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We describe a recursive algorithm that decomposes an algebraic set into locally closed equidimensional sets, i.e. sets which each have irreducible components of the same dimension. At the core of this algorithm, we combine ideas from the…
A criticism sometimes made of the causal set quantum gravity program is that there is no practical scheme for identifying manifoldlike causal sets and finding embeddings of them into manifolds. A computational method for constructing an…
The development and identification of effective optimization algorithms for non-convex real-world problems is a challenge in global optimization. Because theoretical performance analysis is difficult, and problems based on models of…
According to the published papers and books since the turn of the century, Pareto optimization is the dominating assessment method for multi-objective nonlinear optimization problems treated by population-based optimizers like Evolutionary…
In multi-objective optimization, a single decision vector must balance the trade-offs between many objectives. Solutions achieving an optimal trade-off are said to be Pareto optimal: these are decision vectors for which improving any one…
In this study, a nondominated-solution-based multi-objective greedy method is proposed and applied to a sensor selection problem based on the multiple indices of the optimal design of experiments. The proposed method simultaneously…
The reduction of constraints to obtain minimal representations of sets is a very common problem in many engineering applications. While well-established methodologies exist for the case of linear constraints, the problem of how to detect…
We use Sidon sets to present an elementary method to study some combinatorial problems in finite fields, such as sum product estimates, solubility of some equations and distribution of sequences in small intervals. We obtain classic and…
Benchmark problems play a central role in assessing the performance of numerical optimization algorithms. However, many existing constrained multiobjective optimization benchmark problems rely on overly restricted constructions or lack…
The aim of this paper is to provide the results that answer the Kuratowski problem posed in 1935 concerning the existence of nonmeasurable sets. The Kuratowski problem was considered for partitions, here we provide a generalization to…
Many real-world applications require the joint optimization of a large number of flexible devices over time. The flexibility of, e.g., multiple batteries, thermostatically controlled loads, or electric vehicles can be used to support grid…
Generally, multi-objective optimisation problems are solved exactly or approximated by solving a series of scalarisations, for example by dichotomic search. In this paper, we take a different approach and attempt to compute the set of all…
In this article we show that the boundary of the Pareto critical set of an unconstrained multiobjective optimization problem (MOP) consists of Pareto critical points of subproblems considering subsets of the objective functions. If the…
The Minkowski product of unit quaternion sets is introduced and analyzed, motivated by the desire to characterize the overall variation of compounded spatial rotations that result from individual rotations subject to known uncertainties in…
We investigate the extrinsic geometry of causal sets in $(1+1)$-dimensional Minkowski spacetime. The properties of boundaries in an embedding space can be used not only to measure observables, but also to supplement the discrete action in…
We present a new method for embedding a causal set into an interval of Minkowski spacetime. The method uses spacetime volumes for causally related elements to define causal set analogs of Minkowski inner products. These are used to…
Budgeted uncertainty sets have been established as a major influence on uncertainty modeling for robust optimization problems. A drawback of such sets is that the budget constraint only restricts the global amount of cost increase that can…
The "Subset Sum problem" is a very well-known NP-complete problem. In this work, a top-k variation of the "Subset Sum problem" is considered. This problem has wide application in recommendation systems, where instead of k best objects the k…
For effective decision support in scenarios with conflicting objectives, sets of potentially optimal solutions can be presented to the decision maker. We explore both what policies these sets should contain and how such sets can be computed…
The problem of selecting a small, yet high quality subset of patterns from a larger collection of itemsets has recently attracted lot of research. Here we discuss an approach to this problem using the notion of decomposable families of…