Algorithm Portfolio for Individual-based Surrogate-Assisted Evolutionary Algorithms

Surrogate-assisted evolutionary algorithms (SAEAs) are powerful optimisation tools for computationally expensive problems (CEPs). However, a randomly selected algorithm may fail in solving unknown problems due to no free lunch theorems, and it will cause more computational resource if we re-run the algorithm or try other algorithms to get a much solution, which is more serious in CEPs. In this paper, we consider an algorithm portfolio for SAEAs to reduce the risk of choosing an inappropriate algorithm for CEPs. We propose two portfolio frameworks for very expensive problems in which the maximal number of fitness evaluations is only 5 times of the problem's dimension. One framework named Par-IBSAEA runs all algorithm candidates in parallel and a more sophisticated framework named UCB-IBSAEA employs the Upper Confidence Bound (UCB) policy from reinforcement learning to help select the most appropriate algorithm at each iteration. An effective reward definition is proposed for the UCB policy. We consider three state-of-the-art individual-based SAEAs on different problems and compare them to the portfolios built from their instances on several benchmark problems given limited computation budgets. Our experimental studies demonstrate that our proposed portfolio frameworks significantly outperform any single algorithm on the set of benchmark problems

Self-Adaptive Surrogate-Assisted Covariance Matrix Adaptation Evolution Strategy

This paper presents a novel mechanism to adapt surrogate-assisted population-based algorithms. This mechanism is applied to ACM-ES, a recently proposed surrogate-assisted variant of CMA-ES. The resulting algorithm, saACM-ES, adjusts online the lifelength of the current surrogate model (the number of CMA-ES generations before learning a new surrogate) and the surrogate hyper-parameters. Both heuristics significantly improve the quality of the surrogate model, yielding a significant speed-up of saACM-ES compared to the ACM-ES and CMA-ES baselines. The empirical validation of saACM-ES on the BBOB-2012 noiseless testbed demonstrates the efficiency and the scalability w.r.t the problem dimension and the population size of the proposed approach, that reaches new best results on some of the benchmark problems.Comment: Genetic and Evolutionary Computation Conference (GECCO 2012) (2012

A Learnheuristic Approach to A Constrained Multi-Objective Portfolio Optimisation Problem

Multi-objective portfolio optimisation is a critical problem researched across various fields of study as it achieves the objective of maximising the expected return while minimising the risk of a given portfolio at the same time. However, many studies fail to include realistic constraints in the model, which limits practical trading strategies. This study introduces realistic constraints, such as transaction and holding costs, into an optimisation model. Due to the non-convex nature of this problem, metaheuristic algorithms, such as NSGA-II, R-NSGA-II, NSGA-III and U-NSGA-III, will play a vital role in solving the problem. Furthermore, a learnheuristic approach is taken as surrogate models enhance the metaheuristics employed. These algorithms are then compared to the baseline metaheuristic algorithms, which solve a constrained, multi-objective optimisation problem without using learnheuristics. The results of this study show that, despite taking significantly longer to run to completion, the learnheuristic algorithms outperform the baseline algorithms in terms of hypervolume and rate of convergence. Furthermore, the backtesting results indicate that utilising learnheuristics to generate weights for asset allocation leads to a lower risk percentage, higher expected return and higher Sharpe ratio than backtesting without using learnheuristics. This leads us to conclude that using learnheuristics to solve a constrained, multi-objective portfolio optimisation problem produces superior and preferable results than solving the problem without using learnheuristics

Partial Evaluation Strategies for Expensive Evolutionary Constrained Optimization

Constrained optimization problems (COPs) are frequently encountered in real-world design applications. For some COPs, the evaluation of the objective(s) and/or constraint(s) may involve significant computational/temporal/financial cost. Such problems are referred to as expensive COPs (ECOPs). Surrogate modeling has been widely used in conjunction with optimization methods for such problems, wherein the search is partially driven by an approximate function instead of true expensive evaluations. However, for any true evaluation, nearly all existing methods compute all objective and constraint values together as one batch. Such full evaluation approaches may be inefficient for cases where the objective/constraint(s) can be evaluated independently of each other. In this article, we propose and study a constraint handling strategy for ECOPs using partial evaluations. The constraints are evaluated in a sequence determined based on their likelihood of being violated; and the evaluation is aborted if a constraint violation is encountered. Modified ranking strategies are introduced to effectively rank the solutions using the limited information thus obtained, while saving on significant function evaluations. The proposed algorithm is compared with a number of its variants to establish the utility of its key components systematically. Numerical experiments and benchmarking are conducted on a range of mathematical and engineering design problems to demonstrate the efficacy of the approach compared to state-of-The-Art evolutionary optimization approaches

