Analysis of modular CMA-ES on strict box-constrained problems in the SBOX-COST benchmarking suite

Box-constraints limit the domain of decision variables and are common in real-world optimization problems, for example, due to physical, natural or spatial limitations. Consequently, solutions violating a box-constraint may not be evaluable. This assumption is often ignored in the literature, e.g., existing benchmark suites, such as COCO/BBOB, allow the optimizer to evaluate infeasible solutions. This paper presents an initial study on the strict-box-constrained benchmarking suite (SBOX-COST), which is a variant of the well-known BBOB benchmark suite that enforces box-constraints by returning an invalid evaluation value for infeasible solutions. Specifically, we want to understand the performance difference between BBOB and SBOX-COST as a function of two initialization methods and six constraint-handling strategies all tested with modular CMA-ES. We find that, contrary to what may be expected, handling box-constraints by saturation is not always better than not handling them at all. However, across all BBOB functions, saturation is better than not handling, and the difference increases with the number of dimensions. Strictly enforcing box-constraints also has a clear negative effect on the performance of classical CMA-ES (with uniform random initialization and no constraint handling), especially as problem dimensionality increases

Sufficient Conditions for Feasibility and Optimality of Real-Time Optimization Schemes - I. Theoretical Foundations

The idea of iterative process optimization based on collected output measurements, or "real-time optimization" (RTO), has gained much prominence in recent decades, with many RTO algorithms being proposed, researched, and developed. While the essential goal of these schemes is to drive the process to its true optimal conditions without violating any safety-critical, or "hard", constraints, no generalized, unified approach for guaranteeing this behavior exists. In this two-part paper, we propose an implementable set of conditions that can enforce these properties for any RTO algorithm. The first part of the work is dedicated to the theory behind the sufficient conditions for feasibility and optimality (SCFO), together with their basic implementation strategy. RTO algorithms enforcing the SCFO are shown to perform as desired in several numerical examples - allowing for feasible-side convergence to the plant optimum where algorithms not enforcing the conditions would fail.Comment: Working paper; supplementary material available at: http://infoscience.epfl.ch/record/18807

Constrained Optimization with Evolutionary Algorithms: A Comprehensive Review

Global optimization is an essential part of any kind of system. Various algorithms have been proposed that try to imitate the learning and problem solving abilities of the nature up to certain level. The main idea of all nature-inspired algorithms is to generate an interconnected network of individuals, a population. Although most of unconstrained optimization problems can be easily handled with Evolutionary Algorithms (EA), constrained optimization problems (COPs) are very complex. In this paper, a comprehensive literature review will be presented which summarizes the constraint handling techniques for COP

An Optimisation-Driven Prediction Method for Automated Diagnosis and Prognosis

open access articleThis article presents a novel hybrid classification paradigm for medical diagnoses and prognoses prediction. The core mechanism of the proposed method relies on a centroid classification algorithm whose logic is exploited to formulate the classification task as a real-valued optimisation problem. A novel metaheuristic combining the algorithmic structure of Swarm Intelligence optimisers with the probabilistic search models of Estimation of Distribution Algorithms is designed to optimise such a problem, thus leading to high-accuracy predictions. This method is tested over 11 medical datasets and compared against 14 cherry-picked classification algorithms. Results show that the proposed approach is competitive and superior to the state-of-the-art on several occasions

Application of Genetic Algorithm in Multi-objective Optimization of an Indeterminate Structure with Discontinuous Space for Support Locations

