Adaptive Reference Vector Generation for Inverse Model Based Evolutionary Multiobjective Optimization with Degenerate and Disconnected Pareto Fronts

Inverse model based multiobjective evolutionary algorithm aims to sample candidate solutions directly in the objective space, which makes it easier to control the diversity of non-dominated solutions in multiobjective optimization. To facilitate the process of inverse modeling, the objective space is partitioned into several subregions by predefining a set of reference vectors. In the previous work, the reference vectors are uniformly distributed in the objective space. Uniformly distributed reference vectors, however, may not be efficient for problems that have nonuniform or disconnected Pareto fronts. To address this issue, an adaptive reference vector generation strategy is proposed in this work. The basic idea of the proposed strategy is to adaptively adjust the reference vectors according to the distribution of the candidate solutions in the objective space. The proposed strategy consists of two phases in the search procedure. In the first phase, the adaptive strategy promotes the population diversity for better exploration, while in the second phase, the strategy focused on convergence for better exploitation. To assess the performance of the proposed strategy, empirical simulations are carried out on two DTLZ benchmark problems, namely, DTLZ5 and DTLZ7, which have a degenerate and a disconnected Pareto front, respectively. Our results show that the proposed adaptive reference vector strategy is promising in tacking multiobjective optimization problems whose Pareto front is disconnected

Decomposition-Based-Sorting and Angle-Based-Selection for Evolutionary Multiobjective and Many-Objective Optimization

Multiobjective evolutionary algorithm based on decomposition (MOEA/D) decomposes a multiobjective optimization problem (MOP) into a number of scalar optimization subproblems and then solves them in parallel. In many MOEA/D variants, each subproblem is associated with one and only one solution. An underlying assumption is that each subproblem has a different Pareto-optimal solution, which may not be held, for irregular Pareto fronts (PFs), e.g., disconnected and degenerate ones. In this paper, we propose a new variant of MOEA/D with sorting-and-selection (MOEA/D-SAS). Different from other selection schemes, the balance between convergence and diversity is achieved by two distinctive components, decomposition-based-sorting (DBS) and angle-based-selection (ABS). DBS only sorts ${L}$ closest solutions to each subproblem to control the convergence and reduce the computational cost. The parameter ${L}$ has been made adaptive based on the evolutionary process. ABS takes use of angle information between solutions in the objective space to maintain a more fine-grained diversity. In MOEA/D-SAS, different solutions can be associated with the same subproblems; and some subproblems are allowed to have no associated solution, more flexible to MOPs or many-objective optimization problems (MaOPs) with different shapes of PFs. Comprehensive experimental studies have shown that MOEA/D-SAS outperforms other approaches; and is especially effective on MOPs or MaOPs with irregular PFs. Moreover, the computational efficiency of DBS and the effects of ABS in MOEA/D-SAS are also investigated and discussed in detail

Using Optimality Theory and Reference Points to Improve the Diversity and Convergence of a Fuzzy-Adaptive Multi-Objective Particle Swarm Optimizer

Particle Swarm Optimization (PSO) has received increasing attention from the evolutionary optimization research community in the last twenty years. PSO is a metaheuristic approach based on collective intelligence obtained by emulating the swarming behavior of bees. A number of multi-objective variants of the original PSO algorithm that extend its applicability to optimization problems with conflicting objectives have also been developed; these multi-objective PSO (MOPSO) algorithms demonstrate comparable performance to other state-of-the-art metaheuristics. The existence of multiple optimal solutions (Pareto-optimal set) in optimization problems with conflicting objectives is not the only challenge posed to an optimizer, as the latter needs to be able to identify and preserve a well-distributed set of solutions during the search of the decision variable space. Recent attempts by evolutionary optimization researchers to incorporate mathematical convergence conditions into genetic algorithm optimizers have led to the derivation of a point-wise proximity measure, which is based on the solution of the achievement scalarizing function (ASF) optimization problem with a complementary slackness condition that quantifies the violation of the Karush-Kuhn-Tucker necessary conditions of optimality. In this work, the aforementioned KKT proximity measure is incorporated into the original Adaptive Coevolutionary Multi-Objective Swarm Optimizer (ACMOPSO) in order to monitor the convergence of the sub-swarms towards the Pareto-optimal front and provide feedback to Mamdani-type fuzzy logic controllers (FLCs) that are utilized for online adaptation of the algorithmic parameters. The proposed Fuzzy-Adaptive Multi-Objective Optimization Algorithm with the KKT proximity measure (FAMOPSOkkt) utilizes a set of reference points to cluster the computed nondominated solutions. These clusters interact with their corresponding sub-swarms to provide the swarm leaders and are also utilized to manage the external archive of nondominated solutions. The performance of the proposed algorithm is evaluated on benchmark problems chosen from the multi-objective optimization literature and compared to the performance of state-of-the-art multi-objective optimization algorithms with similar features