Numerical and Evolutionary Optimization 2020

This book was established after the 8th International Workshop on Numerical and Evolutionary Optimization (NEO), representing a collection of papers on the intersection of the two research areas covered at this workshop: numerical optimization and evolutionary search techniques. While focusing on the design of fast and reliable methods lying across these two paradigms, the resulting techniques are strongly applicable to a broad class of real-world problems, such as pattern recognition, routing, energy, lines of production, prediction, and modeling, among others. This volume is intended to serve as a useful reference for mathematicians, engineers, and computer scientists to explore current issues and solutions emerging from these mathematical and computational methods and their applications

A portfolio approach to massively parallel Bayesian optimization

One way to reduce the time of conducting optimization studies is to evaluate designs in parallel rather than just one-at-a-time. For expensive-to-evaluate black-boxes, batch versions of Bayesian optimization have been proposed. They work by building a surrogate model of the black-box that can be used to select the designs to evaluate efficiently via an infill criterion. Still, with higher levels of parallelization becoming available, the strategies that work for a few tens of parallel evaluations become limiting, in particular due to the complexity of selecting more evaluations. It is even more crucial when the black-box is noisy, necessitating more evaluations as well as repeating experiments. Here we propose a scalable strategy that can keep up with massive batching natively, focused on the exploration/exploitation trade-off and a portfolio allocation. We compare the approach with related methods on deterministic and noisy functions, for mono and multiobjective optimization tasks. These experiments show similar or better performance than existing methods, while being orders of magnitude faster

Evolutionary multi-objective worst-case robust optimisation

Many real-world problems are subject to uncertainty, and often solutions should not only be good, but also robust against environmental disturbances or deviations from the decision variables. While most papers dealing with robustness aim at finding solutions with a high expected performance given a distribution of the uncertainty, we examine the trade-off between the allowed deviations from the decision variables (tolerance level), and the worst case performance given the allowed deviations. In this research work, we suggest two multi-objective evolutionary algorithms to compute the available trade-offs between allowed tolerance level and worst-case quality of the solutions, and the tolerance level is defined as robustness which could also be the variations from parameters. Both algorithms are 2-level nested algorithms. While the first algorithm is point-based in the sense that the lower level computes a point of worst case for each upper level solution, the second algorithm is envelope-based, in the sense that the lower level computes a whole trade-off curve between worst-case fitness and tolerance level for each upper level solution. Our problem can be considered as a special case of bi-level optimisation, which is computationally expensive, because each upper level solution is evaluated by calling a lower level optimiser. We propose and compare several strategies to improve the efficiency of both algorithms. Later, we also suggest surrogate-assisted algorithms to accelerate both algorithms

Towards Better Integration of Surrogate Models and Optimizers

Surrogate-Assisted Evolutionary Algorithms (SAEAs) have been proven to be very effective in solving (synthetic and real-world) computationally expensive optimization problems with a limited number of function evaluations. The two main components of SAEAs are: the surrogate model and the evolutionary optimizer, both of which use parameters to control their respective behavior. These parameters are likely to interact closely, and hence the exploitation of any such relationships may lead to the design of an enhanced SAEA. In this chapter, as a first step, we focus on Kriging and the Efficient Global Optimization (EGO) framework. We discuss potentially profitable ways of a better integration of model and optimizer. Furthermore, we investigate in depth how different parameters of the model and the optimizer impact optimization results. In particular, we determine whether there are any interactions between these parameters, and how the problem characteristics impact optimization results. In the experimental study, we use the popular Black-Box Optimization Benchmarking (BBOB) testbed. Interestingly, the analysis finds no evidence for significant interactions between model and optimizer parameters, but independently their performance has a significant interaction with the objective function. Based on our results, we make recommendations on how best to configure EGO