Stopping criteria in evolutionary algorithms for multi-objective performance optimization of integrated inductors

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.

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.

A ring-hierarchy-based evolutionary algorithm for multimodal multi-objective optimization

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.

Dual-space distribution metric-based evolutionary algorithm for multimodal multi-objective optimization

This study compared the performances of three state-of-theart evolutionary multi-objective optimization algorithms: the Non-Dominated Sorted Genetic Algorithm II (NSGA-II), the Epsilon-Dominance Non-Dominated Sorted Genetic Algorithm II (e -NSGA-II) and the Epsilon-Dominance Multi-Objective Evolutionary Algorithm ( e MOEA), on a constrained biobjective crop-mix planning problem (BCP). The BCP test case objectives were to: (i) maximize crop production and (ii) minimize planting area. The BCP problem was enumerated to provide the true Pareto-optimal solution set to facilitate rigorous testing of the evolutionary multi-objective optimization algorithms. The performances of the three algorithms were assessed and compared using three performance metrics (additive epsilon indicator, inverted generational distance and spacing). For the comparative study, a graphical comparison with respect to true Pareto front of optimal crop planning problem was provided. Results of the analyses indicated that the e MOEA greatly outperforms the NSGAII and the e -NSGA-II.

An innovative method for the automatic design of optical systems is presented and verified. The proposed method is based on a multi-objective evolutionary memetic optimization algorithm. The multi-objective approach simultaneously, but separately, addresses the image quality, tolerance, and complexity of the system. The memetic technique breaks down the search for optical designs in to three different parts or phases: optical glass selection, exploration, and exploitation. The optical glass selection phase defines the most appropriate set of glasses for the system under design. The glass selection phase limits the available glasses from hundreds to just a few, drastically reducing the design space and significantly increasing the efficiency of the automatic design method. The exploration phase is based on an evolutionary algorithm (EA), more specifically, on a problem-tailored generalized extremal optimization (GEO) algorithm, named Optical GEO (O-GEO). The new EA incorporates many features customized for lens design, such as optical system codification and diversity operators. The trade-off systems found in the exploration phase are refined by a local search, based on the damped least square method in the exploitation phase. As a result, the method returns a set of trade-off solutions, generating a Pareto front. Our method delivers alternative and useful insights for the compromise solutions in a lens design problem. The efficiency of the proposed method is verified through real-world examples, showing excellent results for the tested problems.

A method of designing fuzzy rule based classification systems (FRBCSs) using multi-objective optimization evolutionary algorithms (MOEAs) clearly depends on evolutionary quality. There are two types of such algorithms: Genetic Algorithms (GAs) and Swarm Intelligence (SI). Naturally arises a question how strongly utilized evolutionary algorithms influence on the efficiency of a method of designing FRBCS making this better than another. Particle swarm optimization (PSO) algorithm [13, 14] is among SI series. This paper represents an application of the multi-objective PSO algorithm with fitness sharing (MO-PSO) proposed in [8] to optimize the semantic parameters of linguistic variables and fuzzy rule selection in designing FRBCSs based on hedge algebras proposed as in [7] (using GSA-genetic simulated annealing algorithm). By simulation, MO-PSO is shown to be more efficient and produces better results than GSA-algorithm. That is to show a method of the FRBCS design is better than another one using MOEA, the same MOEA must be used.

An evolutionary algorithm for multiobjective optimization of the structural elements of the large spatial sections of ships is presented. The evolutionary algorithm where selection takes place based on the aggregated objective function combined with domination attributes as well as distance to the asymptotic solution is proposed and applied to solve the problem of optimizing structural elements with respect to their weight and surface area on a high-speed vehicle-passenger catamaran structure with several design variables such as plate thickness, scantlings of longitudinal stiffeners and transverse frames, and spacing between longitudinal and transversal structural members. Details of the computational models were at the level typical for conceptual design. Scantlings were analyzed using the selected rules of a classification society. The results of numerical experiments with the use of the developed algorithm are presented. They show that the proposed genetic algorithm can be a foundation of the effective multiobjective optimization tool for ship structure optimization. Further development of the tool should include more advanced methods for ship structural analysis.

Immunity-based hybrid evolutionary algorithm for multi-objective optimization in global container repositioning

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

In recent years, multi-objective evolutionary optimization algorithms have shown success in different areas of research. Due to their efficiency and power, many researchers have concentrated on adapting evolutionary algorithms to generate Pareto solutions. This paper proposes a new memetic adaptive multi-objective evolutionary algorithm that is based on a three-term backpropagation network (MAMOT). This algorithm is an automatic search method for optimizing the parameters and performance of neural networks, and it relies on the use of the adaptive non-dominated sorting genetic algorithm-II integrated with the backpropagation algorithm, being used as a local search method. The presented MAMOT employs a self-adaptive mechanism toward improving the performance of the proposed algorithm and a local optimizer improving all the individuals in a population in order to obtain better accuracy and connection weights. In addition, it selects an appropriate number of hidden nodes simultaneously. The proposed method was applied to 11 datasets representing pattern classification problems, including two-class, multi-class and complex data reflecting real problems. Experiments were performed, and the results indicated that the proposed method is viable in pattern classification tasks compared to a multi-objective genetic algorithm based on a three-term backpropagation network (MOGAT) and some of the methods mentioned in the literature. The statistical analysis results of the t test and Wilcoxon signed-ranks test also show that the performance of the proposed method is significantly better than MOGAT.

A software package for development, analysis and application of multiobjective evolutionary algorithms is described. The object-oriented design of this kit for evolutionary algorithms (KEA) offers a good suitable environment for various kinds of optimization tasks. It provides an interface to evaluate multi-objective fitness functions written in Java or C/C++ using a variety of multi-objective evolutionary algorithms (MOEA). In addition KEAcontains several state-of-the-art comparison methods for performance measure of algorithms. Furthermore KEAis able to display the progress of optimization in a dynamic display or just to display the results of optimization in a static visualization mode. This paper introduces the main concepts of the KEA-tool. Examples illustrate how to work with it and how to extend its functionality.

Many simple decision processes are based on a single objective such as minimizing cost, maximizing profit, minimizing runtime and so forth. However decisions must be made in an environment where more than one objective, constrains the problem, and the relative value of each of these objective is different. Such problems where multiple objectives are to be optimized are known as Multi-objective optimization (MOO) problems. The problem becomes challenging in case of mutually conflicting objectives i.e. the optimal solution widely varies with the shifting of focus from one objective to the other while all of them are quite relevant for the problem. MOO is used in various fields viz. Production Planning, Structural Design etc. There are various genetic approaches to solve multi-objective optimization problems like Non-dominated sorting GA (NSGA-II), Strength Pareto Evolutionary Approach (SPEA) etc. Each of these methods has their pros and cons and none of these is found to be perfect. In this paper we present a comparative study of the various available methods based on evolutionary genetic algorithms for Multi-Objective Optimization on different performance metrics.

Enhanced evolutionary algorithms for single and multiobjective optimization in the job shop scheduling problem