Heiner Zille

Weighted Optimization Framework for Large-scale Multi-objective Optimization

In this work we introduce a new method for solving multi-objective optimization problems that involve a large number of decision variables. The proposed Weighted Optimization Framework (WOF) relies on variable grouping and weighting to transform the original optimization problem and is designed as a generic method that can be used with any population-based algorithm. Our experiments use the WFG benchmark problems with 2 and 3 objectives and 1000 variables. Using WOF on two well-known algorithms (NSGA-II and SMPSO), we show that our method can significantly improve their performance on all of the test problems.

Properties of scalable Distance Minimization Problems using the Manhattan metric

In multi-objective optimization, scalable test problems are required to test and compare the search abilities of the algorithms in solving large and small-dimensional problems. In this paper, we analyze a generalized Distance Minimization Problem (DMP) that is scalable in the number of decision variables and objectives and can be used with any distance function. Since previous research mostly regarded the behaviour of algorithms for Euclidean distances, in this work, we propose to use the Manhattan metric to measure the distances of solutions towards a set of predefined locations in the decision space. The structure of the Pareto-fronts of this problem widely differ from those of the euclidean problem. We perform an analytical analysis exemplary for low-dimensional instances of the problem to provide an understanding of the general properties and structure, and the challenges that might arise in many-objective many-variable instances. The negative effects on the search behaviour of algorithms are theoretically described, and three different optimization methods (MOEA/D, NSGA-II, SMPSO) are tested to give an understanding of different instances of the problem. The experimental results support our expectations and show that the proposed Manhattan metric DMP is difficult to solve for optimization algorithms even in low-dimensional spaces.

A Framework for Large-Scale Multiobjective Optimization Based on Problem Transformation

In this paper, we propose a new method for solving multiobjective optimization problems with a large number of decision variables. The proposed method called weighted optimization framework is intended to serve as a generic method that can be used with any population-based metaheuristic algorithm. After explaining some general issues of large-scale optimization, we introduce a problem transformation scheme that is used to reduce the dimensionality of the search space and search for improved solutions in the reduced subspace. This involves so-called weights that are applied to alter the decision variables and are also subject to optimization. Our method relies on grouping mechanisms and employs a population-based algorithm as an optimizer for both original variables and weight variables. Different grouping mechanisms and transformation functions within the framework are explained and their advantages and disadvantages are examined. Our experiments use test problems with 2–3 objectives 40–5000 variables. Using our approach on three well-known algorithms and comparing its performance with other large-scale optimizers, we show that our method can significantly outperform most existing methods in terms of solution quality as well as convergence rate on almost all tested problems for many-variable instances.

Mutation operators based on variable grouping for multi-objective large-scale optimization

In this paper, we study the influence of using variable grouping inside mutation operators for large-scale multi-objective optimization. We introduce three new mutation operators based on the well-known Polynomial Mutation. The variable grouping in these operators is performed using two different grouping mechanisms, including Differential Grouping from the literature. In our experiments, two popular algorithms (SMPSO and NSGA-II) are used with the proposed operators on the WFG1-9 test problems. We examine the performance of the proposed mutation operators and take a look at the impact of the different grouping mechanisms on the performance. Using the Hypervolume and IGD indicators, we show that mutation using variable grouping can significantly improve the results on all tested problems in terms of both convergence and diversity of solutions. Furthermore, the performance of SMPSO and NSGA-II with the proposed operators is compared with a large-scale multi-objective algorithm (CCGDE3). The results show that the proposed operators can significantly outperform CCGDE3.

Transfer strategies from single- to multi-objective grouping mechanisms

In large-scale optimisation, most algorithms require a separation of the variables into multiple smaller groups and aim to optimise these variable groups independently. In single-objective optimisation, a variety of methods aim to identify best variable groups, most recently the Differential Grouping 2. However, it is not trivial to apply these methods to multiple objectives, as the variable interactions might differ between objective functions. In this work, we introduce four different transfer strategies that allow to use any single-objective grouping mechanisms directly on multi-objective problems. We apply these strategies to a popular single-objective grouping method (Differential Grouping 2) and compare the performance of the obtained groups inside three recent large-scale multi-objective algorithms (MOEA/DVA, LMEA, WOF). The results show that the performance of the original MOEA/DVA and LMEA can in some cases be improved by our proposed grouping variants or even random groups. At the same time the computational budget is dramatically reduced. In the WOF algorithm, a significant improvement in performance compared to random groups or the standard version of the algorithm can on average not be observed.

