A Survey on Learnable Evolutionary Algorithms for Scalable Multiobjective Optimization

In this paper we propose a methodology based on an evolutionary multiobjective optimization algorithm for the problem of up-grading (expansion) the physical topology of transparent optical networks. The aim is to define the new topology layout and the specification of the new optical devices that should be deployed in an existing network in order to improve its performance, considering simultaneously the total installation cost (capital cost) and the total network blocking probability (performance criteria). To accomplish that, we propose a capital cost model for the network. We considered the following physical layer impairments: losses in optical devices, amplified spontaneous emission in optical amplifier and homodyne crosstalk in optical cross connect. The multiobjective optimization evolutionary algorithm used in the optimization process is the NSGA-II. Our proposed methodology can solve the expand physical topology design problem taking into account the physical layer impairments and the capital costs simultaneously. We also present a case study to show the effectiveness of our methodology.

A fast sampling based evolutionary algorithm for million-dimensional multiobjective optimization

A performance comparison of multi-objective optimization algorithms for solving nearly-zero-energy-building design problems

Evolutionary algorithms have been widely used to tackle multi-objective optimization problems. Despite many successful applications there is a lack of theoretical knowledge on how and why this type of algorithm works particularly well for multi-objective problems. This special issue presents current advances to the theoretical understanding of evolutionary algorithms for multi-objective optimization. It comprises four very high quality papers which have been selected via a rigorous reviewing process. The first paper “On the Effect of Populations in Evolutionary Multi-Objective Optimisation” by Oliver Giel and Per Kristian Lehre studies the basic question whether a population is provably useful to compute the whole Pareto front of a multi-objective optimization problem. They compare restart strategies of several single-objective approaches based on one individual to a natural multi-objective approach using a population. Their analyses point out the benefits of the multi-objective evolutionary algorithm in a rigorous way. Using illustrative example functions they provide not only proven results but also a good intuition about why population-based approaches can outperform individual-based approaches in multi-objective optimization. The paper “Exploring the Runtime of an Evolutionary Algorithm for the Multi-Objective Shortest Path Problem” by Christian Horoba examines the behavior of evolutionary algorithms for the classical NP-hard multi-objective shortest path problem. The author considers an evolutionary approach based on -dominance and proves that this algorithm constitutes a fully polynomial-time randomized approximation scheme (FPRAS) for the problem. The algorithm achieves this by mimicking a problemspecific algorithm for that problem. This provides general insight into why evolutionary algorithms can perform well for problems that allow for efficient problem-specific algorithms. Hypervolume-based algorithms have become very popular in evolutionary multiobjective optimization. In the paper, “An Efficient Algorithm for Computing Hypervolume Contributions,” Karl Bringmann and Tobias Friedrich present a faster algorithm for determining the individual with the smallest hypervolume contribution in a given population. Furthermore, they study the problem of removing λ > 1 individuals with the smallest hypervolume contribution from a given population and present an elegant and fast method to carry out this task.

An Enhanced multi-objective evolutionary optimization algorithm based on decomposition (E-MOEA-D) proposed for optimal placement of Distributed Generation (DG) and Electric Vehicle (EV) Fast Charging Station (FCS) in distribution system. The diversity of the evolutionary algorithm improves the convergence and diverse solution in the process of evolutionary optimization. The proposed algorithm is improved using enhanced diversity algorithm, which yield diverse candidate solutions in population. The optimal placement of DGs and FCS are formulated using three objective functions as i) Active power loss ii) Voltage deviation iii) DG cost. The proposed algorithm is simulated on IEEE-33 bus distribution system. The proposed algorithm is compared with other competitive multi-objective evolutionary algorithms such as decomposition based multi-objective evolutionary algorithm (MOEA-D) and Non-dominated sorting multi-objective evolutionary algorithm (NSGA-II).

Despite the success of Evolutionary Algorithms in solving complex problems, they may require many function evaluations. This becomes an issue when dealing with costly problems. Surrogate models may overcome this difficulty, though their use in problems with medium to large dimensionality is underexplored in the literature. Problems with multiple conflicting objectives can be formulated as Multi-objective Optimization Problems (MOPs). MOPs have received a great attention lately, mainly with Multi-objective Evolutionary Algorithms (MOEAs). This paper proposes ELMOEA/D-DE, a surrogate-assisted MOEA, for solving expensive MOPs in small evaluation budgets. ELMOEA/D-DE encompasses a state-of-the-art MOEA based on decomposition, Differential Evolution (DE) operators and Extreme Learning Machines. This paper tests three variants of ELMOEA/D-DE, using different DE operators, for solving five known benchmark MOPs with 10 to 60 decision variables. All variants achieve good results in terms of hyper volume metric and the best variant with operator DE/rand/1/bin is compared with two state-of-the-art approaches (MOEA/D-RBF and a non-surrogate-based MOEA), achieving the best results in all but one problems instances.

Parameter-less Pareto local search for multi-objective neural architecture search with the Interleaved Multi-start Scheme

In multi-objective optimization problems (MOPs), set-based performance indicators are commonly used to assess the convergence and diversity of Pareto front approximation. Performance indicators can be used as the selection strategies. The selection strategy of indicator based evolutionary multi-objective algorithms (EMOAs) is guided by a general preference information, which maps objectives into a single contribution value by means of a set of utility functions. R2-EMOA is one of the most important indicator-based algorithms to solve MOPs. We use fast R2-ranking to rank the individuals of EMOAs. This paper suggests a new weight generator strategy, which is based on direction angles, for MOPs. Our main purpose is to explore the relationship among direction angles, weight vectors and direction vectors. Our proposed weight generator scheme is incorporated to two different search engines, resulting in two new EMOAs, named IR2-MOGA and IR2-MODE. The performance of our proposed method is validated and compared with other R2-EMOAs on a number of unconstraint benchmark problems. Experimental results demonstrate that our algorithms can significantly improve the convergence and diversity of R2-EMOA.

