Amin Ibrahim

3D-RadVis: Visualization of Pareto front in many-objective optimization

In many-objective optimization, visualization of true Pareto front or obtained non-dominated solutions is difficult. A proper visualization tool must be able to show the location, range, shape, and distribution of obtained non-dominated solutions. However, existing commonly used visualization tools in many-objective optimization (e.g., parallel coordinates) fail to show the shape of the Pareto front. In this paper, we propose a simple yet powerful visualization method, called 3-dimensional radial coordinate visualization (3D-RadVis). This method is capable of mapping M-dimensional objective space to a 3-dimensional radial coordinate plot while preserving the relative location of solutions, shape of the Pareto front, distribution of solutions, and convergence trend of an optimization process. Furthermore, 3D-RadVis can be used by decision-makers to visually navigate large many-objective solution sets, observe the evolution process, visualize the relative location of a solution, evaluate trade-off among objectives, and select preferred solutions. The visual effectiveness of the proposed method is demonstrated on widely used many-objective benchmark problems containing variety of Pareto fronts (linear, concave, convex, mixed, and disconnected). In addition, we demonstrated the capability of 3D-RadVis for visual progress tracking of the NSGA-III algorithm through generations. It is worthwhile to mention that a suitable visualization is a crucial prerequisite for an effective interactive optimization.

EliteNSGA-III: An improved evolutionary many-objective optimization algorithm

Evolutionary algorithms are the most studied and successful population-based algorithms for solving single- and multi-objective optimization problems. However, many studies have shown that these algorithms fail to perform well when handling many-objective (more than three objectives) problems due to the loss of selection pressure to pull the population towards the Pareto front. As a result, there has been a number of efforts towards developing evolutionary algorithms that can successfully handle many-objective optimization problems without deteriorating the effect of evolutionary operators. A reference-point based NSGA-II (NSGA-III) is one such algorithm designed to deal with many-objective problems, where the diversity of the solution is guided by a number of well-spread reference points. However, NSGA-III still has difficulty preserving elite population as new solutions are generated. In this paper, we propose an improved NSGA-III algorithm, called EliteNSGA-III to improve the diversity and accuracy of the NSGA-III algorithm. EliteNSGA-III algorithm maintains an elite population archive to preserve previously generated elite solutions that would probably be eliminated by NSGA-IIIs selection procedure. The proposed EliteNSGA-III algorithm is applied to II many-objective test problems with three to I5 objectives. Experimental results show that the proposed EliteNSGA-III algorithm outperforms the NSGA-III algorithm in terms of diversity and accuracy of the obtained solutions, especially for test problems with higher objectives.

Simulated Raindrop algorithm for global optimization

In this paper, we propose a novel single-solution based metaheuristic algorithm called Simulated Raindrop (SRD). The SRD algorithm is inspired by the principles of raindrops. When rain falls on the land, it normally flows from higher altitude to a lower due to gravity, while choosing the optimum path towards the lowest point on the landscape. We compared the performance of simulated annealing (SA) against the proposed SRD method on 8 commonly utilized benchmark functions. Experimental results confirm that SRD outperforms SA on all test problems in terms of variant performance measures, such as convergence speed, accuracy of the solution, and robustness.

Optimal Photovoltaic System Design with Multi-Objective Optimization

Recently, several parts of the world suffer from electrical black-outs due to high electrical demands during peak hours. Stationary photovoltaic PV collector arrays produce clean and sustainable energy especially during peak hours which are generally day time. In addition, PVs do not emit any waste or emissions, and are silent in operation. The incident energy collected by PVs is mainly dependent on the number of collector rows, distance between collector rows, dimension of collectors, collectors inclination angle and collectors azimuth, which all are involved in the proposed modeling in this article. The objective is to achieve optimal design of a PV farm yielding two conflicting objectives namely maximum field incident energy and minimum of the deployment cost. Two state-of-the-art multi-objective evolutionary algorithms MOEAs called Non-dominated Sorting Genetic Algorithm-II NSGA-II and Generalized Differential Evolution Generation 3 GDE3 are compared to design PV farms in Toronto, Canada area. The results are presented and discussed to illustrate the advantage of utilizing MOEA in PV farms design and other energy related real-world problems.

Fusion of Many-Objective Non-dominated Solutions Using Reference Points

With recent advancements of multi- or many-objective optimization algorithms, researchers and decision-makers are increasingly faced with the dilemma of choosing the best algorithm to solve their problems. In this paper, we propose a simple hybridization of population-based multi- or many-objective optimization algorithms called fusion of non-dominated fronts using reference points FNFR to gain combined benefits of several algorithms. FNFR combines solutions from multiple optimization algorithms during or after several runs and extracts well-distributed solutions from a large set of non-dominated solutions using predefined structured reference points or user-defined reference points. The proposed FNFR is applied to non-dominated solutions obtained by the Generalized Differential Evolution Generation 3 GDE3, Speed-constrained Multi-objective Particle Swarm Optimization SMPSO, and the Strength Pareto Evolutionary Algorithm 2 SPEA2 on seven unconstrained many-objective test problems with three to ten objectives. Experimental results show FNFR is an effective way for combining and extracting fusion of well-distributed non-dominated solutions among a large set of solutions. In fact, the proposed method is a solution-level hybridization approach. FNFR showed promising results when selecting well-distributed solutions around a specific region of interest.

