Mixed-Integer Benchmark Problems for Single-and Bi-Objective Optimization

International audienceWe introduce two suites of mixed-integer benchmark problems to be used for analyzing and comparing black-box optimization algorithms. They contain problems of diverse difficulties that are scalable in the number of decision variables. The bbob-mixint suite is designed by partially discretizing the established BBOB (Black-Box Optimization Benchmarking) problems. The bi-objective problems from the bbob-biobj-mixint suite are, on the other hand, constructed by using the bbob-mixint functions as their separate objectives. We explain the rationale behind our design decisions and show how to use the suites within the COCO (Comparing Continuous Optimizers) platform. Analyzing two chosen functions in more detail, we also provide some unexpected findings about their properties

Multi-surrogate Assisted Efficient Global Optimization for Discrete Problems

Decades of progress in simulation-based surrogate-assisted optimization and unprecedented growth in computational power have enabled researchers and practitioners to optimize previously intractable complex engineering problems. This paper investigates the possible benefit of a concurrent utilization of multiple simulation-based surrogate models to solve complex discrete optimization problems. To fulfill this, the so-called Self-Adaptive Multi-surrogate Assisted Efficient Global Optimization algorithm (SAMA-DiEGO), which features a two-stage online model management strategy, is proposed and further benchmarked on fifteen binary-encoded combinatorial and fifteen ordinal problems against several state-of-the-art non-surrogate or single surrogate assisted optimization algorithms. Our findings indicate that SAMA-DiEGO can rapidly converge to better solutions on a majority of the test problems, which shows the feasibility and advantage of using multiple surrogate models in optimizing discrete problems

IOHanalyzer: Performance Analysis for Iterative Optimization Heuristic

Benchmarking and performance analysis play an important role in understanding the behaviour of iterative optimization heuristics (IOHs) such as local search algorithms, genetic and evolutionary algorithms, Bayesian optimization algorithms, etc. This task, however, involves manual setup, execution, and analysis of the experiment on an individual basis, which is laborious and can be mitigated by a generic and well-designed platform. For this purpose, we propose IOHanalyzer, a new user-friendly tool for the analysis, comparison, and visualization of performance data of IOHs. Implemented in R and C++, IOHanalyzer is fully open source. It is available on CRAN and GitHub. IOHanalyzer provides detailed statistics about fixed-target running times and about fixed-budget performance of the benchmarked algorithms on real-valued, single-objective optimization tasks. Performance aggregation over several benchmark problems is possible, for example in the form of empirical cumulative distribution functions. Key advantages of IOHanalyzer over other performance analysis packages are its highly interactive design, which allows users to specify the performance measures, ranges, and granularity that are most useful for their experiments, and the possibility to analyze not only performance traces, but also the evolution of dynamic state parameters. IOHanalyzer can directly process performance data from the main benchmarking platforms, including the COCO platform, Nevergrad, and our own IOHexperimenter. An R programming interface is provided for users preferring to have a finer control over the implemented functionalities

Marginal Probability-Based Integer Handling for CMA-ES Tackling Single-and Multi-Objective Mixed-Integer Black-Box Optimization

This study targets the mixed-integer black-box optimization (MI-BBO) problem where continuous and integer variables should be optimized simultaneously. The CMA-ES, our focus in this study, is a population-based stochastic search method that samples solution candidates from a multivariate Gaussian distribution (MGD), which shows excellent performance in continuous BBO. The parameters of MGD, mean and (co)variance, are updated based on the evaluation value of candidate solutions in the CMA-ES. If the CMA-ES is applied to the MI-BBO with straightforward discretization, however, the variance corresponding to the integer variables becomes much smaller than the granularity of the discretization before reaching the optimal solution, which leads to the stagnation of the optimization. In particular, when binary variables are included in the problem, this stagnation more likely occurs because the granularity of the discretization becomes wider, and the existing integer handling for the CMA-ES does not address this stagnation. To overcome these limitations, we propose a simple integer handling for the CMA-ES based on lower-bounding the marginal probabilities associated with the generation of integer variables in the MGD. The numerical experiments on the MI-BBO benchmark problems demonstrate the efficiency and robustness of the proposed method. Furthermore, in order to demonstrate the generality of the idea of the proposed method, in addition to the single-objective optimization case, we incorporate it into multi-objective CMA-ES and verify its performance on bi-objective mixed-integer benchmark problems.Comment: Camera-ready version for ACM Transactions on Evolutionary Learning and Optimization (TELO). This paper is an extended version of the work presented in arXiv:2205.1348

Mixed-Integer Benchmark Problems for Single-and Bi-Objective Optimization

submitted to GECCO 2019International audienceWe introduce two suites of mixed-integer benchmark problems to be used for analyzing and comparing black-box optimization algorithms. They contain problems of diverse difficulties that are scalable in the number of decision variables. The bbob-mixint suite is designed by partially discretizing the established BBOB (Black-Box Optimization Benchmarking) problems. The bi-objective problems from the bbob-biobj-mixint suite are, on the other hand, constructed by using the bbob-mixint functions as their separate objectives. We explain the rationale behind our design decisions and show how to use the suites within the COCO (Comparing Continuous Optimizers) platform. Analyzing two chosen functions in more detail, we also provide some unexpected findings about their properties