Evolutionary algorithm has gained a worldwide popularity among multi-objective optimization. The paper proposes a self-adaptive evolutionary algorithm (called SEA) for multi-objective optimization. In the SEA, the probability of crossover and mutation, P cand P m, are varied depending on the fitness values of the solutions. Fitness assignment of SEA realizes the twin goals of maintaining diversity in the population and guiding the population to the true Pareto Front; fitness value of individual not only depends on improved density estimation but also depends on non-dominated rank. The density estimation can keep diversity in all instances including when scalars of all objectives are much different from each other. SEA is compared against the Non-dominated Sorting Genetic Algorithm (NSGA-II) on a set of test problems introduced by the MOEA community. Simulated results show that SEA is as effective as NSGA-II in most of test functions, but when scalar of objectives are much different from each other, SEA has better distribution of non-dominated solutions.

In a real life situation, due to the complexity of the industrial systems and non-linearity of their behavior, it is very difficult to achieve optimum performance of system for desired industrial goals using uncertain, vague and imprecise data. Herein, an approach has been proposed through which the behavior of the system is analyzed in the form of well- known six reliability indices by using triangular fuzzy numbers which allow the consideration of expert opinions, linguistic variables, operating conditions in reliability information. Using their behavior analysis a fuzzy multi-objective optimization problem (FMOOP) has been formulated. Due to the conflicting nature of the multiple objectives, the decision making is difficult and it leads to the Pareto optimal solutions instead of single optimal solutions. Many evolutionary algorithms (EAs) already exist in the literature for solving a multi-objective optimization problem (MOOP), and are termed as multi-objective evolutionary algorithms (MOEAs). Particle swarm optimization (PSO) is one of such MOEA which demonstrates the ability to identity a Pareto-optimal front efficiently. Here, a crisp optimization problem is reformulated from FMOOP by taking into account the preference of decision maker (DM) and then PSO is applied to solve the resulting fuzzified MOOP. The presented approach is applied in order to solve the multi-objective series-parallel system reliability optimization problem for a crystallization unit of a urea plant.

Various evolutionary multiobjective optimization (EMO) algorithms have been used in the field of evolutionary fuzzy systems (EFS), because EMO algorithms can easily handle multiple objective functions such as the accuracy maximization and complexity minimization for fuzzy system design. Most EMO algorithms used in EFS are Pareto dominance-based algorithms such as NSGA-II, SPEA2, and PAES. There are a few studies where other types of EMO algorithms are used in EFS. In this paper, we apply a multiobjective evolutionary algorithm based on decomposition called MOEA/D to EFS for fuzzy classifier design. MOEA/D is one of the most well-known decomposition-based EMO algorithms. The key idea is to divide a multiobjective optimization problem into a number of single-objective problems using a set of uniformly distributed weight vectors in a scalarizing function. We propose a new scalarizing function called an accuracy-oriented function (AOF) which is specialized for classifier design. We examine the effects of using AOF in MOEA/D on the search ability of our multiobjective fuzzy genetics-based machine learning (GBML). We also examine the synergy effect of MOEA/D with AOF and parallel distributed implementation of fuzzy GBML on the generalization ability.

An improved multiobjective differential evolution based on Pareto-adaptive -dominance and orthogonal design

Many real-world optimization problems are characterized by multiple conflicting objectives, which are known as multi-objective optimization problems (MOPs). In the last two decades, evolutionary algorithms have shown promising performance in solving various MOPs, and a large number of multi-objective evolutionary algorithms (MOEAs) have been proposed. In order to determine the most suitable MOEA for a specific MOP, it is usually necessary to perform experiments to compare the performance of multiple candidate MOEAs. In 2017, an evolutionary multi-objective optimization platform was proposed by us, called PlatEMO, which provides the source codes of many state-of-the-art MOEAs and helps researchers perform batch experiments on these MOEAs. In this work, we illustrate the method of using the newest version of PlatEMO to solve MOPs in applications, by means of a case study on the feature selection problem, which is an important and difficult task in machine learning and data mining. This paper details the method of adding the feature selection problem to PlatEMO, and presents the experimental results of eight MOEAs on nine datasets in feature selection.

Multi-objective optimization problems can be divided into continuous multi-objective optimization problems and discrete multi-objective optimization problems, and discrete multi-objective optimization is not universal. In practical applications, there are many discrete multi-objective optimization problems. The solution of different problems needs to design different evolutionary multi-objective algorithms according to their specific conditions. The threshold in the traditional multi-objective optimization of wireless network is a preset constant. It has relatively poor performance in the synthesis of images with different noise levels. An adaptive wireless network multi-objective optimization algorithm based on image synthesis is proposed. Based on the maximum inter class variance and maximum peak signal to noise ratio (SNR), an adaptive wireless network multi-objective optimization algorithm is established. The accuracy and noise immunity of image synthesis are also considered. In order to avoid the effect of threshold increase on algorithm efficiency, multi-objective optimization algorithm is introduced into the algorithm. Experiments show that the method proposed in this paper is accurate and robust and has good universality for the synthesis of different noise images.

Digital IIR filter design using multi-objective optimization evolutionary algorithm