Evolutionary Multi-objective Optimization Framework Research Articles

A systematic framework for evolutionary multi-objective optimization to complex building design problems at the early design stage

As in biology, multi-objective evolutionary algorithms cross-reference various design parameters in the search to maximize or minimize one or more specific objectives, thus finding the best solution for the specified purposes. In addition, it is possible to perform the appendment of many variables simultaneously and make numerous real-time simulations. This paper proposes a systematic framework for evolutionary multi-objective optimization to complex building design problems at the early stage. The framework is demonstrated by optimizing the courtyard geometry as a case study. The methods include generating courtyard geometry (i.e., height/width ratios and orientations) as design variables according to solar geometry. Simulations are explored, providing recommendations to maximize solar access in winter and filled shade during summer. The outcomes are a framework resumed systematically to address the contrasting objectives of the given building problems. The framework’s application can adapt to each case’s architectural, environmental, and technical criteria.

Benchmarking large-scale subset selection in evolutionary multi-objective optimization

In the field of evolutionary multi-objective optimization (EMO), the standard practice is to present the final population of an EMO algorithm as the output. However, it has been shown that the final population often includes solutions which are dominated by other solutions generated and discarded in previous generations. Recently, a novel EMO framework has been developed to solve this issue by storing all the non-dominated solutions generated during the evolution in an archive, and selecting a subset of solutions from the archive as the output. The key component of this framework is the subset selection from the archive, which typically stores a large number of candidate solutions. However, most relevant studies have focused on small candidate solution sets for environmental selection. There is no benchmark test suite for large-scale subset selection. This study aims to fill this research gap by proposing a benchmark test suite for large-scale subset selection, and providing a comparison between several representative subset selection algorithms using the proposed test suite. The proposed test suite together with the benchmarking studies provides a baseline for researchers to understand, use, compare, and develop large-scale subset selection algorithms in the EMO field.

An evolutionary multi-objective optimization framework of discretization-based feature selection for classification

Abstract Feature selection (FS) aims to identify the most relevant and non-redundant feature subset for improving the classification accuracy, which is regarded as a NP-hard problem. Some heuristic methods, such as particle swarm optimization (PSO) have achieved great success, however, with the increase of feature quantity, the solution space is too large, resulting in lower search efficiency. Recent discretization-based FS methods map the search of feature domain into cut-point domain, which shrinks the solution space and improve the performances significantly. In this paper, considering the conflicts between different objectives, we proposed an evolutionary multi-objective optimization framework for discretization-based FS. To obtain the Pareto solutions, a flexible cut-point PSO (FCPSO) which can select an arbitrary number of cut-points for discretization is introduced to help better explore the relevant features. In FCPSO, a particle update and a novel adaptive mutation operator are alternatively used to effectively find the relevant features and remove the redundant features. At last, to select the best feature subset, a Pareto ensemble method is designed to generate a number of feasible solutions based on Pareto set followed by a hierarchical solution selection process. We implemented the proposed framework by using three representative multi-objective evolutionary algorithms and compared them with some state-of-the-art methods. Experimental results on ten benchmark microarray gene datasets demonstrate that our proposed framework significantly outperforms other methods in terms of test classification accuracy with a competitive size of feature subset.

<inline-formula> <tex-math notation="LaTeX">$I_{\rm SDE}$ </tex-math> </inline-formula>+—An Indicator for Multi and Many-Objective Optimization

In this letter, an efficient indicator for multi and many-objective optimization is proposed. The proposed indicator ( $I_{{SDE}}$ +) is a combination of sum of objectives and shift-based density estimation and benefits from their ability to promote convergence and diversity, respectively. An evolutionary multiobjective optimization framework based on the proposed indicator is shown to perform comparably or better than the state-of-the-art on a variety of scalable benchmark problems.

Handling Multiple Scenarios in Evolutionary Multiobjective Numerical Optimization

Solutions to most practical numerical optimization problems must be evaluated for their performance over a number of different loading or operating conditions, which we refer here as scenarios. Therefore, a meaningful and resilient optimal solution must be such that it remains feasible under all scenarios and performs close to an individual optimal solution corresponding to each scenario. Despite its practical importance, multiscenario consideration has received a lukewarm attention, particularly in the context of multiobjective optimization. The usual practice is to optimize for the worst-case scenario. In this paper, we review existing methodologies in this direction and set our goal to suggest a new and potential population-based method for handling multiple scenarios by defining scenario-wise domination principle and scenario-wise diversity-preserving operators. To evaluate, the proposed method is applied to a number of numerical test problems and engineering design problems with a detail explanation of the obtained results and compared with an existing method. This first systematic evolutionary-based multiscenario, multiobjective optimization study on numerical problems indicates that multiple scenarios can be handled in an integrated manner using an evolutionary multiobjective optimization framework to find a well-balanced compromise set of solutions to multiple scenarios and maintain a tradeoff among multiple objectives. In comparison to an existing serial multiple optimization approach, the proposed approach finds a set of compromised tradeoff solutions simultaneously. An achievement of multiobjective tradeoff and multiscenario tradeoff is algorithmically challenging, but due to its practical appeal, further research and application must be spent.

