Hybrid non-dominated sorting genetic algorithm with adaptive operators selection

Multiobjective optimization entails minimizing or maximizing multiple objective functions subject to a set of constraints. Many real world applications can be formulated as multi-objective optimization problems (MOPs), which often involve multiple conflicting objectives to be optimized simultaneously. Recently, a number of multi-objective evolutionary algorithms (MOEAs) were developed suggested for these MOPs as they do not require problem specific information. They find a set of non-dominated solutions in a single run. The evolutionary process on which they are based, typically relies on a single genetic operator. Here, we suggest an algorithm which uses a basket of search operators. This is because it is never easy to choose the most suitable operator for a given problem. The novel hybrid non-dominated sorting genetic algorithm (HNSGA) introduced here in this paper and tested on the ZDT (Zitzler-Deb-Thiele) and CEC’09 (2009 IEEE Conference on Evolutionary Computations) benchmark problems specifically formulated for MOEAs. Numerical results prove that the proposed algorithm is competitive with state-of-the-art MOEAs

Interval-based ranking in noisy evolutionary multiobjective optimization

As one of the most competitive approaches to multi-objective optimization, evolutionary algorithms have been shown to obtain very good results for many realworld multi-objective problems. One of the issues that can affect the performance of these algorithms is the uncertainty in the quality of the solutions which is usually represented with the noise in the objective values. Therefore, handling noisy objectives in evolutionary multi-objective optimization algorithms becomes very important and is gaining more attention in recent years. In this paper we present ?-degree Pareto dominance relation for ordering the solutions in multi-objective optimization when the values of the objective functions are given as intervals. Based on this dominance relation, we propose an adaptation of the non-dominated sorting algorithm for ranking the solutions. This ranking method is then used in a standardmulti-objective evolutionary algorithm and a recently proposed novel multi-objective estimation of distribution algorithm based on joint variable-objective probabilistic modeling, and applied to a set of multi-objective problems with different levels of independent noise. The experimental results show that the use of the proposed method for solution ranking allows to approximate Pareto sets which are considerably better than those obtained when using the dominance probability-based ranking method, which is one of the main methods for noise handling in multi-objective optimization

Non-dominated sorting gravitational search algorithm for multi-objective optimization of power transformer design

Transformers are crucial components in power systems. Due to market globalization, power transformer manufacturers are facing an increasingly competitive environment that mandates the adoption of design strategies yielding better performance at lower mass and losses. Multi-objective Optimization Problems (MOPs) consist of several competing and incommensurable objective functions. Recently, as a search optimization technique inspired by nature, evolutionary algorithms have been broadly applied to solve MOPs. In this paper, a power Transformer Design (TD) methodology using Non-dominated Sorting Gravitational Search Algorithm (NSGSA) is proposed. Results are obtained and presented for NSGSA approach. The obtained results for the study case are compared with those results obtained when using other multi objective optimization algorithms which are Novel Gamma Differential Evolution (NGDE) Algorithm, Chaotic Multi-Objective Algorithm (CMOA), and Multi- Objective Harmony Search (MOHS) algorithm. From the analysis of the obtained results, it has been concluded that NSGSA algorithm provides the most optimum solution and the best results in terms of normalized arithmetic mean value of two objective functions using NSGSA to the TD optimization

MaOMFO: Many-objective moth flame optimizer using reference-point based non-dominated sorting mechanism for global optimization problems

Many-objective optimization (MaO) deals with a large number of conflicting objectives in optimization problems to acquire a reliable set of appropriate non-dominated solutions near the true Pareto front, and for the same, a unique mechanism is essential. Numerous papers have reported multi-objective evolutionary algorithms to explain the absence of convergence and diversity variety in many-objective optimization problems. One of the most encouraging methodologies utilizes many reference points to segregate the solutions and guide the search procedure. The above-said methodology is integrated into the basic version of the Moth Flame Optimization (MFO) algorithm for the first time in this paper. The proposed Many-Objective Moth Flame Optimization (MaOMFO) utilizes a set of reference points progressively decided by the hunt procedure of the moth flame. It permits the calculation to combine with the Pareto front yet synchronize the decent variety of the Pareto front. MaOMFO is employed to solve a wide range of unconstrained and constrained benchmark functions and compared with other competitive algorithms, such as non-dominated sorting genetic algorithm, multi-objective evolutionary algorithm based on dominance and decomposition, and novel multi-objective particle swarm optimization using different performance metrics. The results demonstrate the superiority of the algorithm as a new many-objective algorithm for complex many-objective optimization problems

