This paper proposes a dynamic lexicographic approach to tackle multi-objective optimization problems. In this method, the ordering of objectives, which reflects their relative preferences, is changed in a dynamic fashion during the search. This approach eliminates the need for the decision-maker to establish fixed preferences among the competing objectives, which is often difficult. At the same...

We present a global consistency algorithm for the lexicographic ordering constraint on two vectors of n variables. The algorithm maintains arcconsistency, runs in O(n) time on posting plus amortized O(1) time per propagation event, and detects entailment or rewrites itself to a simpler constraint whenever possible. The algorithm was derived from a finite automaton operating on a string which ca...

lexicographic ordering by spectral moments ($s$-order) among all trees is discussed in this‎ ‎paper‎. ‎for two given positive integers $p$ and $q$ with $pleqslant q$‎, ‎we denote $mathscr{t}_n^{p‎, ‎q}={t‎: ‎t$ is a tree of order $n$ with a $(p‎, ‎q)$-bipartition}‎. furthermore, ‎the last four trees‎, ‎in the $s$-order‎, ‎among $mathscr{t}_n^{p‎, ‎q},(4leqslant pleqslant q)$ are characterized‎.

The Knuth-Bendix ordering is usually preferred over the lexicographic path ordering in successful implementations of resolution and superposition, but it is incompatible with certain requirements of hierarchic superposition calculi. Moreover, it does not allow non-linear definition equations to be oriented in a natural way. We present an extension of the Knuth-Bendix ordering that makes it poss...

A linear ordering is said to be representable if it can be order-embedded into the reals. Representable linear orderings have been characterized as those which are separable in the order topology and have at most countably many jumps. We use this characterization to study the representability of a lexicographic product of linear orderings. First we count the jumps in a lexicographic product in ...

In this paper we present three new characterizations of Sturmian words based on the lexicographic ordering of their factors.

This paper introduces and studies the leximin Paretian ordering, which refines the consensual leximin ordering by adding the Pareto principle to the concept of lexicographic egalitarianism. We also provide an alternative characterization of the consensual Rawlsian ordering. We introduce several new axioms, including the Permutation Pareto Principle and Internal Dominance, and study their logica...

It is shown that small fragments of the first-order theory of the subword order, the (partial) lexicographic path ordering on words, the homomorphism preorder, and the infix order are undecidable. This is in contrast to the decidability of the monadic second-order theory of the prefix order [M.O. Rabin, Trans. Amer. Math. Soc., 1969] and of the theory of the total lexicographic path ordering [P...