Advanced p-Metric Based Many-Objective Evolutionary Algorithm

Evolutionary many objective based optimization has been gaining a lot of attention from the evolutionary computation researchers and computational intelligence community. Many of the state-of-the-art multi-objective and many-objective optimization problems (MOPs, MaOPs) are inefficient in maintaining the convergence and diversity performances as the number of objectives increases in the modern-day real-world applications. This phenomenon is obvious indeed as Pareto-dominance based EAs employ non-dominated sorting which fails considerably in providing enough convergent pressure towards the Pareto front (PF). Researchers invested much more time and effort in addressing this issue by improving the scalability in MaOPs and they have come up with non-Pareto-dominance-based EAs such as decomposition-based, indicator-based and reference-based approaches. In addition to that, the algorithm has to account for the additional computational budget. This thesis proposes an advanced polar-metric (p-metric) based Many-objective EA (in short APMOEA) for tackling both MOPs and MaOPs. p-metric, a recently proposed performance based visualization metric, employs an array of uniformly, distributed direction vectors. In APMOEA, a two-phase selection scheme is employed which combines both non-dominated sorting and p-metric. Moreover, this thesis also proposes a modified P-metric methodology in order to adjust the direction vectors dynamically. In the experiments, we compare APMOEA with four state-of-the-art Many-objective EAs under, three performance indicators. According to the empirical results, APMOEA shows much improved performances on most of the test problems, involving both MOPs and MaOPs.Electrical Engineerin

Многофакторный конвергенционо-нацеленный оператор для генетического алгоритма

Cкладні пакети моделювання транспорту частинок можна оптимізувати за допомогою генетичних алгоритмів, що дає змогу застосовувати для таких задач підходи статистичного навчання та методи оптимізації декількох цільових функцій. Поєднання генетичного алгоритму та неконтрольованого машинного навчання значно підвищує збіжність алгоритму до істинного парето-фронту. У межах багатофакторного аналізу запропоновано додатковий оператор, який може бути застосований для задач оптимізації багатоцільових функцій, що потребують великого обсягу ресурсів та часу, зокрема для пришвидшення збіжності задачі оптимізації "чорного ящика". Отримані результати показують, що запропонований підхід можна використовувати для генетичного алгоритму будь-якого типу, а додатковий оператор розглядати як окремий генетичний оператор.Optimization of complex particle transport simulation packages could be managed using genetic algorithms as a tuning instrument for learning statistics and behavior of multi-objective optimisation functions. Combination of genetic algorithm and unsupervised machine learning could significantly increase convergence of algorithm to true Pareto Front (PF). We tried to apply specific multivariate analysis operator that can be used in case of expensive fitness function evaluations, in order to speed-up the convergence of the "black-box" optimization problem. The results delivered in the article shows that current approach could be used for any type of genetic algorithm and deployed as a separate genetic operator.Сложные пакеты моделирования транспорта частиц можно оптимизировать с помощью генетических алгоритмов, что позволяет применять для таких задач подходы статистического обучения и методы оптимизации нескольких целевых функций. Сочетание генетического алгоритма и неконтролируемого машинного обучения может значительно повышает сходимость алгоритма к истинному парето-фронта. В рамках многофакторного анализа предложен дополнительный оператор, который может быть применен для задач оптимизации многоцелевых функций, требующих большого объема ресурсов и времени, в частности для ускорения сходимости задачи оптимизации "черного ящика". Полученные результаты показывают, что предложенный подход можно использовать для генетического алгоритма любого типа, а дополнительный оператор рассматривать как отдельный генетический оператор

Evolutionary Many-objective Optimization of Hybrid Electric Vehicle Control: From General Optimization to Preference Articulation

Many real-world optimization problems have more than three objectives, which has triggered increasing research interest in developing efficient and effective evolutionary algorithms for solving many-objective optimization problems. However, most many-objective evolutionary algorithms have only been evaluated on benchmark test functions and few applied to real-world optimization problems. To move a step forward, this paper presents a case study of solving a many-objective hybrid electric vehicle controller design problem using three state-of-the-art algorithms, namely, a decomposition based evolutionary algorithm (MOEA/D), a non-dominated sorting based genetic algorithm (NSGA-III), and a reference vector guided evolutionary algorithm (RVEA). We start with a typical setting aiming at approximating the Pareto front without introducing any user preferences. Based on the analyses of the approximated Pareto front, we introduce a preference articulation method and embed it in the three evolutionary algorithms for identifying solutions that the decision-maker prefers. Our experimental results demonstrate that by incorporating user preferences into many-objective evolutionary algorithms, we are not only able to gain deep insight into the trade-off relationships between the objectives, but also to achieve high-quality solutions reflecting the decision-maker’s preferences. In addition, our experimental results indicate that each of the three algorithms examined in this work has its unique advantages that can be exploited when applied to the optimization of real-world problems

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

Ph.DDOCTOR OF PHILOSOPH

EVOLUTIONARY MULTI-OBJECTIVE OPTIMIZATION VIA DIFFERENTIAL EVOLUTION

Ph.DDOCTOR OF PHILOSOPH