Characterizations of bivariate conic, extreme value, and Archimax copulas

Based on a general construction method by means of bivariate ultramodular copulas we construct, for particular settings, special bivariate conic, extreme value, and Archimax copulas. We also show that the sets of copulas obtained in this way are dense in the sets of all conic, extreme value, and Archimax copulas, respectively

Invariant copulas

summary:Copulas which are invariant with respect to the construction of the corresponding survival copula and other related dualities are studied. A full characterization of invariant associative copulas is given

Copulas: compatibility and Fr\'echet classes

We determine under which conditions three bivariate copulas are compatible, viz. they are the bivariate marginals of the same trivariate copula, and, then, construct the class of these copulas. In particular, the upper and lower bounds for this class of trivariate copulas are determined.Comment: LaTeX, 14 page

DECMO2: a robust hybrid and adaptive multi-objective evolutionary algorithm.

We describe a hybrid and adaptive coevolutionary optimization method that can efficiently solve a wide range of multi-objective optimization problems (MOOPs) as it successfully combines positive traits from three main classes of multi-objective evolutionary algorithms (MOEAs): classical approaches that use Pareto-based selection for survival criteria, approaches that rely on differential evolution, and decomposition-based strategies. A key part of our hybrid evolutionary approach lies in the proposed fitness sharing mechanism that is able to smoothly transfer information between the coevolved subpopulations without negatively impacting the specific evolutionary process behavior that characterizes each subpopulation. The proposed MOEA also features an adaptive allocation of fitness evaluations between the coevolved populations to increase robustness and favor the evolutionary search strategy that proves more successful for solving the MOOP at hand. Apart from the new evolutionary algorithm, this paper also contains the description of a new hypervolume and racing-based methodology aimed at providing practitioners from the field of multi-objective optimization with a simple means of analyzing/reporting the general comparative run-time performance of multi-objective optimization algorithms over large problem sets

Performance comparison of generational and steady-state asynchronous multi-objective evolutionary algorithms for computationally-intensive problems.

In the last two decades, multi-objective evolutionary algorithms (MOEAs) have become ever more used in scientific and industrial decision support and decision making contexts the require an a posteriori articulation of preference. The present work is focused on a comparative analysis of the performance of two master–slave parallelization (MSP) methods, the canonical generational scheme and the steady-state asynchronous scheme. Both can be used to improve the convergence speed of multi-objective evolutionary algorithms that must use computationally-intensive fitness evaluation functions. Both previous and present experiments show that a correct choice for one or the other parallelization method can lead to substantial improvements with regard to the overall duration of the optimization process. Our main aim is to provide practitioners of MOEAs with a simple but effective method of deciding which MSP option is better given the particularities of the concrete optimization process. This in turn, would give the decision maker more time for articulating preferences (i.e., more flexibility). Our analysis is performed based on 15 well-known MOOP benchmark problems and two simulation-based industrial optimization processes from the field of electrical drive design. For the first industrial MOOP, when comparing with a preliminary study, applying the steady-state asynchronous MSP enables us to achieve an overall speedup (in terms of total wall-clock computation time) of ≈25%. For the second industrial MOOP, applying the steady-state MSP produces an improvement of ≈12%. We focus our study on two of the best known and most widely used MOEAs: the Non-dominated Sorting Genetic Algorithm II (NSGA-II) and the Strength Pareto Evolutionary Algorithm (SPEA2)

Coherence and avoidance of sure loss for standardized functions and semicopulas

We discuss avoidance of sure loss and coherence results for semicopulas and standardized functions, i.e., for grounded, 1-increasing functions with value $1$ at $(1,1,\ldots, 1)$. We characterize the existence of a $k$-increasing $n$-variate function $C$ fulfilling $A\leq C\leq B$ for standardized $n$-variate functions $A,B$ and discuss the method for constructing this function. Our proofs also include procedures for extending functions on some countably infinite mesh to functions on the unit box. We provide a characterization when $A$ respectively $B$ coincides with the pointwise infimum respectively supremum of the set of all $k$-increasing $n$-variate functions $C$ fulfilling $A\leq C\leq B$.Comment: 31 pages, 2 figure