A multiobjective optimization problem involves several conflicting objectives and has a set of Pareto optimal solutions. By evolving a population of solutions, multiobjective evolutionary algorithms (MOEAs) are able to approximate the Pareto optimal set in a single run. MOEAs have attracted a lot of research effort during the last 20 years, and they are still one of the hottest research areas in the field of evolutionary computation. This paper surveys the development of MOEAs primarily during the last eight years. It covers algorithmic frameworks such as decomposition-based MOEAs (MOEA/Ds), memetic MOEAs, coevolutionary MOEAs, selection and offspring reproduction operators, MOEAs with specific search methods, MOEAs for multimodal problems, constraint handling and MOEAs, computationally expensive multiobjective optimization problems (MOPs), dynamic MOPs, noisy MOPs, combinatorial and discrete MOPs, benchmark problems, performance indicators, and applications. In addition, some future research issues are also presented.

Multiobjective evolutionary algorithms: A survey of the state of the art

Differential Evolution (DE) is arguably one of the most powerful and versatile evolutionary optimizers for the continuous parameter spaces in recent times. Almost 5 years have passed since the first comprehensive survey article was published on DE by Das and Suganthan in 2011. Several developments have been reported on various aspects of the algorithm in these 5 years and the research on and with DE have now reached an impressive state. Considering the huge progress of research with DE and its applications in diverse domains of science and technology, we find that it is a high time to provide a critical review of the latest literatures published and also to point out some important future avenues of research. The purpose of this paper is to summarize and organize the information on these current developments on DE. Beginning with a comprehensive foundation of the basic DE family of algorithms, we proceed through the recent proposals on parameter adaptation of DE, DE-based single-objective global optimizers, DE adopted for various optimization scenarios including constrained, large-scale, multi-objective, multi-modal and dynamic optimization, hybridization of DE with other optimizers, and also the multi-faceted literature on applications of DE. The paper also presents a dozen of interesting open problems and future research issues on DE.

Recent advances in differential evolution – An updated survey

Multidisciplinary design optimization is a field of research that studies the application of numerical optimization techniques to the design of engineering systems involving multiple disciplines or components. Since the inception of multidisciplinary design optimization, various methods (architectures) have been developed and applied to solve multidisciplinary design-optimization problems. This paper provides a survey of all the architectures that have been presented in the literature so far. All architectures are explained in detail using a unified description that includes optimization problem statements, diagrams, and detailed algorithms. The diagrams show both data and process flow through the multidisciplinary system and computational elements, which facilitate the understanding of the various architectures, and how they relate to each other. A classification of the multidisciplinary design-optimization architectures based on their problem formulations and decomposition strategies is also provided, a...

Multidisciplinary design optimization: A survey of architectures

This paper provides an overview of the recent developments in data-based techniques focused on modern industrial applications. As one of the hottest research topics for complicated processes, the data-based techniques have been rapidly developed over the past two decades and widely used in numerous industrial sectors nowadays. The core of data-based techniques is to take full advantage of the huge amounts of available process data, aiming to acquire the useful information within. Compared with the well-developed model-based approaches, data-based techniques provide efficient alternative solutions for different industrial issues under various operating conditions. The main objective of this paper is to review and summarize the recent achievements in data-based techniques, especially for complicated industrial applications, thus providing a referee for further study on the related topics both from academic and practical points of view. This paper begins with a brief evolutionary overview of data-based techniques in the last two decades. Then, the methodologies only based on process measurements and the model-data integrated techniques will be further introduced. The recent developments for modern industrial applications are, respectively, presented mainly from perspectives of monitoring and control. The new trends of data-based technique as well as potential application fields are finally discussed.

Data-Based Techniques Focused on Modern Industry: An Overview

In their original versions, nature-inspired search algorithms such as evolutionary algorithms and those based on swarm intelligence, lack a mechanism to deal with the constraints of a numerical optimization problem. Nowadays, however, there exists a considerable amount of research devoted to design techniques for handling constraints within a nature-inspired algorithm. This paper presents an analysis of the most relevant types of constraint-handling techniques that have been adopted with nature-inspired algorithms. From them, the most popular approaches are analyzed in more detail. For each of them, some representative instantiations are further discussed. In the last part of the paper, some of the future trends in the area, which have been only scarcely explored, are briefly discussed and then the conclusions of this paper are presented.

http://www.cs.cinvestav.mx/~constraint/papers/swevo-mezura.pdf

Constraint-Handling in Nature-Inspired Numerical Optimization: Past, Present and Future

A new graphical visualization of n-dimensional Pareto front for decision-making in multiobjective optimization

Model-based predictive control of greenhouse climate for reducing energy and water consumption

Controller tuning using evolutionary multi-objective optimisation: Current trends and applications

In industrial applications, several objectives are often managed simultaneously (e.g., minimizing the cost and the weight of a mechanical structure satisfying some constraints). Although lots of optimization studies deal with only one objective, this approach is often not realistic for engineering optimization. Therefore, improvements in multiobjective optimization methods are required. This paper presents the formulation of a new utopia hyperplane that improves the proposal of the original normalized normal constraint method using two approaches: a redefinition of the anchor points and an exact linear transformation between the design objectives space and the normalized space. Both approaches always produce a normalized space with equal scales that improves the even distribution of the solutions over the Pareto frontier. Examples of the method proposed are presented related with mechanical engineering and structure design including a challenging non-convex Pareto frontier.

A new perspective on multiobjective optimization by enhanced normalized normal constraint method

A holistic multi-objective optimization design technique for controller tuning is presented. This approach gives control engineers greater flexibility to select a controller that matches their specifications. Furthermore, for a given controller it is simple to analyze the tradeoff achieved between conflicting objectives. By using the multi-objective design technique it is also possible to perform a global comparison between different control strategies in a simple and robust way. This approach thereby enables an analysis to be made of whether a preference for a certain control technique is justified. This proposal is evaluated and validated in a nonlinear multiple-input multiple-output system using two control strategies: a classical proportional-integral-derivative control scheme and a feedback state controller.

/pdf/controller-tuning-by-means-of-multi-objective-optimization-4ofca4xet2.pdf

Javier Sanchis

Papers

A new graphical visualization of n-dimensional Pareto front for decision-making in multiobjective optimization

Model-based predictive control of greenhouse climate for reducing energy and water consumption

Controller tuning using evolutionary multi-objective optimisation: Current trends and applications

A new perspective on multiobjective optimization by enhanced normalized normal constraint method

Controller Tuning by Means of Multi-Objective Optimization Algorithms: A Global Tuning Framework