A dynamic multi-objective evolutionary algorithm based on polynomial regression and adaptive clustering

In this paper, a dynamic multi-objective evolutionary algorithm is proposed based on polynomial regression and adaptive clustering, called DMOEA-PRAC. As the Pareto-optimal solutions and fronts of dynamic multi-objective optimization problems (DMOPs) may dynamically change in the optimization process, two corresponding change response strategies are presented for the decision space and objective space, respectively. In the decision space, the potentially useful information contained in all historical populations is obtained by the proposed predictor based on polynomial regression, which extracts the linear or nonlinear relationship in the historical change. This predictor can generate good initial population for the new environment. In the objective space, in order to quickly adapt to the new environment, an adaptive reference vector regulator is designed in this paper based on K-means clustering for the complex changes of Pareto-optimal fronts, in which the adjusted reference vectors can effectively guide the evolution. Finally, DMOEA-PRAC is compared with some recently proposed dynamic multi-objective evolutionary algorithms and the experimental results verify the effectiveness of DMOEA-PRAC in dealing with a variety of DMOPs

An Evolutionary Algorithm with Advanced Goal and Priority Specification for Multi-objective Optimization

This paper presents an evolutionary algorithm with a new goal-sequence domination scheme for better decision support in multi-objective optimization. The approach allows the inclusion of advanced hard/soft priority and constraint information on each objective component, and is capable of incorporating multiple specifications with overlapping or non-overlapping objective functions via logical 'OR' and 'AND' connectives to drive the search towards multiple regions of trade-off. In addition, we propose a dynamic sharing scheme that is simple and adaptively estimated according to the on-line population distribution without needing any a priori parameter setting. Each feature in the proposed algorithm is examined to show its respective contribution, and the performance of the algorithm is compared with other evolutionary optimization methods. It is shown that the proposed algorithm has performed well in the diversity of evolutionary search and uniform distribution of non-dominated individuals along the final trade-offs, without significant computational effort. The algorithm is also applied to the design optimization of a practical servo control system for hard disk drives with a single voice-coil-motor actuator. Results of the evolutionary designed servo control system show a superior closed-loop performance compared to classical PID or RPT approaches

Multi-objective trajectory optimization of Space Maneuver Vehicle using adaptive differential evolution and modified game theory

Highly constrained trajectory optimization for Space Manoeuvre Vehicles (SMV) is a challenging problem. In practice, this problem becomes more difficult when multiple mission requirements are taken into account. Because of the nonlinearity in the dynamic model and even the objectives, it is usually hard for designers to generate a compromised trajectory without violating strict path and box constraints. In this paper, a new multi-objective SMV optimal control model is formulated and parameterized using combined shooting-collocation technique. A modified game theory approach, coupled with an adaptive differential evolution algorithm, is designed in order to generate the pareto front of the multi-objective trajectory optimization problem. In addition, to improve the quality of obtained solutions, a control logic is embedded in the framework of the proposed approach. Several existing multi-objective evolutionary algorithms are studied and compared with the proposed method. Simulation results indicate that without driving the solution out of the feasible region, the proposed method can perform better in terms of convergence ability and convergence speed than its counterparts. Moreover, the quality of the pareto set generated using the proposed method is higher than other multi-objective evolutionary algorithms, which means the newly proposed algorithm is more attractive for solving multi-criteria SMV trajectory planning problem

A Data-Driven Evolutionary Transfer Optimization for Expensive Problems in Dynamic Environments

Many real-world problems are usually computationally costly and the objective functions evolve over time. Data-driven, a.k.a. surrogate-assisted, evolutionary optimization has been recognized as an effective approach for tackling expensive black-box optimization problems in a static environment whereas it has rarely been studied under dynamic environments. This paper proposes a simple but effective transfer learning framework to empower data-driven evolutionary optimization to solve dynamic optimization problems. Specifically, it applies a hierarchical multi-output Gaussian process to capture the correlation between data collected from different time steps with a linearly increased number of hyperparameters. Furthermore, an adaptive source task selection along with a bespoke warm staring initialization mechanisms are proposed to better leverage the knowledge extracted from previous optimization exercises. By doing so, the data-driven evolutionary optimization can jump start the optimization in the new environment with a strictly limited computational budget. Experiments on synthetic benchmark test problems and a real-world case study demonstrate the effectiveness of our proposed algorithm against nine state-of-the-art peer algorithms

