Can Single Solution Optimisation Methods Be Structurally Biased?

Abstract

This paper investigates whether optimisation methods with the population made up of one solution can suffer from structural bias just like their multisolution variants. Following recent results highlighting the importance of choice of strategy for handling solutions generated outside the domain, a selection of single solution methods are considered in conjunction with several such strategies. Obtained results are tested for the presence of structural bias by means of a traditional approach from literature and a newly proposed here statistical approach. These two tests are demonstrated to be not fully consistent. All tested methods are found to be structurally biased with at least one of the tested strategies. Confirming results for multisolution methods, it is such strategy that is shown to control the emergence of structural bias in single solution methods. Some of the tested methods exhibit a kind of structural bias that has not been observed before.

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

“…• the execution of statistical tests for comparing stochastic optimisation algorithms (described in section 4); • the execution of the novel procedure to compare couples of optimisation algorithms presented in section 4.3; • the generation of plottable files suitable for simple Tikz, Python Matplotlib, Gnuplot or Matlab scripts for displaying best/median/worse/average fitness trends as shown in section 5 and appendix A; • the generations of files containing further plottable information such as histograms, relative to final bests distribution amongst several runs, and graphs describing infeasibility and structural bias in optimisation algorithms (see [1,15,40,41] for details); • the generation of L A T E X tables (both source code and PDF files are produced) showing results in terms average fitness value (or average fitness error) with corresponding standard deviations and further statistical evidence as explained in section 4 and graphically shown in in section 5.…”

“…In this light, the algorithmic design process is not very different to the process performed to choose the less disruptive correction method for handling infeasible solutions generated while addressing a problem [1,15,40] and to the fine-tuning process performed to find the most appropriate set of parameters for an algorithm A meant to address specific problem P.…”

“…are known, we can understand what the effect of the parameters is when the fitness landscape displays particular mathematical features. As a result, specific regions of the parameters space could be detected to obtain a robust general-purpose behaviour rather then a very problem-specific one, or to strengthen exploitation capabilities rather than exploration capabilities, or to minimise the rise of algorithmic structural biases, as done in [1,11,40], the generation of a high number of infeasible solutions, as done in [1,15] or premature convergence [46] and stagnation [47], as done in [10].…”

“…• libraries with implementations of the most popular algorithmic operators such as mutation methods, crossover methods, parent and survivor selection mechanisms, heuristics seleection methods for memetic computing (MC) and hyperheuristic approaches, etc; • utility methods for generating random numbers, solutions or population of solutions, keeping track of the best newly found solutions and save them to plot fitness trends, handling infeasible solutions [1,14,15];…”

Can Compact Optimisation Algorithms Be Structurally Biased?

“…To identify SB, we build on the previous studies [14,13] where Kolmogorov-Smirnov test has been used for hypothesis testing. Here, we propose a different statistical approach which tests the uniformity of final points per dimension via a non-parametric goodness-of-fit test -the Anderson-Darling (AD) test is chosen given its high statistical power [20].…”