareto optimal set of plans that meet all dosimetric protocol criteria in a feasible amount of time. It optimizes not only beamlet intensities but also objective function parameters on a patient-specific basis

Evolutionary Multiobjective Optimization Driven by Generative Adversarial Networks (GANs)

Recently, increasing works have proposed to drive evolutionary algorithms using machine learning models. Usually, the performance of such model based evolutionary algorithms is highly dependent on the training qualities of the adopted models. Since it usually requires a certain amount of data (i.e. the candidate solutions generated by the algorithms) for model training, the performance deteriorates rapidly with the increase of the problem scales, due to the curse of dimensionality. To address this issue, we propose a multi-objective evolutionary algorithm driven by the generative adversarial networks (GANs). At each generation of the proposed algorithm, the parent solutions are first classified into real and fake samples to train the GANs; then the offspring solutions are sampled by the trained GANs. Thanks to the powerful generative ability of the GANs, our proposed algorithm is capable of generating promising offspring solutions in high-dimensional decision space with limited training data. The proposed algorithm is tested on 10 benchmark problems with up to 200 decision variables. Experimental results on these test problems demonstrate the effectiveness of the proposed algorithm

A new hybrid evolutionary algorithm for the treatment of equality constrained MOPs

Multi-objective evolutionary algorithms are widely used by researchers and practitioners to solve multi-objective optimization problems (MOPs), since they require minimal assumptions and are capable of computing a finite size approximation of the entire solution set in one run of the algorithm. So far, however, the adequate treatment of equality constraints has played a minor role. Equality constraints are particular since they typically reduce the dimension of the search space, which causes problems for stochastic search algorithms such as evolutionary strategies. In this paper, we show that multi-objective evolutionary algorithms hybridized with continuation-like techniques lead to fast and reliable numerical solvers. For this, we first propose three new problems with different characteristics that are indeed hard to solve by evolutionary algorithms. Next, we develop a variant of NSGA-II with a continuation method. We present numerical results on several equality-constrained MOPs to show that the resulting method is highly competitive to state-of-the-art evolutionary algorithms.Peer ReviewedPostprint (published version

ETEA: A euclidean minimum spanning tree-Based evolutionary algorithm for multiobjective optimization

© the Massachusetts Institute of TechnologyAbstract The Euclidean minimum spanning tree (EMST), widely used in a variety of domains, is a minimum spanning tree of a set of points in the space, where the edge weight between each pair of points is their Euclidean distance. Since the generation of an EMST is entirely determined by the Euclidean distance between solutions (points), the properties of EMSTs have a close relation with the distribution and position information of solutions. This paper explores the properties of EMSTs and proposes an EMST-based Evolutionary Algorithm (ETEA) to solve multiobjective optimization problems (MOPs). Unlike most EMO algorithms that focus on the Pareto dominance relation, the proposed algorithm mainly considers distance-based measures to evaluate and compare individuals during the evolutionary search. Specifically in ETEA, four strategies are introduced: 1) An EMST-based crowding distance (ETCD) is presented to estimate the density of individuals in the population; 2) A distance comparison approach incorporating ETCD is used to assign the fitness value for individuals; 3) A fitness adjustment technique is designed to avoid the partial overcrowding in environmental selection; 4) Three diversity indicators-the minimum edge, degree, and ETCD-with regard to EMSTs are applied to determine the survival of individuals in archive truncation. From a series of extensive experiments on 32 test instances with different characteristics, ETEA is found to be competitive against five state-of-the-art algorithms and its predecessor in providing a good balance among convergence, uniformity, and spread.Engineering and Physical Sciences Research Council (EPSRC) of the United Kingdom under Grant EP/K001310/1, and the National Natural Science Foundation of China under Grant 61070088

