The use of surrogate based optimization (SBO) is widely spread in engineering design to reduce the number of computational expensive simulations. However, “real-world” problems often consist of multiple, conflicting objectives leading to a set of competitive solutions (the Pareto front). The...

Let <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\{a_i:i\in I\}$$</EquationSource> </InlineEquation> be a finite set in <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$\mathbb R ^n$$</EquationSource> </InlineEquation>. The illumination problem addressed in this work is about selecting an apex <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$z$$</EquationSource> </InlineEquation> in a prescribed set <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$$Z\subseteq \mathbb R ^n$$</EquationSource> </InlineEquation> and a unit vector <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$$y\in \mathbb R ^n$$</EquationSource> </InlineEquation> so that the conic light beam <Equation ID="Equ55"> <EquationSource Format="TEX">$$\begin{aligned}...</equationsource></equation></equationsource></inlineequation></equationsource></inlineequation></equationsource></inlineequation></equationsource></inlineequation></equationsource></inlineequation>

Using local search method, this paper provides a polynomial time approximation scheme for the minimum vertex cover problem on <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$d$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>d</mi> </math> </EquationSource> </InlineEquation>-dimensional ball graphs where <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$d \ge 3$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi>d</mi> <mo>≥</mo> <mn>3</mn> </mrow> </math> </EquationSource> </InlineEquation>. The key to the proof is a new separator theorem for ball graphs in higher dimensional space....</equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation>

New versions and extensions of Benson’s outer approximation algorithm for solving linear vector optimization problems are presented. Primal and dual variants are provided in which only one scalar linear program has to be solved in each iteration rather than two or three as in previous...

The problem of finding large complete subgraphs in bipartite graphs (that is, bicliques) is a well-known combinatorial optimization problem referred to as the maximum-edge biclique problem (MBP), and has many applications, e.g., in web community discovery, biological data analysis and text...

McCormick (Math Prog 10(1):147–175, <CitationRef CitationID="CR23">1976</CitationRef>) provides the framework for convex/concave relaxations of factorable functions, via rules for the product of functions and compositions of the form <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$F\circ f$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi>F</mi> <mo>∘</mo> <mi>f</mi> </mrow> </math> </EquationSource> </InlineEquation>, where <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$F$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>F</mi> </math> </EquationSource> </InlineEquation> is a univariate function. Herein, the composition...</equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></citationref>

In deterministic continuous constrained global optimization, upper bounding the objective function generally resorts to local minimization at several nodes/iterations of the branch and bound. We propose in this paper an alternative approach when the constraints are inequalities and the feasible...

In the recent paper (Locatelli and Schoen in Math Program, <CitationRef CitationID="CR11">2013</CitationRef>) it is shown that the value of the convex envelope of some bivariate functions over polytopes can be computed by solving a continuously differentiable convex problem. In this paper we show how this result can be exploited to derive...</citationref>

Packing problems are <Emphasis Type="SmallCaps">np-hard problems with several practical applications. A variant of a <Emphasis Type="SmallCaps">2d Packing Problem (2<Emphasis Type="SmallCaps">dpp) was proposed in the <Emphasis Type="SmallCaps">gecco 2008 competition session. In this paper, Memetic Algorithms (<Emphasis Type="SmallCaps">mas) and Hyperheuristics are applied to a multiobjectivised version of the 2<Emphasis Type="SmallCaps">dpp....</emphasis></emphasis></emphasis></emphasis></emphasis></emphasis>

A set of ellipses, with given semi-major and semi-minor axes, is to be cut from a rectangular design plate, while minimizing the area of the design rectangle. The design plate is subject to lower and upper bounds of its widths and lengths; the ellipses are free of any orientation restrictions....