Quantitative Comparison of Approximate Solution Sets for Multicriteria Optimization Problems with Weighted Tchebycheff Preference Function

Bozkurt, Bilge
Fowler, John W.
Gel, Esma S.
Kim, Bosun
Köksalan, Mustafa Murat
Wallenius, Jyrki
We consider. the problem of evaluating the quality of solution sets generated by heuristics for multiple-objective combinatorial optimization problems. We extend previous research on the integrated preference functional (IPF), which assigns a scalar value to a given discrete set of nondominated points so that the weighted Tchebycheff function can be used as the underlying implicit value function. This extension is useful because modeling the decision maker's value function with the weighted Tchebycheff function reflects the impact of unsupported points when evaluating sets of nondominated points. We present an exact calculation method for the IPF measure in this case for an arbitrary number of criteria. We show that every nondominated point has its optimal weight interval for the weighted Tchebycheff function. Accordingly, all nondominated points, and not only the supported points in a set, contribute to the value of the IPF measure when using the weighted Tchebycheff function. Two- and three-criteria numerical examples illustrate the desirable properties of the weighted Tchebycheff function, providing a richer measure than the original IPF based on a convex combination of objectives.


Emotional-motivational responses predicting choices: The role of asymmetrical frontal cortical activity
Ravaja, Niklas; Korhonen, Pekka; Köksalan, Mustafa Murat; Lipsanen, Jari; Salminen, Mikko; Somervuori, Outi; Wallenius, Jyrki (2016-02-01)
We examined (a) how emotional attachment to a choice option as indexed by state-related changes in electroencephalographic (EEG) asymmetry over the prefrontal cortex and electrodermal activity predicts choices and mediates the endowment effect and (b) the emotional-motivational responses to trade-off choices. Thirty-eight participants made choices between three 4-product packages, in which the frequency of each of the products varied. Greater relative left frontal activation and high peak skin conductance l...
Competitive newsvendor problems with the same Nash and Stackelberg solutions
Serin, Yaşar Yasemin (2007-01-01)
Consider two newsvendors: (i) they compete satisfying substitutable demands searching Nash equilibrium or (ii) one is the leader deciding first, the other responds optimally playing a Stackelberg game. The leader profits more than she does in (i). We present conditions under which the leader's profit does not improve from (i) to (ii).
Paracompactness of spaces which have covering properties weaker than paracompactness
Onal, S (Elsevier BV, 2001-07-16)
We prove that (i) a collectionwise normal, orthocompact, theta (m)-refinable, [m, N-0]-submetacompact space is paracompact, (ii) a collectionwise normal, [infinity, m]-paracompact [m, N-0]-submetacompact space is paracompact. This gives a sufficient condition for the paracompactness of para-Lindelof, collectionwise normal spaces.
Calculation of the dielectric constant as a function of temperature near the smectic AC* phase transition in ferroelectric liquid crystals
Kilit, E.; Yurtseven, Hasan Hamit (Informa UK Limited, 2008-01-01)
We calculate here. the dielectric constant E as a function of temperature for the AC* phase transition of a ferroelectric liquid crystal using a mean field model. Using the values of the polarization P and the tilt angle theta, calculated from the mean field model with the P-2 theta(2) coupling for 4-(3-methyl-2-chlorobutanoyloxy)-4'-heptyloxybiphenyl, the dielectric constant E is calculated in the smectic C* phase of this ferroelectric liquid crystal at various temperatures at constant electric fields.
Optimal lot-sizing/vehicle-dispatching policies under stochastic lead times and stepwise fixed costs
Alp, O; Erkip, NK; Gullu, R (Institute for Operations Research and the Management Sciences (INFORMS), 2003-01-01)
We characterize optimal policies of a dynamic lot-sizing/vehicle-dispatching problem under dynamic deterministic demands and stochastic lead times. An essential feature of the problem is the structure of the ordering cost, where a fixed cost is incurred every time a batch is initiated (or a vehicle is hired) regardless of the portion of the batch (or vehicle) utilized. Moreover, for every unit of demand not satisfied on time, holding and backorder costs are incurred. Under mild assumptions we show that the ...
Citation Formats
B. Bozkurt, J. W. Fowler, E. S. Gel, B. Kim, M. M. Köksalan, and J. Wallenius, “Quantitative Comparison of Approximate Solution Sets for Multicriteria Optimization Problems with Weighted Tchebycheff Preference Function,” OPERATIONS RESEARCH, pp. 650–659, 2010, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/57476.