3D-RadVis Antenna: Visualization and performance measure for many-objective optimization

Abstract So far the focus of almost all multi- or many-objective performance metrics has been the convergence and distribution of solutions in the objective space (Pareto-surface). Pareto-surface metrics such as IGD, HV, and Spread are simple and provide knowledge about the overall performance of the solution set. However, these measures do not provide any insight into the distribution or spread of a solution set with respect to each objective. Further, in many-objective optimization, visualization of true Pareto fronts or obtained non-dominated solutions is difficult. A proper visualization tool must be able to show the location, range, shape, and distribution of obtained non-dominated solutions (both Pareto-surface and objective-wise distribution). Existing commonly used visualization tools in many-objective optimization (e.g., parallel coordinates) fail to show the shape of the Pareto front or distribution of solutions along each objective. In this paper, we propose an extension of recently proposed visualization method called 3D-RadVis (we call it 3D-RadVis Antenna) to visualize the distribution of solutions along each objective. 3D-RadVis Antenna is capable of mapping M-dimensional objective space to a 3-dimensional radial coordinate plot while seeking to preserve the relative location of solutions, shape of the Pareto front, and distribution of solutions along each objective. Furthermore, 3D-RadVis Antenna can be used by decision-makers to visually navigate large many-objective solution sets, to observe the evolutionary process, to visualize the relative location of a solution, to evaluate trade-offs among objectives, and to select preferred solutions. Along with this visualization tool, we propose two novel performance measures, named objective-wise inverse generational distance (ObjIGD) and line distribution ( ∆ Line ) to measure the convergence and distribution of solutions along each objective as well as the overall performance of approximate solutions. The effectiveness of the proposed methods are demonstrated on widely used many-objective benchmark problems containing a variety of Pareto fronts (linear, concave, convex, mixed, and disconnected). In addition, for a case study, we have demonstrated the capability of 3D-RadVis Antenna combined with the proposed performance measures for visual progress tracking of the NSGA-III algorithm through generations. Experimental results show that the proposed visualization method can effectively be used to compare and track the performance of many-objective algorithms. Moreover, the proposed measures can be used as reliable complementary measures along with other widely used performance measures to compare many-objective solution sets.

Fusion-based hybrid many-objective optimization algorithm

In the last three decades there have been a number of efficient multi-objective optimization algorithms capable of solving real-world problems. However, due to the complexity of most real-world problems (high-dimensionality of problems, computationally expensive, and unknown function properties) researchers and decision-makers are increasingly facing the challenge of selecting an optimization algorithm capable of solving their hard problems. In this paper, we propose a simple yet efficient hybridization of multi- and many-objective optimization algorithms framework called hybrid many-objective optimization algorithm using fusion of solutions obtained by several many-objective algorithms (fusion) to gain the combined benefits of several algorithms and reducing the challenge of choosing one optimization algorithm to solve complex problems. During the optimization process, the Fusion framework (1) executes all optimization algorithms in parallel, (2) it combines solutions of these algorithms and extracts well-distributed solutions using predefined structured reference points or user-defined reference points, and (3) adaptively selects best-performing algorithm to tackle the problem at different stages of the search process. A case study of the fusion framework by considering GDE3, SMPSO, and SPEA2 as multi-objective optimization algorithms is presented. Experimental results on five unconstrained and four constrained benchmark test problems with three to ten objectives show that the Fusion framework significantly outperforms all algorithms involved in the hybridization process as well as the NSGA-III algorithm in terms of diversity and convergence of obtained solutions. Furthermore, the proposed framework is consistently able to find accurate solutions for all test problems which can be interpreted as its high robustness characteristic.

MDE: Differential evolution with merit-based mutation strategy

Currently Differential Evolution (DE) is arguably the most powerful and widely used stochastic population-based real-parameter optimization algorithm. There have been variant DE-based algorithms in the literature since its introduction in 1995. This paper proposes a novel merit-based mutation strategy for DE (MDE); it is based on the performance of each individual in the past and current generations to improve the solution accuracy. MDE is compared with three commonly used mutation strategies on 28 standard numerical benchmark functions introduced in the IEEE Congress on Evolutionary Computation (CEC-2013) special session on real parameter optimization. Experimental results confirm that MDE outperforms the classical DE mutation strategies for most of the test problems in terms of convergence speed and solution accuracy.

Detecting and Preventing the Electronic Transmission of Illicit Images and Its Network Performance

Child exploitation through the use of the Internet as a delivery and exchange tool is a growing method of abuse towards children. It is shown that a Stochastic Learning Weak Estimator learning algorithm and a Maximum Likelihood Estimator learning algorithm can be applied against Linear Classifiers to identify and filter illicit pornographic images. In this paper, these two learning algorithms were combined with distance algorithms such as the Non-negative Vector Similarity Coefficient-based Distance algorithm, Euclidian Distance, and a Weighted Euclidian Distance algorithm. Experimental results showed that classification accuracies and the network overhead did have a significant effect on routing devices.

Addressing privacy constraints for efficient monitoring of network traffic for illicit images

The sexual exploitation of children remains a very serious problem and is rapidly increasing globally through the use of the Internet. This paper focuses on the privacy issues involved in design and implementation of a system capable of image classification at the network layer. In this paper, we examined two learning algorithms, namely the Maximum Likelihood Estimator (MLE), and the Stochastic Learning Weak Estimator (SLWE) as well as six distance measures including the Euclidian Distance (ED), the Weighted Euclidian Distance (WED), and the Cosine Distance (CosD). Our experiments indicate that the SLWE algorithm has slightly better classification accuracy than MLE and as a result the SLWE algorithm combined with a Linear Classifier can be used to actively filter illicit pornographic images as they are transmitted over the network layer.