Adaptive Global WASF-GA to Handle Many-objective Optimization Problems

In this paper, a new version of the aggregation-based evolutionary algorithm Global WASF-GA (GWASF-GA) for many-objective optimization is proposed, called Adaptive Global WASF-GA (A-GWASF-GA). The fitness function of GWASF-GA is defined by an achievement scalarizing function (ASF) based on the Tchebychev distance, which considers two reference points (the nadir and utopian points) and a set of weight vectors. Despite of the benefits of using these two reference points simultaneously and a well- distributed set of weight vectors, it is necessary to go a step further to get better approximations in problems with complicated Pareto optimal fronts. For this, in A-GWASF-GA, some of the weight vectors are re-calculated during the optimization process based on the sparsity of the solutions found so far, and taking into account some theoretical results demonstrated in this paper regarding the ASF considered. Different strategies are carried out to accelerate the convergence and to maintain the diversity. The computational results, carried out in comparison with NSGA-III and different versions of MOEA/D, show the good performance of A-GWASF-GA in well-known but also in novel many-objective optimization benchmark problems.This work has been supported by the Spanish Ministry of Econ- omy and Competitiveness (project ECO2017-88883-R) co-financed by FEDER funds, and by the Regional Government of Andalucía (PAI group SEJ-532), This research has also been partially supported by grant num- bers TIN2017-88213-R (http://6city.lcc.uma.es) and RTC-2017-6714- 5 (http://ecoiot.lcc.uma.es) and by Universidad de Málaga, Campus Internacional de Excelencia Andalucía TECH. Sandra Gonzalez-Gallardo is recipient of a technical research contract within “Sistema Nacional de Garantía Juvenil y del Programa Operativo de Empleo Juvenil 2014– 2020 - Fondos FEDER” also acknowledges the training received from the University of Malaga PhD Programme in Economy and Business (Programa de Doctorado en Economía y Empresa de la Universidad de Málaga). Rubén Saborido is recipient of a Juan de la Cierva grant (refer- ence FJC2018-038537-I), funded by the Spanish State Research Agency. Ana B. Ruiz is recipient of the postdoctoral fellowship “Captación de Talento para la Investigación” at the Universidad de Málaga (Spain)

Hybrid of memory andprediction strategies for dynamic multiobjective optimization

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Dynamic multiobjective optimization problems (DMOPs) are characterized by a time-variant Pareto optimal front (PF) and/or Pareto optimal set (PS). To handle DMOPs, an algorithm should be able to track the movement of the PF/PS over time efficiently. In this paper, a novel dynamic multiobjective evolutionary algorithm (DMOEA) is proposed for solving DMOPs, which includes a hybrid of memory and prediction strategies (HMPS) and the multiobjective evolutionary algorithm based on decomposition (MOEA/D). In particular, the resultant algorithm (MOEA/D-HMPS) detects environmental changes and identifies the similarity of a change to the historical changes, based on which two different response strategies are applied. If a detected change is dissimilar to any historical changes, a differential prediction based on the previous two consecutive population centers is utilized to relocate the population individuals in the new environment; otherwise, a memory-based technique devised to predict the new locations of the population members is applied. Both response mechanisms mix a portion of existing solutions with randomly generated solutions to alleviate the effect of prediction errors caused by sharp or irregular changes. MOEA/D-HMPS was tested on 14 benchmark problems and compared with state-of-the-art DMOEAs. The experimental results demonstrate the efficiency of MOEA/D-HMPS in solving various DMOPs

On the evolutionary optimisation of many conflicting objectives

This inquiry explores the effectiveness of a class of modern evolutionary algorithms, represented by Non-dominated Sorting Genetic Algorithm (NSGA) components, for solving optimisation tasks with many conflicting objectives. Optimiser behaviour is assessed for a grid of mutation and recombination operator configurations. Performance maps are obtained for the dual aims of proximity to, and distribution across, the optimal trade-off surface. Performance sweet-spots for both variation operators are observed to contract as the number of objectives is increased. Classical settings for recombination are shown to be suitable for small numbers of objectives but correspond to very poor performance for higher numbers of objectives, even when large population sizes are used. Explanations for this behaviour are offered via the concepts of dominance resistance and active diversity promotion

Hybrid adaptive evolutionary algorithm based on decomposition

The performance of search operators varies across the different stages of the search/optimization process of evolutionary algorithms (EAs). In general, a single search operator may not do well in all these stages when dealing with different optimization and search problems. To mitigate this, adaptive search operator schemes have been introduced. The idea is that when a search operator hits a difficult patch (under-performs) in the search space, the EA scheme “reacts” to that by potentially calling upon a different search operator. Hence, several multiple-search operator schemes have been proposed and employed within EA. In this paper, a hybrid adaptive evolutionary algorithm based on decomposition (HAEA/D) that employs four different crossover operators is suggested. Its performance has been evaluated on the well-known IEEE CEC’09 test instances. HAEA/D has generated promising results which compare well against several well-known algorithms including MOEA/D, on a number of metrics such as the inverted generational distance (IGD), the hyper-volume, the Gamma and Delta functions. These results are included and discussed in this paper

The MOEADr Package – A Component-Based Framework for Multiobjective Evolutionary Algorithms Based on Decomposition

Multiobjective Evolutionary Algorithms based on Decomposition (MOEA/D) represent a widely used class of population-based metaheuristics for the solution of multicriteria optimization problems. We introduce the MOEADr package, which offers many of these variants as instantiations of a component-oriented framework. This approach contributes for easier reproducibility of existing MOEA/D variants from the literature, as well as for faster development and testing of new composite algorithms. The package offers an standardized, modular implementation of MOEA/D based on this framework, which was designed aiming at providing researchers and practitioners with a standard way to discuss and express MOEA/D variants. In this paper we introduce the design principles behind the MOEADr package, as well as its current components. Three case studies are provided to illustrate the main aspects of the package