Dynamic Distance Minimization Problems for dynamic multi-objective optimization

In this article we propose a new dynamic multi-objective optimization problem. This dynamic Distance Minimization Problem (dDMP) functions as a benchmark problem for dynamic multi-objective optimization and is based on the static versions from the literature. The dDMP introduces a useful property and challenge for dynamic multi-objective algorithms. Not only the positions of the Pareto-optimal solutions in the search space change over time, but also the complexity of the problem can be adjusted dynamically. In addition the problem is based on a simple geometric structure, which makes it useful to visualize the search behaviour of algorithms. We describe the basic principles of the problem, and introduce the possible dynamic changes and their implementation and effects of the Pareto-optimal areas. Our experiments show how a possible instance of the dynamic DMP can be defined and how different algorithms react to the dynamic changes.

Elitism and aggregation methods in partial redundant evolutionary swarms solving a multi-objective tasks

In evolutionary swarms adaptability and diversity are closely related concepts. In order to get a better understanding of their codependency we study a heterogeneous evolutionary multi-agent system with different rates of redundancy within the genetic material. The agents process a dynamic multi-objective task, where their genetic material defines their efficiency concerning the different objective functions of that task. One focus of this study is the influence of an elitist behavior performed by the agents during the evolutionary process, where an agent can decline the genetic material of another agent if it does not meet specific requirements. Further we analyze the impact of three different methods to aggregate the objective values into a single fitness value that is applicable for the evolutionary mechanism of the system. The results show that heterogeneity in the optimization behavior of the agents is very beneficial as it maintains a higher diversity in the system. The elitist behavior of the agents slows the evolutionary process but gives it a stronger pull towards qualitatively higher positions in the objective space. Indeed, the pace of the evolutionary process ultimately has a higher impact on the adaptability of the system than the amount of redundancy in the genetic information.

Multi-objective fitness-proportional attraction approach with weights

This paper proposes a new multi-objective optimization algorithm that is called Fitness-Proportional Attraction with Weights (F-PAW). In contrast to many other approaches, this work was inspired by physics rather than biology. It is based on concepts from several methods, including the attraction principle of gravity from the Gravitational Search Algorithm (GSA), the weight sum approach from Multi-Objective Evolutionary Algorithm based on Decomposition (MOEA/D) as well as particle swarm optimization methods. These and other algorithms that were providing inspiration are introduced during the text and their techniques are investigated for the use in F-PAW. The performance of F-PAW is compared to three well-known multi-objective algorithms through an experiment on 16 common test problems taken from the WFG and DTLZ benchmarks. The results indicate two conclusions. On the one side, the proposed approach with the weight sum obtains a good diversity. On the other side, the currently implemented local search is lacking reliability and speed.

Functional brain network extraction using a genetic algorithm with a kick-out method

This paper proposed the method to reduce the calculating time to reveal the functional brain network associated with a task using a genetic algorithm and functional near-infrared spectroscopy (fNIRS) data. Changes in the cerebral blood flow during a task are obtained as time series data is analyzed using fNIRS, and a correlation matrix for multiple fNIRS channels is created for each subject. The subject group is divided into two groups, and a classifier of the two groups learns the correlation matrix as a feature quantity. The correlation matrix changes as the feature quantity changes with the combinations of channels, which affects classifier accuracy. If the combination of channels with the best classifier accuracy is identified, these channels can be considered important to the creation of the functional brain network for a target task. In our study, a genetic algorithm (GA) is used for channel selection. However, learning the classifier to calculate the evaluation value and optimization by the GA requires significant time. Thus, to increase search efficiency, we propose the kick-out method to skip the evaluation value calculation for poor individuals according to a previous evaluation value. We evaluated the effectiveness of the proposed method using fNIRS data recorded during a mental rotation test. Results show that important channels that express the functional brain network were selected and that processing time was reduced significantly by the proposed method.

Using ?-Dominance for Hidden and Degenerated Pareto-Fronts

Scalable multi-objective test problems are known to be useful in testing and analyzing the abilities of algorithms. In this paper we focus on test problems with degenerated Pareto-fronts and provide an in-depth insight into the properties of some problems which show these characteristics. In some of the problems with degenerated fronts such as Distance Minimization Problem (DMP) with the Manhattan metric, it is very difficult to dominate some of the non-optimal solutions as the optimal solutions are hidden within a set of so called pseudo-optimal solutions. Hence the algorithms based on Pareto-domination criterion are shown to be inefficient. In this paper, we explore the pseudo-optimal solutions and examine how and why the use of ε-dominance can help to achieve a better approximation of the hidden Pareto-fronts or of degenerated fronts in general. We compare the performance of the ε-MOEA with 3 other algorithms (NSGA-II, NSGA-III and MOEA/D) and show that ε- dominance performs better when dealing with pseudo-optimal kind of solutions. Furthermore, we analyze the performance on the WFG3 test problem and illustrate the advantages and disadvantages of ε-dominance for this degenerated problem.