A New Evolutionary Approach to Optimal Sensor Placement in Water Distribution Networks

The sensor placement problem is modeled as a multi-objective optimization problem with Boolean decision variables. A new multi objective evolutionary algorithm (MOEA) is proposed for approximating and analyzing the set of Pareto optimal solutions. The evaluation of the objective functions requires the execution of a hydraulic simulation model of the network. To organize the simulation results a data structure is proposed which enables the dynamic representation of a sensor placement and its fitness as a heatmap. This allows the definition of information spaces, in which the fitness of a placement can be represented as a matrix or, in probabilistic terms as a histogram. The key element in the new algorithm is this probabilistic representation which is embedded in a space endowed with a metric based on a specific notion of distance. Among several distances between probability distributions the Wasserstein (WST) distance has been selected: WST has enabled to derive new genetic operators, indicators of the quality of the Pareto set and criteria to choose among the Pareto solutions. The new algorithm has been tested on a benchmark water distribution network with two objective functions showing an improvement over NSGA-II, in particular for low generation counts, making it a good candidate for expensive black-box multi-objective optimizatio

A comparative study of evolutionary approaches to the bi-objective dynamic Travelling Thief Problem

Dynamic evolutionary multi-objective optimization is a thriving research area. Recent contributions span the development of specialized algorithms and the construction of challenging benchmark problems. Here, we continue these research directions through the development and analysis of a new bi-objective problem, the dynamic Travelling Thief Problem (TTP), including three modes of dynamic change: city locations, item profit values, and item availability. The interconnected problem components embedded in the dynamic problem dictate that the effective tracking of good trade-off solutions that satisfy both objectives throughout dynamic events is non-trivial. Consequently, we examine the relative contribution to the non-dominated set from a variety of population seeding strategies, including exact solvers and greedy algorithms for the knapsack and tour components, and random techniques. We introduce this responsive seeding extension within an evolutionary algorithm framework. The efficacy of alternative seeding mechanisms is evaluated across a range of exemplary problem instances using ranking-based and quantitative statistical comparisons, which combines performance measurements taken throughout the optimization. Our detailed experiments show that the different dynamic TTP instances present varying difficulty to the seeding methods tested. We posit the dynamic TTP as a suitable benchmark capable of generating problem instances with different controllable characteristics aligning with many real-world problems

Landscape-based Evolutionary Algorithms for Dynamic Optimization Problems

In real-world structured optimization problems, specific objective functions, decision variables, constraints, data and/or parameters may vary over time. These problems are generally recognized as dynamic optimization problems (DOPs). Evolutionary computation (EC) is a stochastic global search approach that has been successfully used to find optimal or near-optimal solutions for a wide range of optimization problems. EC is conceptually simple and imposes no specific mathematical properties requirement, thus showing competitive performance in dealing with static optimization problems. However, EC encounters challenges in dynamic problems on adaptability and efficiency. For the employment of EC in DOPs, two key points should be considered: the nature of optimization problems to be solved and the class of algorithms to be designed, where the crucial element of the former is landscape analysis and the latter frequently leads to the type of the algorithm. A new approach named Landscape Influenced Dynamic Optimization Algorithm (LIDOA) is proposed to incorporate landscape analysis information into the search process, where a landscape-based strategy is integrated with appropriately designed evolutionary algorithms. In LIDOA, the knowledge learned in each landscape is archived and re-utilized in the new environment. Several classical evolutionary algorithms, including genetic algorithm (GA), self-adaptive differential evolution algorithm (jDE) and covariance matrix adaptation evolution strategy (CMA-ES), are employed to examine the efficiency of LIDOA, and four landscape measures are considered. Experimental results showed the overall advantage of LIDOA. LIDOA with a single landscape measure is then expanded to multiple landscape measures. Three multi-measure methods are designed that are able to achieve good performance on evolutionary algorithms with appropriately integrated multiple landscape measures. According to the experimental results, LIDOA with multi-measure methods also improves the performance of GA, jDE and CMA-ES. The second key point in employing multiple evolutionary algorithms in DOPs is also studied. Three multi-algorithm methods are investigated based on jDE and GA, where an information sharing strategy and a self-adjusted parameter strategy are designed. Experimental results show that with an appropriate integration mechanism, all three multi-algorithm methods can obtain better performance over a single algorithm. Two key parameters in multi-algorithm methods are discussed. The similarity check strategy with multi-measure is also integrated with three multi-algorithm methods, and experimental results demonstrate the efficacy of both multi-algorithm methods and multi-measure strategies. Furthermore, to show the applicability of the concept in other algorithms, it is tested on quantum-inspired evolutionary algorithms. The performance of LIDOA with quantum-inspired evolutionary algorithms shows that LIDOA and quantum operators are beneficial for jDE, GA and CMA-ES, though their contributions vary. Finally, the proposed algorithms are applied to two practical problems (parameter estimation for frequency-modulated (FM) sound waves and spread spectrum radar polyphase code design). With appropriately selected landscape measure(s), LIDOA is able to improve the performance on both problems. When the complexity of the two applicable problems increases, the proposed hybrid framework with a multi-algorithm and multi-measure method is more reliable

