Regularity Model for Noisy Multiobjective Optimization

Regularity models have been used in dealing with noise-free multiobjective optimization problems. This paper studies the behavior of a regularity model in noisy environments and argues that it is very suitable for noisy multiobjective optimization. We propose to embed the regularity model in an existing multiobjective evolutionary algorithm for tackling noises. The proposed algorithm works well in terms of both convergence and diversity. In our experimental studies, we have compared several state-of-the-art of algorithms with our proposed algorithm on benchmark problems with different levels of noises. The experimental results showed the effectiveness of the regularity model on noisy problems, but a degenerated performance on some noisy-free problems

Hybrid of memory andprediction strategies for dynamic multiobjective optimization

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Dynamic multiobjective optimization problems (DMOPs) are characterized by a time-variant Pareto optimal front (PF) and/or Pareto optimal set (PS). To handle DMOPs, an algorithm should be able to track the movement of the PF/PS over time efficiently. In this paper, a novel dynamic multiobjective evolutionary algorithm (DMOEA) is proposed for solving DMOPs, which includes a hybrid of memory and prediction strategies (HMPS) and the multiobjective evolutionary algorithm based on decomposition (MOEA/D). In particular, the resultant algorithm (MOEA/D-HMPS) detects environmental changes and identifies the similarity of a change to the historical changes, based on which two different response strategies are applied. If a detected change is dissimilar to any historical changes, a differential prediction based on the previous two consecutive population centers is utilized to relocate the population individuals in the new environment; otherwise, a memory-based technique devised to predict the new locations of the population members is applied. Both response mechanisms mix a portion of existing solutions with randomly generated solutions to alleviate the effect of prediction errors caused by sharp or irregular changes. MOEA/D-HMPS was tested on 14 benchmark problems and compared with state-of-the-art DMOEAs. The experimental results demonstrate the efficiency of MOEA/D-HMPS in solving various DMOPs

Decomposition Evolutionary Algorithms for Noisy Multiobjective Optimization

Multi-objective problems are a category of optimization problem that contain more than one objective function and these objective functions must be optimized simultaneously. Should the objective functions be conflicting, then a set of solutions instead of a single solution is required. This set is known as Pareto optimal. Multi-objective optimization problems arise in many real world applications where several competing objectives must be evaluated and optimal solutions found for them, in the presence of trade offs among conflicting objectives. Maximizing returns while minimizing the risk of stock market investments, or maximizing performance whilst minimizing fuel consumption and hazardous gas emission when buying a car are typical examples of real world multi-objective optimization problems. In this case a number of optimal solutions can be found, known as non-dominated or Pareto optimal solutions. Pareto optimal solutions are reached when it is impossible to improve one objective without making the others worse. Classical ways to address this problem used direct or gradient based methods that rendered them insufficient or computationally expensive for large scale or combinatorial problems. Other difficulties attended the classical methods, such as problem knowledge, which may not be available, or sensitivity to some problem features. For example, finding solutions on the entire Pareto optimal set can only be guaranteed for convex problems. Classical methods for generating the Pareto front set aggregate the objectives into a single or parametrized function before search. Thus, several runs and parameter settings are performed to achieve a set of solutions that approximate the Pareto optimals. Subsequently new methods have been developed, based on computer experiments with meta-heuristic algorithms. Most of these meta-heuristics implement some sort of stochastic search method, amongst which the 'Evolutionary Algorithm' is garnering much attention. It possesses several characteristics that make it a desirable method for confronting multi-objective problems. As a result, a number of studies in recent decades have developed or modified the MOEA for different purposes. This algorithm works with a population of solutions which are capable of searching for multiple Pareto optimal solutions in a single run. At the same time, only the fittest individuals in each generation are offered the chance for reproduction and representation in the next generation. The fitness assignment function is the guiding system of MOEA. Fitness value represents the strength of an individual. Unfortunately, many real world applications bring with them a certain degree of noise due to natural disasters, inefficient models, signal distortion or uncertain information. This noise affects the performance of the algorithm's fitness function and disrupts the optimization process. This thesis explores and targets the effect of this disruptive noise on the performance of the MOEA. In this thesis, we study the noisy MOP and modify the MOEA/D to improve its performance in noisy environments. To achieve this, we will combine the basic MOEA/D with the 'Ordinal Optimization' technique to handle uncertainties. The major contributions of this thesis are as follows. First, MOEA/D is tested in a noisy environment with different levels of noise, to give us a deeper understanding of where the basic algorithm fails to handle the noise. Then, we extend the basic MOEA/D to improve its noise handling by employing the ordinal optimization technique. This creates MOEA/D+OO, which will outperform MOEA/D in terms of diversity and convergence in noisy environments. It is tested against benchmark problems of varying levels of noise. Finally, to test the real world application of MOEA/D+OO, we solve a noisy portfolio optimization with the proposed algorithm. The portfolio optimization problem is a classic one in finance that has investors wanting to maximize a portfolio's return while minimizing risk of investment. The latter is measured by standard deviation of the portfolio's rate of return. These two objectives clearly make it a multi-objective problem

Evolutionary multi-objective optimization in uncertain environments

Ph.DDOCTOR OF PHILOSOPH

Evolutionary multi-objective optimization using neural-based estimation of distribution algorithms