In this thesis, an indeterminate structure was developed with multiple competing objectives including the equalization of the load distribution among the supports while maximizing the stability of the structure. Two different coding algorithms named “Continuous Method” and “Discretized Method” were used to solve the optimal support locations using Genetic Algorithms (GAs). In continuous method, a continuous solution space was considered to find optimal support locations. The failure of this method to stick to the acceptable optimal solution led towards the development of the second method. The latter approach divided the solution space into rectangular grids, and GAs acted on the index number of the nodal points to converge to the optimality. The average value of the objective function in the discretized method was found to be 0.147 which was almost onethird of that obtained by the continuous method. The comparison based on individual components of the objective function also proved that the proposed method outperformed the continuous method. The discretized method also showed faster convergence to the optima. Three circular discontinuities were added to the structure to make it more realistic and three different penalty functions named flat, linear and non-linear penalty were used to handle the constraints. The performance of the two methods was observed with the penalty functions while increasing the radius of the circles by 25% and 50% which showed no significant difference. Later, the discretized method was coded to eliminate the discontinuous area from the solution space which made the application of the penalty functions redundant. A paired t-test (α=5%) showed no statistical difference between these two methods. Finally, to make the proposed method compatible with irregular shaped discontinuous areas, “FEA Integrated Coded Discretized Method (FEAICDM)” was developed. The manual elimination of the infeasible areas from the candidate surface was replaced by the nodal points of the mesh generated by Solid Works. A paired t-test (α=5%) showed no statistical difference between these two methods. Though FEAICDM was applied only to a class of problem, it can be concluded that FEAICDM is more robust and efficient than the continuous method for a class of constrained optimization problem

A Clustering System for Dynamic Data Streams Based on Metaheuristic Optimisation

open access articleThis article presents the Optimised Stream clustering algorithm (OpStream), a novel approach to cluster dynamic data streams. The proposed system displays desirable features, such as a low number of parameters and good scalability capabilities to both high-dimensional data and numbers of clusters in the dataset, and it is based on a hybrid structure using deterministic clustering methods and stochastic optimisation approaches to optimally centre the clusters. Similar to other state-of-the-art methods available in the literature, it uses “microclusters” and other established techniques, such as density based clustering. Unlike other methods, it makes use of metaheuristic optimisation to maximise performances during the initialisation phase, which precedes the classic online phase. Experimental results show that OpStream outperforms the state-of-the-art methods in several cases, and it is always competitive against other comparison algorithms regardless of the chosen optimisation method. Three variants of OpStream, each coming with a different optimisation algorithm, are presented in this study. A thorough sensitive analysis is performed by using the best variant to point out OpStream’s robustness to noise and resiliency to parameter changes

The SOS Platform: Designing, Tuning and Statistically Benchmarking Optimisation Algorithms

open access articleWe present Stochastic Optimisation Software (SOS), a Java platform facilitating the algorithmic design process and the evaluation of metaheuristic optimisation algorithms. SOS reduces the burden of coding miscellaneous methods for dealing with several bothersome and time-demanding tasks such as parameter tuning, implementation of comparison algorithms and testbed problems, collecting and processing data to display results, measuring algorithmic overhead, etc. SOS provides numerous off-the-shelf methods including: (1) customised implementations of statistical tests, such as the Wilcoxon rank-sum test and the Holm–Bonferroni procedure, for comparing the performances of optimisation algorithms and automatically generating result tables in PDF and formats; (2) the implementation of an original advanced statistical routine for accurately comparing couples of stochastic optimisation algorithms; (3) the implementation of a novel testbed suite for continuous optimisation, derived from the IEEE CEC 2014 benchmark, allowing for controlled activation of the rotation on each testbed function. Moreover, we briefly comment on the current state of the literature in stochastic optimisation and highlight similarities shared by modern metaheuristics inspired by nature. We argue that the vast majority of these algorithms are simply a reformulation of the same methods and that metaheuristics for optimisation should be simply treated as stochastic processes with less emphasis on the inspiring metaphor behind them

Can compact optimisation algorithms be structurally biased?

In the field of stochastic optimisation, the so-called structural bias constitutes an undesired behaviour of an algorithm that is unable to explore the search space to a uniform extent. In this paper, we investigate whether algorithms from a subclass of estimation of distribution algorithms, the compact algorithms, exhibit structural bias. Our approach, justified in our earlier publications, is based on conducting experiments on a test function whose values are uniformly distributed in its domain. For the experiment, 81 combinations of compact algorithms and strategies of dealing with infeasible solutions have been selected as test cases. We have applied two approaches for determining the presence and severity of structural bias, namely an (existing) visual and an (updated) statistical (Anderson-Darling) test. Our results suggest that compact algorithms are more immune to structural bias than their counterparts maintaining explicit populations. Both tests indicate that strong structural bias is found only in the cBFO algorithm, regardless of the choice of strategy of dealing with infeasible solutions, and cPSO with mirror strategy. For other test cases, statistical and visual tests disagree on some cases classified as having mild or strong structural bias: the former one tends to make harsher decisions, thus needing further investigation