Improved sampling of the pareto-front in multiobjective genetic optimizations by steady-state evolution: a Pareto converging genetic algorithm

Previous work on multiobjective genetic algorithms has been focused on preventing genetic drift and the issue of convergence has been given little attention. In this paper, we present a simple steady-state strategy, Pareto Converging Genetic Algorithm (PCGA), which naturally samples the solution space and ensures population advancement towards the Pareto-front. PCGA eliminates the need for sharing/niching and thus minimizes heuristically chosen parameters and procedures. A systematic approach based on histograms of rank is introduced for assessing convergence to the Pareto-front, which, by definition, is unknown in most real search problems. We argue that there is always a certain inheritance of genetic material belonging to a population, and there is unlikely to be any significant gain beyond some point; a stopping criterion where terminating the computation is suggested. For further encouraging diversity and competition, a nonmigrating island model may optionally be used; this approach is particularly suited to many difficult (real-world) problems, which have a tendency to get stuck at (unknown) local minima. Results on three benchmark problems are presented and compared with those of earlier approaches. PCGA is found to produce diverse sampling of the Pareto-front without niching and with significantly less computational effort

Statistical Methods for Convergence Detection of Multi-Objective Evolutionary Algorithms

In this paper, two approaches for estimating the generation in which a multi-objective evolutionary algorithm (MOEA) shows statistically significant signs of convergence are introduced. A set-based perspective is taken where convergence is measured by performance indicators. The proposed techniques fulfill the requirements of proper statistical assessment on the one hand and efficient optimisation for real-world problems on the other hand. The first approach accounts for the stochastic nature of the MOEA by repeating the optimisation runs for increasing generation numbers and analysing the performance indicators using statistical tools. This technique results in a very robust offline procedure. Moreover, an online convergence detection method is introduced as well. This method automatically stops the MOEA when either the variance of the performance indicators falls below a specified threshold or a stagnation of their overall trend is detected. Both methods are analysed and compared for two MOEA and on different classes of benchmark functions. It is shown that the methods successfully operate on all stated problems needing less function evaluations while preserving good approximation duality at the same time.Article / Letter to editorLeiden Inst. Advanced Computer Science

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

Effective and efficient algorithm for multiobjective optimization of hydrologic models

Practical experience with the calibration of hydrologic models suggests that any single-objective function, no matter how carefully chosen, is often inadequate to properly measure all of the characteristics of the observed data deemed to be important. One strategy to circumvent this problem is to define several optimization criteria (objective functions) that measure different (complementary) aspects of the system behavior and to use multicriteria optimization to identify the set of nondominated, efficient, or Pareto optimal solutions. In this paper, we present an efficient and effective Markov Chain Monte Carlo sampler, entitled the Multiobjective Shuffled Complex Evolution Metropolis (MOSCEM) algorithm, which is capable of solving the multiobjective optimization problem for hydrologic models. MOSCEM is an improvement over the Shuffled Complex Evolution Metropolis (SCEM-UA) global optimization algorithm, using the concept of Pareto dominance (rather than direct single-objective function evaluation) to evolve the initial population of points toward a set of solutions stemming from a stable distribution (Pareto set). The efficacy of the MOSCEM-UA algorithm is compared with the original MOCOM-UA algorithm for three hydrologic modeling case studies of increasing complexity

Metaheuristic optimization of power and energy systems: underlying principles and main issues of the 'rush to heuristics'

In the power and energy systems area, a progressive increase of literature contributions containing applications of metaheuristic algorithms is occurring. In many cases, these applications are merely aimed at proposing the testing of an existing metaheuristic algorithm on a specific problem, claiming that the proposed method is better than other methods based on weak comparisons. This 'rush to heuristics' does not happen in the evolutionary computation domain, where the rules for setting up rigorous comparisons are stricter, but are typical of the domains of application of the metaheuristics. This paper considers the applications to power and energy systems, and aims at providing a comprehensive view of the main issues concerning the use of metaheuristics for global optimization problems. A set of underlying principles that characterize the metaheuristic algorithms is presented. The customization of metaheuristic algorithms to fit the constraints of specific problems is discussed. Some weaknesses and pitfalls found in literature contributions are identified, and specific guidelines are provided on how to prepare sound contributions on the application of metaheuristic algorithms to specific problems

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

Metaheuristic Optimization of Power and Energy Systems: Underlying Principles and Main Issues of the `Rush to Heuristics'

In the power and energy systems area, a progressive increase of literature contributions that contain applications of metaheuristic algorithms is occurring. In many cases, these applications are merely aimed at proposing the testing of an existing metaheuristic algorithm on a specific problem, claiming that the proposed method is better than other methods that are based on weak comparisons. This ‘rush to heuristics’ does not happen in the evolutionary computation domain, where the rules for setting up rigorous comparisons are stricter but are typical of the domains of application of the metaheuristics. This paper considers the applications to power and energy systems and aims at providing a comprehensive view of the main issues that concern the use of metaheuristics for global optimization problems. A set of underlying principles that characterize the metaheuristic algorithms is presented. The customization of metaheuristic algorithms to fit the constraints of specific problems is discussed. Some weaknesses and pitfalls that are found in literature contributions are identified, and specific guidelines are provided regarding how to prepare sound contributions on the application of metaheuristic algorithms to specific problems

Statistical Methods for Convergence Detection of Multi-Objective Evolutionary Algorithms

In this paper, two approaches for estimating the generation in which a multi-objective evolutionary algorithm (MOEA) shows statistically significant signs of convergence are introduced. A set-based perspective is taken where convergence is measured by performance indicators. The proposed techniques fulfill the requirements of proper statistical assessment on the one hand and efficient optimisation for real-world problems on the other hand. The first approach accounts for the stochastic nature of the MOEA by repeating the optimisation runs for increasing generation numbers and analysing the performance indicators using statistical tools. This technique results in a very robust offline procedure. Moreover, an online convergence detection method is introduced as well. This method automatically stops the MOEA when either the variance of the performance indicators falls below a specified threshold or a stagnation of their overall trend is detected. Both methods are analysed and compared for two MOEA and on different classes of benchmark functions. It is shown that the methods successfully operate on all stated problems needing less function evaluations while preserving good approximation duality at the same time.FWN – Publicaties zonder aanstelling Universiteit Leide