Ph.DDOCTOR OF PHILOSOPH

Evolutionary Algorithms for Static and Dynamic Multiobjective Optimization

Many real-world optimization problems consist of a number of conflicting objectives that have to be optimized simultaneously. Due to the presence of multiple conflicting ob- jectives, there is no single solution that can optimize all the objectives. Therefore, the resulting multiobjective optimization problems (MOPs) resort to a set of trade-off op- timal solutions, called the Pareto set in the decision space and the Pareto front in the objective space. Traditional optimization methods can at best find one solution in a sin- gle run, thereby making them inefficient to solve MOPs. In contrast, evolutionary algo- rithms (EAs) are able to approximate multiple optimal solutions in a single run. This strength makes EAs good candidates for solving MOPs. Over the past several decades, there have been increasing research interests in developing EAs or improving their perfor- mance, resulting in a large number of contributions towards the applicability of EAs for MOPs. However, the performance of EAs depends largely on the properties of the MOPs in question, e.g., static/dynamic optimization environments, simple/complex Pareto front characteristics, and low/high dimensionality. Different problem properties may pose dis- tinct optimization difficulties to EAs. For example, dynamic (time-varying) MOPs are generally more challenging than static ones to EAs. Therefore, it is not trivial to further study EAs in order to make them widely applicable to MOPs with various optimization scenarios or problem properties. This thesis is devoted to exploring EAs’ ability to solve a variety of MOPs with dif- ferent problem characteristics, attempting to widen EAs’ applicability and enhance their general performance. To start with, decomposition-based EAs are enhanced by incorpo- rating two-phase search and niche-guided solution selection strategies so as to make them suitable for solving MOPs with complex Pareto fronts. Second, new scalarizing functions are proposed and their impacts on evolutionary multiobjective optimization are exten- sively studied. On the basis of the new scalarizing functions, an efficient decomposition- based EA is introduced to deal with a class of hard MOPs. Third, a diversity-first- and-convergence-second sorting method is suggested to handle possible drawbacks of convergence-first based sorting methods. The new sorting method is then combined with strength based fitness assignment, with the aid of reference directions, to optimize MOPs with an increase of objective dimensionality. After that, we study the field of dynamic multiobjective optimization where objective functions and constraints can change over time. A new set of test problems consisting of a wide range of dynamic characteristics is introduced at an attempt to standardize test environments in dynamic multiobjective optimization, thereby aiding fair algorithm comparison and deep performance analysis. Finally, a dynamic EA is developed to tackle dynamic MOPs by exploiting the advan- tages of both generational and steady-state algorithms. All the proposed approaches have been extensively examined against existing state-of-the-art methods, showing fairly good performance in a variety of test scenarios. The research work presented in the thesis is the output of initiative and novel attempts to tackle some challenging issues in evolutionary multiobjective optimization. This re- search has not only extended the applicability of some of the existing approaches, such as decomposition-based or Pareto-based algorithms, for complex or hard MOPs, but also contributed to moving forward research in the field of dynamic multiobjective optimiza- tion with novel ideas including new test suites and novel algorithm design

10361 Abstracts Collection and Executive Summary -- Theory of Evolutionary Algorithms

From September 5 to 10, the Dagstuhl Seminar 10361 ``Theory of Evolutionary Algorithms \u27\u27 was held in Schloss Dagstuhl~--~Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general

Adaptive decomposition-based evolutionary approach for multiobjective sparse reconstruction

© 2018 Elsevier Inc. This paper aims at solving the sparse reconstruction (SR) problem via a multiobjective evolutionary algorithm. Existing multiobjective evolutionary algorithms for the SR problem have high computational complexity, especially in high-dimensional reconstruction scenarios. Furthermore, these algorithms focus on estimating the whole Pareto front rather than the knee region, thus leading to limited diversity of solutions in knee region and waste of computational effort. To tackle these issues, this paper proposes an adaptive decomposition-based evolutionary approach (ADEA) for the SR problem. Firstly, we employ the decomposition-based evolutionary paradigm to guarantee a high computational efficiency and diversity of solutions in the whole objective space. Then, we propose a two-stage iterative soft-thresholding (IST)-based local search operator to improve the convergence. Finally, we develop an adaptive decomposition-based environmental selection strategy, by which the decomposition in the knee region can be adjusted dynamically. This strategy enables to focus the selection effort on the knee region and achieves low computational complexity. Experimental results on simulated signals, benchmark signals and images demonstrate the superiority of ADEA in terms of reconstruction accuracy and computational efficiency, compared to five state-of-the-art algorithms

EVOLUTIONARY MULTI-OBJECTIVE OPTIMIZATION IN STATIC AND DYNAMIC ENVIRONMENTS

Ph.DDOCTOR OF PHILOSOPH

Evolutionary Computation 2020

Intelligent optimization is based on the mechanism of computational intelligence to refine a suitable feature model, design an effective optimization algorithm, and then to obtain an optimal or satisfactory solution to a complex problem. Intelligent algorithms are key tools to ensure global optimization quality, fast optimization efficiency and robust optimization performance. Intelligent optimization algorithms have been studied by many researchers, leading to improvements in the performance of algorithms such as the evolutionary algorithm, whale optimization algorithm, differential evolution algorithm, and particle swarm optimization. Studies in this arena have also resulted in breakthroughs in solving complex problems including the green shop scheduling problem, the severe nonlinear problem in one-dimensional geodesic electromagnetic inversion, error and bug finding problem in software, the 0-1 backpack problem, traveler problem, and logistics distribution center siting problem. The editors are confident that this book can open a new avenue for further improvement and discoveries in the area of intelligent algorithms. The book is a valuable resource for researchers interested in understanding the principles and design of intelligent algorithms