Evolutionary Multiobjective Optimization Driven by Generative Adversarial Networks (GANs)

Recently, increasing works have proposed to drive evolutionary algorithms using machine learning models. Usually, the performance of such model based evolutionary algorithms is highly dependent on the training qualities of the adopted models. Since it usually requires a certain amount of data (i.e. the candidate solutions generated by the algorithms) for model training, the performance deteriorates rapidly with the increase of the problem scales, due to the curse of dimensionality. To address this issue, we propose a multi-objective evolutionary algorithm driven by the generative adversarial networks (GANs). At each generation of the proposed algorithm, the parent solutions are first classified into real and fake samples to train the GANs; then the offspring solutions are sampled by the trained GANs. Thanks to the powerful generative ability of the GANs, our proposed algorithm is capable of generating promising offspring solutions in high-dimensional decision space with limited training data. The proposed algorithm is tested on 10 benchmark problems with up to 200 decision variables. Experimental results on these test problems demonstrate the effectiveness of the proposed algorithm

Stochastic Fractal Based Multiobjective Fruit Fly Optimization

The fruit fly optimization algorithm (FOA) is a global optimization algorithm inspired by the foraging behavior of a fruit fly swarm. In this study, a novel stochastic fractal model based fruit fly optimization algorithm is proposed for multiobjective optimization. A food source generating method based on a stochastic fractal with an adaptive parameter updating strategy is introduced to improve the convergence performance of the fruit fly optimization algorithm. To deal with multiobjective optimization problems, the Pareto domination concept is integrated into the selection process of fruit fly optimization and a novel multiobjective fruit fly optimization algorithm is then developed. Similarly to most of other multiobjective evolutionary algorithms (MOEAs), an external elitist archive is utilized to preserve the nondominated solutions found so far during the evolution, and a normalized nearest neighbor distance based density estimation strategy is adopted to keep the diversity of the external elitist archive. Eighteen benchmarks are used to test the performance of the stochastic fractal based multiobjective fruit fly optimization algorithm (SFMOFOA). Numerical results show that the SFMOFOA is able to well converge to the Pareto fronts of the test benchmarks with good distributions. Compared with four state-of-the-art methods, namely, the non-dominated sorting generic algorithm (NSGA-II), the strength Pareto evolutionary algorithm (SPEA2), multi-objective particle swarm optimization (MOPSO), and multiobjective self-adaptive differential evolution (MOSADE), the proposed SFMOFOA has better or competitive multiobjective optimization performance

Dynamic multi-objective optimisation using deep reinforcement learning::benchmark, algorithm and an application to identify vulnerable zones based on water quality

Dynamic multi-objective optimisation problem (DMOP) has brought a great challenge to the reinforcement learning (RL) research area due to its dynamic nature such as objective functions, constraints and problem parameters that may change over time. This study aims to identify the lacking in the existing benchmarks for multi-objective optimisation for the dynamic environment in the RL settings. Hence, a dynamic multi-objective testbed has been created which is a modified version of the conventional deep-sea treasure (DST) hunt testbed. This modified testbed fulfils the changing aspects of the dynamic environment in terms of the characteristics where the changes occur based on time. To the authors’ knowledge, this is the first dynamic multi-objective testbed for RL research, especially for deep reinforcement learning. In addition to that, a generic algorithm is proposed to solve the multi-objective optimisation problem in a dynamic constrained environment that maintains equilibrium by mapping different objectives simultaneously to provide the most compromised solution that closed to the true Pareto front (PF). As a proof of concept, the developed algorithm has been implemented to build an expert system for a real-world scenario using Markov decision process to identify the vulnerable zones based on water quality resilience in São Paulo, Brazil. The outcome of the implementation reveals that the proposed parity-Q deep Q network (PQDQN) algorithm is an efficient way to optimise the decision in a dynamic environment. Moreover, the result shows PQDQN algorithm performs better compared to the other state-of-the-art solutions both in the simulated and the real-world scenario

A Multiobjective Evolutionary Algorithm Using Gaussian Process-Based Inverse Modeling

Cheng R, Jin Y, Narukawa K, Sendhoff B. A Multiobjective Evolutionary Algorithm Using Gaussian Process-Based Inverse Modeling. IEEE Transactions on Evolutionary Computation. 2015;19(6):838-856.To approximate the Pareto front, most existing multiobjective evolutionary algorithms store the nondominated solutions found so far in the population or in an external archive during the search. Such algorithms often require a high degree of diversity of the stored solutions and only a limited number of solutions can be achieved. By contrast, model-based algorithms can alleviate the requirement on solution diversity and in principle, as many solutions as needed can be generated. This paper proposes a new model-based method for representing and searching nondominated solutions. The main idea is to construct Gaussian process-based inverse models that map all found nondominated solutions from the objective space to the decision space. These inverse models are then used to create offspring by sampling the objective space. To facilitate inverse modeling, the multivariate inverse function is decomposed into a group of univariate functions, where the number of inverse models is reduced using a random grouping technique. Extensive empirical simulations demonstrate that the proposed algorithm exhibits robust search performance on a variety of medium to high dimensional multiobjective optimization test problems. Additional nondominated solutions are generated a posteriori using the constructed models to increase the density of solutions in the preferred regions at a low computational cost