Given n terminals in the Euclidean plane and a positive constant l, find a Steiner tree T interconnecting all terminals with the minimum total cost of Steiner points and a specific material used to construct all edges in T such that the Euclidean length of each edge in T is no more than l. In...

In contrast to classical optimization problems, in multiobjective optimization several objective functions are considered at the same time. For these problems, the solution is not a single optimum but a set of optimal compromises, the so-called Pareto set. In this work, we consider...

In this paper we develop an algorithm to optimise a nonlinear utility function of multiple objectives over the integer efficient set. Our approach is based on identifying and updating bounds on the individual objectives as well as the optimal utility value. This is done using already known...

Only a few attempts in past have been made in adopting a unified outlook towards different paradigms in evolutionary computation (EC). The underlying motivation of these studies was aimed at gaining better understanding of evolutionary methods, both at the level of theory as well as application,...

The purpose of this paper is to show that the iterative scheme recently studied by Xu (J Glob Optim 36(1):115–125, <CitationRef CitationID="CR8">2006</CitationRef>) is the same as the one studied by Kamimura and Takahashi (J Approx Theory 106(2):226–240, <CitationRef CitationID="CR2">2000</CitationRef>) and to give a supplement to these results. With the new technique proposed...</citationref></citationref>

Let (X, d) be a complete metric space and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$${TX \longrightarrow X }$$</EquationSource> </InlineEquation> be a mapping with the property d(Tx, Ty) ≤ ad(x, y) + bd(x, Tx) + cd(y, Ty) + ed(y, Tx) + fd(x, Ty) for all <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$${x, y \in X}$$</EquationSource> </InlineEquation>, where 0 a 1, b, c, e, f ≥ 0, a + b + c + e + f=1 and b + c 0. We show that if e...</equationsource></inlineequation></equationsource></inlineequation>

We introduce vanishing generalized Morrey spaces <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$${V\mathcal{L}^{p,\varphi}_\Pi (\Omega), \Omega \subseteq \mathbb{R}^n}$$</EquationSource> </InlineEquation> with a general function <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$${\varphi(x, r)}$$</EquationSource> </InlineEquation> defining the Morrey-type norm. Here <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$${\Pi \subseteq \Omega}$$</EquationSource> </InlineEquation> is an arbitrary subset in Ω including the extremal cases <InlineEquation ID="IEq4"> <EquationSource...</equationsource></inlineequation></equationsource></inlineequation></equationsource></inlineequation></equationsource></inlineequation>

In this work, the problem of a company or chain (the leader) that considers the reaction of a competitor chain (the follower) is studied. In particular, the leader wants to set up a single new facility in a planar market where similar facilities of the follower, and possibly of its own chain,...

In this paper we develop and derive the computational cost of an <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$${\varepsilon}$$</EquationSource> </InlineEquation> -approximation algorithm for a class of global optimization problems, where a suitably defined composition of some ratio functions is minimized over a convex set. The result extends a previous one about a class...</equationsource></inlineequation>

The notions of upper and lower exhausters represent generalizations of the notions of exhaustive families of upper convex and lower concave approximations (u.c.a., l.c.a.). The notions of u.c.a.’s and l.c.a.’s were introduced by Pshenichnyi (Convex Analysis and Extremal Problems, Series in...