Interrelationship-Based Selection for Decomposition Multiobjective Optimization.

Multiobjective evolutionary algorithm based on decomposition (MOEA/D), which bridges the traditional optimization techniques and population-based methods, has become an increasingly popular framework for evolutionary multiobjective optimization. It decomposes a multiobjective optimization problem (MOP) into a number of optimization subproblems. Each subproblem is handled by an agent in a collaborative manner. The selection of MOEA/D is a process of choosing solutions by agents. In particular, each agent has two requirements on its selected solution: one is the convergence toward the efficient front, the other is the distinction with the other agents' choices. This paper suggests addressing these two requirements by defining mutual-preferences between subproblems and solutions. Afterwards, a simple yet effective method is proposed to build an interrelationship between subproblems and solutions, based on their mutual-preferences. At each generation, this interrelationship is used as a guideline to select the elite solutions to survive as the next parents. By considering the mutual-preferences between subproblems and solutions (i.e., the two requirements of each agent), the selection operator is able to balance the convergence and diversity of the search process. Comprehensive experiments are conducted on several MOP test instances with complicated Pareto sets. Empirical results demonstrate the effectiveness and competitiveness of our proposed algorithm.

Efficient optimization of many objectives by approximation-guided evolution

Abstract Multi-objective optimization problems arise frequently in applications, but can often only be solved approximately by heuristic approaches. Evolutionary algorithms have been widely used to tackle multi-objective problems. These algorithms use different measures to ensure diversity in the objective space but are not guided by a formal notion of approximation. We present a framework for evolutionary multi-objective optimization that allows to work with a formal notion of approximation. This approximation-guided evolutionary algorithm (AGE) has a worst-case runtime linear in the number of objectives and works with an archive that is an approximation of the non-dominated objective vectors seen during the run of the algorithm. Our experimental results show that AGE finds competitive or better solutions not only regarding the achieved approximation, but also regarding the total hypervolume. For all considered test problems, even for many (i.e., more than ten) dimensions, AGE discovers a good approximation of the Pareto front. This is not the case for established algorithms such as NSGA-II, SPEA2, and SMS-EMOA. In this paper we compare AGE with two additional algorithms that use very fast hypervolume-approximations to guide their search. This significantly speeds up the runtime of the hypervolume-based algorithms, which now allows a comparison of the underlying selection schemes.

A general framework for evolutionary multiobjective optimization via manifold learning

Under certain mild condition, the Pareto-optimal set (PS) of a continuous multiobjective optimization problem, with m objectives, is a piece-wise continuous (m−1)-dimensional manifold. This regularity property is important, yet has been unfortunately ignored in many evolutionary multiobjective optimization (EMO) studies. The first work that explicitly takes advantages of this regularity property in EMO is the regularity model-based multiobjective estimation of distribution algorithm (RM-MEDA). However, its performance largely depends on its model parameter, which is problem dependent. Manifold learning, also known as nonlinear dimensionality reduction, is able to discover the geometric property of a low-dimensional manifold embedded in the high-dimensional ambient space. This paper presents a general framework that applies advanced manifold learning techniques in EMO. At each generation, we first use a principal curve algorithm to obtain an approximation of the PS manifold. Then, the Laplacian eigenmaps algorithm is employed to find the low-dimensional representation of this PS approximation. Afterwards, we identify the neighborhood relationship in this low-dimensional representation, which is also applicable for the original high-dimensional data. Based on the neighborhood relationship, we can interpolate new candidate solutions that obey the geometric property of the PS manifold. Empirical results validate the effectiveness of our proposal.

A Hybrid Framework for Evolutionary Multi-Objective Optimization

Evolutionary multi-objective optimization algorithms are widely used for solving optimization problems with multiple conflicting objectives. However, basic evolutionary multi-objective optimization algorithms have shortcomings, such as slow convergence to the Pareto optimal front, no efficient termination criterion, and a lack of a theoretical convergence proof. A hybrid evolutionary multi-objective optimization algorithm involving a local search module is often used to overcome these shortcomings. But there are many issues that affect the performance of hybrid evolutionary multi-objective optimization algorithms, such as the type of scalarization function used in a local search and frequency of a local search. In this paper, we address some of these issues and propose a hybrid evolutionary multi-objective optimization framework. The proposed hybrid evolutionary multi-objective optimization framework has a modular structure, which can be used for implementing a hybrid evolutionary multi-objective optimization algorithm. A sample implementation of this framework considering NSGA-II, MOEA/D, and MOEA/D-DRA as evolutionary multi-objective optimization algorithms is presented. A gradient-based sequential quadratic programming method as a single objective optimization method for solving a scalarizing function used in a local search is implemented. Hence, only continuously differentiable functions were considered for numerical experiments. The numerical experiments demonstrate the usefulness of our proposed framework.