96,047 research outputs found
Optimising a nonlinear utility function in multi-objective integer programming
In this paper we develop an algorithm to optimise a nonlinear utility
function of multiple objectives over the integer efficient set. Our approach is
based on identifying and updating bounds on the individual objectives as well
as the optimal utility value. This is done using already known solutions,
linear programming relaxations, utility function inversion, and integer
programming. We develop a general optimisation algorithm for use with k
objectives, and we illustrate our approach using a tri-objective integer
programming problem.Comment: 11 pages, 2 tables; v3: minor revisions, to appear in Journal of
Global Optimizatio
Multi-objective integer programming: An improved recursive algorithm
This paper introduces an improved recursive algorithm to generate the set of
all nondominated objective vectors for the Multi-Objective Integer Programming
(MOIP) problem. We significantly improve the earlier recursive algorithm of
\"Ozlen and Azizo\u{g}lu by using the set of already solved subproblems and
their solutions to avoid solving a large number of IPs. A numerical example is
presented to explain the workings of the algorithm, and we conduct a series of
computational experiments to show the savings that can be obtained. As our
experiments show, the improvement becomes more significant as the problems grow
larger in terms of the number of objectives.Comment: 11 pages, 6 tables; v2: added more details and a computational stud
An exact method for a discrete multiobjective linear fractional optimization
Integer linear fractional programming problem with multiple objective MOILFP is an important field of research and has not received as much attention as did multiple objective linear fractional programming. In this work, we develop a branch and cut algorithm based on continuous fractional optimization, for generating the whole integer efficient solutions of the MOILFP problem. The basic idea of the computation phase of the algorithm is to optimize one of the fractional objective functions, then generate an integer feasible solution. Using the reduced gradients of the objective functions, an efficient cut is built and a part of the feasible domain not containing efficient solutions is truncated by adding this cut. A sample problem is solved using this algorithm, and the main practical advantages of the algorithm are indicated
A Parametric Simplex Algorithm for Linear Vector Optimization Problems
In this paper, a parametric simplex algorithm for solving linear vector
optimization problems (LVOPs) is presented. This algorithm can be seen as a
variant of the multi-objective simplex (Evans-Steuer) algorithm [12]. Different
from it, the proposed algorithm works in the parameter space and does not aim
to find the set of all efficient solutions. Instead, it finds a solution in the
sense of Loehne [16], that is, it finds a subset of efficient solutions that
allows to generate the whole frontier. In that sense, it can also be seen as a
generalization of the parametric self-dual simplex algorithm, which originally
is designed for solving single objective linear optimization problems, and is
modified to solve two objective bounded LVOPs with the positive orthant as the
ordering cone in Ruszczynski and Vanderbei [21]. The algorithm proposed here
works for any dimension, any solid pointed polyhedral ordering cone C and for
bounded as well as unbounded problems. Numerical results are provided to
compare the proposed algorithm with an objective space based LVOP algorithm
(Benson algorithm in [13]), that also provides a solution in the sense of [16],
and with Evans-Steuer algorithm [12]. The results show that for non-degenerate
problems the proposed algorithm outperforms Benson algorithm and is on par with
Evan-Steuer algorithm. For highly degenerate problems Benson's algorithm [13]
excels the simplex-type algorithms; however, the parametric simplex algorithm
is for these problems computationally much more efficient than Evans-Steuer
algorithm.Comment: 27 pages, 4 figures, 5 table
A REVIEW OF APPLICATIONS OF MULTIPLE - CRITERIA DECISION-MAKING TECHNIQUES TO FISHERIES
Management of public resources, such as fisheries, is a complex task. Society, in general, has a number of goals that it hopes to achieve from the use of public resources. These include conservation, economic, and social objectives. However, these objectives often conflict, due to the varying opinions of the many stakeholders. It would appear that the techniques available in the field of multiple-criteria decision-making (MCDM) are well suited to the analysis and determination of fisheries management regimes. However, to date, relatively few publications exist using such MCDM methods compared to other applicational fields, such as forestry, agriculture, and finance. This paper reviews MCDM applied to fishery management by providing an overview of the research published to date. Conclusions are drawn regarding the success and applicability of these techniques to analyzing fisheries management problems.Resource /Energy Economics and Policy,
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Multi-objective global optimization for hydrologic models
The development of automated (computer-based) calibration methods has focused mainly on the selection of a single-objective measure of the distance between the model-simulated output and the data and the selection of an automatic optimization algorithm to search for the parameter values which minimize that distance. However, practical experience with model calibration suggests that no single-objective function is adequate to measure the ways in which the model fails to match the important characteristics of the observed data. Given that some of the latest hydrologic models simulate several of the watershed output fluxes (e.g. water, energy, chemical constituents, etc.), there is a need for effective and efficient multi-objective calibration procedures capable of exploiting all of the useful information about the physical system contained in the measurement data time series. The MOCOM-UA algorithm, an effective and efficient methodology for solving the multiple-objective global optimization problem, is presented in this paper. The method is an extension of the successful SCE-UA single-objective global optimization algorithm. The features and capabilities of MOCOM-UA are illustrated by means of a simple hydrologic model calibration study
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