A Pareto Corner Search Evolutionary Algorithm and Principal Component Analysis for Objective Dimensionality Reduction

An ACO-based Hyper-heuristic for Sequencing Many-objective Evolutionary Algorithms that Consider Different Ways to Incorporate the DM's Preferences

In many objective optimization problems (MaOPs), more than three distinct objectives are optimized. The challenging part in MaOPs is to get the Pareto approximation (PA) with high diversity and good convergence. In Literature, in order to solve the issue of diversity and convergence in MaOPs, many approaches are proposed using different multi objective evolutionary algorithms (MOEAs). Moreover, to get better results, the researchers use the sets of reference points to differentiate the solutions and to model the search process, it further evaluates and selects the non-dominating solutions by using the reference set of solutions. Furthermore, this technique is used in some of the swarm-based evolutionary algorithms. In this paper, we have used some effective adaptations of bat algorithm with the previous mentioned approach to effectively handle the many objective problems. Moreover, we have called this algorithm as many objective bat algorithm (MaOBAT). This algorithm is a biologically inspired algorithm, which uses echolocation power of micro bats. Each bat represents a complete solution, which can be evaluated based on the problem specific fitness function and then based on the dominance relationship, non-dominated solutions are selected. In proposed MaOBAT, dominance rank is used as dominance relationship (dominance rank of a solution means by how many other solutions a solution dominated). In our proposed strategy, dynamically allocated set of reference points are used, allowing the algorithm to have good convergence and high diversity pareto fronts (PF). The experimental results show that the proposed algorithm has significant advantages over several state-of-the-art algorithms in terms of the quality of the solution.

Pareto-based multi-objective evolutionary algorithms experience grand challenges in solving many-objective optimization problems due to their inability to maintain both convergence and diversity in a high-dimensional objective space. Exiting approaches usually modify the selection criteria to overcome this issue. Different from them, we propose a novel meta-objective (MeO) approach that transforms the many-objective optimization problems in which the new optimization problems become easier to solve by the Pareto-based algorithms. MeO converts a given many-objective optimization problem into a new one, which has the same Pareto optimal solutions and the number of objectives with the original one. Each meta-objective in the new problem consists of two components which measure the convergence and diversity performances of a solution, respectively. Since MeO only converts the problem formulation, it can be readily incorporated within any multi-objective evolutionary algorithms, including those non-Pareto-based ones. Particularly, it can boost the Pareto-based algorithms' ability to solve many-objective optimization problems. Due to separately evaluating the convergence and diversity performances of a solution, the traditional density-based selection criteria, for example, crowding distance, will no longer mistake a solution with poor convergence performance for a solution with low density value. By penalizing a solution in term of its convergence performance in the meta-objective space, the Pareto dominance becomes much more effective for a many-objective optimization problem. Comparative study validates the competitive performance of the proposed meta-objective approach in solving many-objective optimization problems.

Nondominated sorting plays an important role in Pareto-based multiobjective evolutionary algorithms (MOEAs). When faced with many-objective optimization problems multiobjective optimization problems (MOPs) with more than three objectives, the number of comparisons needed in nondominated sorting becomes very large. In view of this, a new corner sort is proposed in this paper. Corner sort first adopts a fast and simple method to obtain a nondominated solution from the corner solutions, and then uses the nondominated solution to ignore the solutions dominated by it to save comparisons. Obtaining the nondominated solutions requires much fewer objective comparisons in corner sort. In order to evaluate its performance, several state-of-the-art nondominated sorts are compared with our corner sort on three kinds of artificial solution sets of MOPs and the solution sets generated from MOEAs on benchmark problems. On one hand, the experiments on artificial solution sets show the performance on the solution sets with different distributions. On the other hand, the experiments on the solution sets generated from MOEAs show the influence that different sorts bring to MOEAs. The results show that corner sort performs well, especially on many-objective optimization problems. Corner sort uses fewer comparisons than others.

Many-objective optimization problems (MaOPs) bring great hardship to most of the existing classical evolutionary multi-objective optimization algorithms, respecting selection operators, computational cost, visualization of the high-dimensional Pareto front, and so on. Objective reduction can help mitigate such hardship by removing the redundant objectives in the original objective set to some extent. Objective reduction problem is inherently a multiobjective optimization problem because we aim to preserve the dominance structure by using as little objectives as possible. In this paper, we propose an objective reduction algorithm based on constrained evolutionary multiobjective algorithm. A novel local search is presented for finding the Pareto-front by searching the neighbor. We compared the proposed algorithm with three algorithms on eleven test instances. The experimental results show the proposed algorithm can obtain a stable performance without any parameter need to fine tune.

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).

A hybridized angle-encouragement-based decomposition approach for many-objective optimization problems

A reference direction and entropy based evolutionary algorithm for many-objective optimization

It is difficult to maintain the balance between convergence and diversity for many-objective optimization problems (MaOPs) in the algorithms of evolutionary multi-objective (EMO). EMO algorithms are useful technology to solve the multi-objective optimization problems (MOPs). However, with the larger of optimization objectives, enough Pareto selection pressure will be loosed, and results in the performance of the algorithms are significantly reduced. The decomposition-based EMO developed for MaOPs have been shown to be effective, and the BBO algorithm is a low-complexity algorithm. In this paper, a hybrid decomposition-based BBO/Complex algorithm (HDB/BBO) for MaOPs is proposed. First, a set of uniformly distributed weight vectors and K-means aggregate method is introduced for decomposing MaOPs into several subsystems. Then, inferior migrated islands will not be chosen unless they pass the Metropolis criterion twice during the within-subsystem migration and cross-subsystem migration. The penalty-based boundary intersection (PBI) distance to calculate neighbor islands distance for balancing the algorithm of convergence and diversity. Finally, after mutation and clear duplication, a uniform distribution Pareto set can be obtained. Experimental results on both DTLZ and WFG benchmarks problems demonstrate the superiority of the proposed algorithm in comparison with three state-of-the-art algorithms in terms of both convergence and diversity.

Broad learning approach to Surrogate-Assisted Multi-Objective evolutionary fuzzy clustering algorithm based on reference points for color image segmentation

Solving optimization problems with multiple (often conflicting) objectives is, generally, a very difficult goal. Evolutionary algorithms (EAs) were initially extended and applied during the mid-eighties in an attempt to stochastically solve problems of this generic class. During the past decade, a variety, of multiobjective EA (MOEA) techniques have been proposed and applied to many scientific and engineering applications. Our discussion's intent is to rigorously define multiobjective optimization problems and certain related concepts, present an MOEA classification scheme, and evaluate the variety of contemporary MOEAs. Current MOEA theoretical developments are evaluated; specific topics addressed include fitness functions, Pareto ranking, niching, fitness sharing, mating restriction, and secondary populations. Since the development and application of MOEAs is a dynamic and rapidly growing activity, we focus on key analytical insights based upon critical MOEA evaluation of current research and applications. Recommended MOEA designs are presented, along with conclusions and recommendations for future work.

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.

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-criteria algorithms for portfolio optimization under practical constraints

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.