Extension of the dominance properties for the unrestricted block relocation problem

Author(s):  
S. Tanaka
Keyword(s):  
Bernoulli ◽  
2013 ◽  
Vol 19 (5B) ◽  
pp. 2200-2221 ◽  
Author(s):  
Tatsuya Kubokawa ◽  
William E. Strawderman

2016 ◽  
Vol 33 (04) ◽  
pp. 1650032 ◽  
Author(s):  
Zhenyou Wang ◽  
Cai-Min Wei ◽  
Yuan-Yuan Lu

In this paper, we consider a three-machine makespan minimization permutation flow shop scheduling problem with shortening job processing times. Shortening job processing times means that its processing time is a nonincreasing function of its execution start time. Optimal solutions are obtained for some special cases. For the general case, several dominance properties and two lower bounds are developed to construct a branch-and-bound (B&B) algorithm. Furthermore, we propose a heuristic algorithm to overcome the inefficiency of the branch-and-bound algorithm.


1998 ◽  
Vol 30 (1) ◽  
pp. 181-196 ◽  
Author(s):  
P. S. Griffin ◽  
R. A. Maller

Let Tr be the first time at which a random walk Sn escapes from the strip [-r,r], and let |STr|-r be the overshoot of the boundary of the strip. We investigate the order of magnitude of the overshoot, as r → ∞, by providing necessary and sufficient conditions for the ‘stability’ of |STr|, by which we mean that |STr|/r converges to 1, either in probability (weakly) or almost surely (strongly), as r → ∞. These also turn out to be equivalent to requiring only the boundedness of |STr|/r, rather than its convergence to 1, either in the weak or strong sense, as r → ∞. The almost sure characterisation turns out to be extremely simple to state and to apply: we have |STr|/r → 1 a.s. if and only if EX2 < ∞ and EX = 0 or 0 < |EX| ≤ E|X| < ∞. Proving this requires establishing the equivalence of the stability of STr with certain dominance properties of the maximum partial sum Sn* = max{|Sj|: 1 ≤ j ≤ n} over its maximal increment.


2014 ◽  
Vol 31 (06) ◽  
pp. 1450046 ◽  
Author(s):  
Wen-Hsiang Wu ◽  
Yunqiang Yin ◽  
Shuenn-Ren Cheng ◽  
Peng-Hsiang Hsu ◽  
Chin-Chia Wu

Scheduling with learning effects has received lots of research attention lately. However, the multiple-agent setting with learning consideration is relatively limited. On the other hand, the actual processing time of a job under an uncontrolled learning effect will drop to zero precipitously as the number of the jobs already processed increases. This is rather absurd in reality. Based on these observations, this paper considers a single-machine two-agent scheduling problem in which the actual processing time of a job depends not only on the job's scheduled position, but also on a control parameter. The objective is to minimize the total weighted completion time of jobs from the first agent with the restriction that no tardy job is allowed for the second agent. A branch-and-bound algorithm incorporated with several dominance properties and lower bounds is proposed to derive the optimal solution for the problem. In addition, genetic algorithms (GAs) are also provided to obtain the near-optimal solution. Finally, a computational experiment is conducted to evaluate the performance of the proposed algorithms.


2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Ju-Yong Lee ◽  
June-Young Bang

This research considers a two-stage assembly-type flowshop scheduling problem with the objective of minimizing the total tardiness. The first stage consists of two independent machines, and the second stage consists of a single machine. Two types of components are fabricated in the first stage, and then they are assembled in the second stage. Dominance properties and lower bounds are developed, and a branch and bound algorithm is presented that uses these properties and lower bounds as well as an upper bound obtained from a heuristic algorithm. The algorithm performance is evaluated using a series of computational experiments on randomly generated instances and the results are reported.


Genetics ◽  
1998 ◽  
Vol 148 (3) ◽  
pp. 1171-1188 ◽  
Author(s):  
James D Fry ◽  
Stefanie L Heinsohn ◽  
Trudy F C Mackay

Abstract If genetic variation for fitness traits in natural populations (“standing” variation) is maintained by recurrent mutation, then quantitative-genetic properties of standing variation should resemble those of newly arisen mutations. One well-known property of standing variation for fitness traits is inbreeding depression, with its converse of heterosis or hybrid vigor. We measured heterosis for three fitness traits, pre-adult viability, female fecundity, and male fertility, among a set of inbred Drosophilia melanogaster lines recently derived from the wild, and also among a set of lines that had been allowed to accumulate spontaneous mutations for over 200 generations. The inbred lines but not the mutation-accumulation (MA) lines showed heterosis for pre-adult viability. Both sets of lines showed heterosis for female fecundity, but heterosis for male fertility was weak or absent. Crosses among a subset of the MA lines showed that they were strongly differentiated for male fertility, with the differences inherited in autosomal fashion; the absence of heterosis for male fertility among the MA lines was therefore not caused by an absence of mutations affecting this trait. Crosses among the inbred lines also gave some, albeit equivocal, evidence for male fertility variation. The contrast between the results for female fecundity and those for male fertility suggests that mutations affecting different fitness traits may differ in their average dominance properties, and that such differences may be reflected in properties of standing variation. The strong differentiation among the MA lines in male fertility further suggests that mutations affecting this trait occur at a high rate.


Author(s):  
D. R. Farenick ◽  
Patrick J. Browne

SynopsisLet Aij, l≦j≦k, be bounded Hermitean operators on Hilbert spaces Hi, 1≦i≦k, and let be the induced operators on . An important operator for multiparameter theory is δ: H →H denned by δ = det the determinant being expanded formally. Various definiteness properties of δ are critical for multiparameter spectral theory.We use the operators Aij to construct a numerical matrix δ(δ) upon which we use Geršgorin theory to investigate the non-singularity and definiteness of δ. Diagonal dominance properties of the array [Aij] are also discussed.


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