A-GWASF-GA: The New Version of GWASF-GA to Solve Many Objective Problems

A new version of the evolutionary algorithm based on GWASF-GA [1] is proposed in this work. GWASF-GA is an aggregation-based algorithm which uses the Tchebychev metric plus an augmentation term as fitness function and two reference points (the utopian and nadir points) to classify the individuals according to a set of widely-distributed weight vectors. Although this algorithm obtains a good approximation of the Pareto front (PF) for multi-objective optimization problems, this may be more difficult to obtain for many-objective optimization problems due to the fact that the weight vectors used are never updated along the search process. For this reason, we propose a new version of the algorithm, called A-GWASF-GA, in which a dynamic adjustment of the weight vectors is carried out. The main idea is to re-calculate some weight vectors in order to obtain solutions in parts of the PF with a lack of solutions. Firstly, a percentage (p) of the total number of evaluations is performed with the original GWASF-GA [1]. Secondly, during the rest of evaluations (1-p), we re-calculate na times the projection directions determined by a subset of Na weight vectors. The re-calculation process is based on a scattering level, a measure based on the distance of each solution and the solutions around it. According to the scattering level of the generated solutions, we detect the Na weight vectors projecting toward overcrowded areas of the PF and we re-calculate them so that their new projection directions point towards areas of the PF which are not so well approximated. In order to show the effectiveness of A-GWASF-GA, we compare it with NSGA-III [2, 3], MOEA/D [4], MOEA/D-AWA [5] and the original GWASF-GA.To evaluate their performance, we use the IGD metric [6]. The results of the computational experiment demonstrate the good performance of A-GWASF-GA in the novel many-objective optimization benchmark problems considered.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

A similarity-based cooperative co-evolutionary algorithm for dynamic interval multi-objective optimization problems

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 interval multi-objective optimization problems (DI-MOPs) are very common in real-world applications. However, there are few evolutionary algorithms that are suitable for tackling DI-MOPs up to date. A framework of dynamic interval multi-objective cooperative co-evolutionary optimization based on the interval similarity is presented in this paper to handle DI-MOPs. In the framework, a strategy for decomposing decision variables is first proposed, through which all the decision variables are divided into two groups according to the interval similarity between each decision variable and interval parameters. Following that, two sub-populations are utilized to cooperatively optimize decision variables in the two groups. Furthermore, two response strategies, rgb0.00,0.00,0.00i.e., a strategy based on the change intensity and a random mutation strategy, are employed to rapidly track the changing Pareto front of the optimization problem. The proposed algorithm is applied to eight benchmark optimization instances rgb0.00,0.00,0.00as well as a multi-period portfolio selection problem and compared with five state-of-the-art evolutionary algorithms. The experimental results reveal that the proposed algorithm is very competitive on most optimization instances