Lexicographic optimization is a kind of Multi-objective optimization. In general, multi-objective optimization deals with optimization problems with two or more objective functions to be optimized simultaneously. Often, the different objectives can be ranked in order of importance to the decision-maker, so that objective is the most important, objective is the next most important, and so on. Lexicographic optimization presumes that the decision-maker prefers even a very small increase in , to even a very large increase in etc. Similarly, the decision-maker prefers even a very small increase in , to even a very large increase in etc. In other words, the decision-maker has lexicographic preferences, ranking the possible solutions according to a lexicographic order of their objective function values. Lexicographic optimization is sometimes called preemptive optimization,[1] since a small increase in one objective value preempts a much larger increase in less important objective values.
As an example, consider a firm which puts safety above all. It wants to maximize the safety of its workers and customers. Subject to attaining the maximum possible safety, it wants to maximize profits. This firm performs lexicographic optimization, where denotes safety and denotes profits.
As another example,[2] in project management, when analyzing PERT networks, one often wants to minimize the mean completion time, and subject to this, minimize the variance of the completion time.
^Sherali, H. D.; Soyster, A. L. (1983-02-01). "Preemptive and nonpreemptive multi-objective programming: Relationship and counterexamples". Journal of Optimization Theory and Applications. 39 (2): 173–186. doi:10.1007/BF00934527. ISSN 1573-2878.
Lexicographicoptimization is a kind of Multi-objective optimization. In general, multi-objective optimization deals with optimization problems with two...
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In economics, lexicographic preferences or lexicographic orderings describe comparative preferences where an agent prefers any amount of one good (X) to...
representations of the computation being optimized and the optimization(s) being performed. Loop optimization can be viewed as the application of a sequence...
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point search: an optimization to A* which may reduce computation time by an order of magnitude using further heuristics Lexicographic breadth-first search...
Jayakrishnan formulated the vehicle reidentification problem as a lexicographicoptimization problem and demonstrated robust performance 2000 – David Brownstone...
1090/conm/636/12729 E. Bonacker, A. Gibali, K-H. Küfer and P. Süss, Speedup of lexicographicoptimization by superiorization and its applications to cancer radiotherapy...
a given string, by lexicographic order. Find successor: Locates the smallest string greater than a given string, by lexicographic order. The datastructure...
are numerical order and lexicographical order, and either ascending or descending. Efficient sorting is important for optimizing the efficiency of other...
levels. This is known as lexicographic or pre-emptive goal programming. Ignizio gives an algorithm showing how a lexicographic goal programme can be solved...
discussed above. Optimized radix sorts can be very fast when working in a domain that suits them. They are constrained to lexicographic data, but for many...
the leximin order.: 34 The same is true for the lexicographic order. Lexicographic max-min optimization is the computational problem of finding a maximal...
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is performed Lexicographic order is imposed on the namespace declarations and attributes of each element In morphology and lexicography, a lemma is the...
range of possible code rates, which can be optimized depending on the scenario. Usually, this optimization is done in order to achieve a low decoding...
identification and optimization. Since then, both terms, cheminformatics and chemoinformatics, have been used,[citation needed] although, lexicographically, cheminformatics...
Sourd, Francis (2010), "Lexicographically minimizing axial motions for the Euclidean TSP", Journal of Combinatorial Optimization, 19 (1): 1–15, doi:10...
language processing, such as finding lexicon of a text corpus.: 73 Lexicographic sorting of a set of string keys can be implemented by building a trie...
machine-readable dictionaries. It is distinguished from computational lexicography, which more properly would be the use of computers in the construction...
parameters are adaptively updated throughout the process, according to some optimization approach. The main difference between 1D and 2D adaptive filters is that...
In mathematical optimization, the revised simplex method is a variant of George Dantzig's simplex method for linear programming. The revised simplex method...
substantial consequence was that computational models of heuristics, such as lexicographic rules (Fishburn, 1974) and elimination-by-aspects (Tversky, 1972), became...
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