No-Free-Lunch Theorems in the continuum

Free Lunch or No Free Lunch: That is not Just a Question?

The increasing popularity of metaheuristic algorithms has attracted a great deal of attention in algorithm analysis and performance evaluations. No-free-lunch theorems are of both theoretical and practical importance, while many important studies on convergence analysis of various metaheuristic algorithms have proven to be fruitful. This paper discusses the recent results on no-free-lunch theorems and algorithm convergence, as well as their important implications for algorithm development in practice. Free lunches may exist for certain types of problem. In addition, we will highlight some open…

Recent Results on No-Free-Lunch Theorems for Optimization

The sharpened No-Free-Lunch-theorem (NFL-theorem) states that the performance of all optimization algorithms averaged over any finite set F of functions is equal if and only if F is closed under permutation (c.u.p.) and each target function in F is equally likely. In this paper, we first summarize some consequences of this theorem, which have been proven recently: The average number of evaluations needed to find a desirable (e.g., optimal) solution can be calculated; the number of subsets c.u.p. can be neglected compared to the overall number of possible subsets; and problem classes relevant i…

Spontaneous Fruit Fly Optimisation for truss weight minimisation: Performance evaluation based on the no free lunch theorem

Over the past decade, several researchers have presented various optimisation algorithms for use in truss design. The no free lunch theorem implies that no optimisation algorithm fits all problems; therefore, the interest is not only in the accuracy and convergence rate of the algorithm but also the tuning effort and population size required for achieving the optimal result. The latter is particularly crucial for computationally intensive or high-dimensional problems. Contrast-based Fruit-fly Optimisation Algorithm (c-FOA) proposed by Kanarachos et al. in 2017 is based on the efficiency of fru…

Free Lunch for Optimisation under the Universal Distribution

Function optimisation is a major challenge in computer science. The No Free Lunch theorems state that if all functions with the same histogram are assumed to be equally probable then no algorithm outperforms any other in expectation. We argue against the uniform assumption and suggest a universal prior exists for which there is a free lunch, but where no particular class of functions is favoured over another. We also prove upper and lower bounds on the size of the free lunch.

排列优化中无免费午餐违反现象的经验评估

Empirical Evaluation of No Free Lunch Violations in Permutation-Based Optimization

本文研究了排列优化中目标改写和基准设计如何产生结构化局部偏离无免费午餐直觉，强调算法选择需考虑问题类别和目标表示。

Nonlocal gradients in bounded domains motivated by Continuum Mechanics: Fundamental Theorem of Calculus and embeddings

In this paper we develop a new set of results based on a nonlocal gradient jointly inspired by the Riesz s-fractional gradient and Peridynamics, in the sense that its integration domain depends on a ball of radius delta > 0 (horizon of interaction among particles, in the terminology of Peridynamics), while keeping at the same time the singularity of the Riesz potential in its integration kernel. Accordingly, we define a functional space suitable for nonlocal models in Calculus of Variations and partial differential equations. Our motivation is to develop the proper functional analysis framewor…