Related papers: Group theory, group actions, evolutionary algorith…
The balance of exploration versus exploitation (EvE) is a key issue on evolutionary computation. In this paper we will investigate how an adaptive controller aimed to perform Operator Selection can be used to dynamically manage the EvE…
This paper presents a piecewise convexification method for solving non-convex multi-objective optimization problems with box constraints. Based on the ideas of the $\alpha$-based Branch and Bound (${\rm \alpha BB}$) method of global…
Beginning with the projectively invariant method for linear programming, interior point methods have led to powerful algorithms for many difficult computing problems, in combinatorial optimization, logic, number theory and non-convex…
The group classification problem for the class of (1+1)-dimensional linear $r$th order evolution equations is solved for arbitrary values of $r>2$. It is shown that a related maximally gauged class of homogeneous linear evolution equations…
Interactions among living organisms, from bacteria colonies to human societies, are inherently more complex than interactions among particles and nonliving matter. Group interactions are a particularly important and widespread class,…
The emergence of collective cooperation in competitive environments is a well-known phenomenon in biology, economics, and social systems. While most evolutionary game models focus on the evolution of strategies for a fixed game, how…
The cryptanalysis of various cipher problems can be formulated as NP-Hard combinatorial problem. Solving such problems requires time and/or memory requirement which increases with the size of the problem. Techniques for solving…
We introduce Genetic AI, a novel method for multi-objective optimization without external parameters or predefined weights. The method can be applied to all problems that can be formulated in matrix form and allows for a data-less training…
In this paper we define a discrete dynamical system that governs the evolution of a population of agents. From the dynamical system, a variant of Differential Evolution is derived. It is then demonstrated that, under some assumptions on the…
In this paper we consider resource allocation problem stated as a convex minimization problem with linear constraints. To solve this problem, we use gradient and accelerated gradient descent applied to the dual problem and prove the…
Current state-of-the-art methods for solving discrete optimization problems are usually restricted to convex settings. In this paper, we propose a general approach based on cutting planes for solving nonlinear, possibly nonconvex, binary…
Machine learning algorithms typically perform optimization over a class of non-convex functions. In this work, we provide bounds on the fundamental hardness of identifying the global minimizer of a non convex function. Specifically, we…
In practice, optimization tasks have some structure that allows developing new algorithms for every problem with faster convergence rates. Using the structure of optimization tasks, we can propose algorithms with more optimistic convergence…
We address the problem of identifying the dynamical law governing the evolution of a population of indistinguishable particles, when only aggregate distributions at successive times are observed. Assuming a Markovian evolution on a discrete…
Understanding how the structure of community interactions is modified by coevolution is vital for understanding system responses to change at all scales. However, in absence of a group selection process, collective community behaviours…
An adaptive regularization algorithm for unconstrained nonconvex optimization is proposed that is capable of handling inexact objective-function and derivative values, and also of providing approximate minimizer of arbitrary order. In…
We study groups, exponential groups and ordered groups equipped with valuations. We investigate algebraic and topological features of such valued structures, and apply our findings in order to solve regular equations over groups using…
In many real world problems, optimization decisions have to be made with limited information. The decision maker may have no a priori or posteriori data about the often nonconvex objective function except from on a limited number of points…
We wish to minimize the resources used for network coding while achieving the desired throughput in a multicast scenario. We employ evolutionary approaches, based on a genetic algorithm, that avoid the computational complexity that makes…
The aim of this paper is to study the evolution of a material point of a body by itself, and not the body as a whole. To do this, we construct a groupoid encoding all the intrinsic properties of the particle and its characteristic…