EMCSO: An Elitist Multi-Objective Cat Swarm Optimization

This paper introduces a novel multi-objective evolutionary algorithm based on cat swarm optimizationalgorithm (EMCSO) and its application to solve a multi-objective knapsack problem. The multi-objective optimizers try to find the closest solutions to true Pareto front (POF) where it will be achieved by finding the less-crowded non-dominated solutions. The proposed method applies cat swarm optimization (CSO), a swarm-based algorithm with ability of exploration and exploitation, to produce offspring solutions and uses thenon-dominated sorting method to findthe solutionsas close as to POFand crowding distance technique toobtain a uniform distribution among thenon-dominated solutions. Also, the algorithm is allowedto keep the elites of population in reproduction processand use an opposition-based learning method for population initialization to enhance the convergence speed.The proposed algorithm is tested on standard test functions (zitzler’ functions: ZDT) and its performance is compared with traditional algorithms and is analyzed based onperformance measures of generational distance (GD), inverted GD, spread,and spacing. The simulation results indicate that the proposed method gets the quite satisfactory results in comparison with other optimization algorithms for functions of ZDT1 and ZDT2. Moreover, the proposed algorithm is applied to solve multi-objective knapsack problem

Stochastic Fractal Based Multiobjective Fruit Fly Optimization

The fruit fly optimization algorithm (FOA) is a global optimization algorithm inspired by the foraging behavior of a fruit fly swarm. In this study, a novel stochastic fractal model based fruit fly optimization algorithm is proposed for multiobjective optimization. A food source generating method based on a stochastic fractal with an adaptive parameter updating strategy is introduced to improve the convergence performance of the fruit fly optimization algorithm. To deal with multiobjective optimization problems, the Pareto domination concept is integrated into the selection process of fruit fly optimization and a novel multiobjective fruit fly optimization algorithm is then developed. Similarly to most of other multiobjective evolutionary algorithms (MOEAs), an external elitist archive is utilized to preserve the nondominated solutions found so far during the evolution, and a normalized nearest neighbor distance based density estimation strategy is adopted to keep the diversity of the external elitist archive. Eighteen benchmarks are used to test the performance of the stochastic fractal based multiobjective fruit fly optimization algorithm (SFMOFOA). Numerical results show that the SFMOFOA is able to well converge to the Pareto fronts of the test benchmarks with good distributions. Compared with four state-of-the-art methods, namely, the non-dominated sorting generic algorithm (NSGA-II), the strength Pareto evolutionary algorithm (SPEA2), multi-objective particle swarm optimization (MOPSO), and multiobjective self-adaptive differential evolution (MOSADE), the proposed SFMOFOA has better or competitive multiobjective optimization performance

Stochastic Fractal Based Multiobjective Fruit Fly Optimization

The fruit fly optimization algorithm (FOA) is a global optimization algorithm inspired by the foraging behavior of a fruit fly swarm. In this study, a novel stochastic fractal model based fruit fly optimization algorithm is proposed for multiobjective optimization. A food source generating method based on a stochastic fractal with an adaptive parameter updating strategy is introduced to improve the convergence performance of the fruit fly optimization algorithm. To deal with multiobjective optimization problems, the Pareto domination concept is integrated into the selection process of fruit fly optimization and a novel multiobjective fruit fly optimization algorithm is then developed. Similarly to most of other multiobjective evolutionary algorithms (MOEAs), an external elitist archive is utilized to preserve the nondominated solutions found so far during the evolution, and a normalized nearest neighbor distance based density estimation strategy is adopted to keep the diversity of the external elitist archive. Eighteen benchmarks are used to test the performance of the stochastic fractal based multiobjective fruit fly optimization algorithm (SFMOFOA). Numerical results show that the SFMOFOA is able to well converge to the Pareto fronts of the test benchmarks with good distributions. Compared with four state-of-the-art methods, namely, the non-dominated sorting generic algorithm (NSGA-II), the strength Pareto evolutionary algorithm (SPEA2), multi-objective particle swarm optimization (MOPSO), and multiobjective self-adaptive differential evolution (MOSADE), the proposed SFMOFOA has better or competitive multiobjective optimization performance

Multi-Objective Self-Organizing Migrating Algorithm: Sensitivity on Controlling Parameters

In this paper, we investigate the sensitivity of a novel Multi-Objective Self-Organizing Migrating Algorithm (MOSOMA) on setting its control parameters. Usually, efficiency and accuracy of searching for a solution depends on the settings of a used stochastic algorithm, because multi-objective optimization problems are highly non-linear. In the paper, the sensitivity analysis is performed exploiting a large number of benchmark problems having different properties (the number of optimized parameters, the shape of a Pareto front, etc.). The quality of solutions revealed by MOSOMA is evaluated in terms of a generational distance, a spread and a hyper-volume error. Recommendations for proper settings of the algorithm are derived: These recommendations should help a user to set the algorithm for any multi-objective task without prior knowledge about the solved problem