14 research outputs found
The stochastic opportunistic replacement problem, part III: improved bounding procedures
We consider the problem to find a schedule for component replacement in a multi-component system, whose components possess stochastic lives and economic dependencies, such that the expected costs for maintenance during a pre-defined time period are minimized. The problem was considered in Patriksson et al. (Ann Oper Res 224:51â75, 2015), in which a two-stage approximation of the problem was optimized through decomposition (denoted the optimization policy). The current paper improves the effectiveness of the decomposition approach by establishing a tighter bound on the value of the recourse function (i.e., the second stage in the approximation). A general lower bound on the expected maintenance cost is also established. Numerical experiments with 100 simulation scenarios for each of four test instances show that the tighter bound yields a decomposition generating fewer optimality cuts. They also illustrate the quality of the lower bound. Contrary to results presented earlier, an age-based policy performs on par with the optimization policy, although most simple policies perform worse than the optimization policy
VerklighetsnÀra matematik : en studie av infÀrgning och autenticitet av uppgifter i lÀroböcker i matematik
LÀroplaner i matematik för gymnasiet tar upp att matematik ska kopplas till karaktÀrsÀmnen. SÀrskilt tydligt Àr det i lÀroplanen för Matematik 1a, som lÀses av alla elever pÄ yrkesprogram. Skolverket har i en modul med titeln "Undervisa matematik pÄ yrkesprogram" förtydligat vad som önskas i frÄga om att koppla samman matematik med karaktÀrsÀmnen. Speciellt finns ett fokus pÄ att uppgifter bör vara autentiska. LÀrare lÄter ofta undervisningen utgÄ frÄn en lÀrobok i matematik, snarare Àn frÄn lÀroplanen. Det Àr dÀrför viktigt att lÀroböcker har god överensstÀmmelse med lÀroplanen. Det föreliggande arbetet Àr en undersökning av huruvida lÀroböcker för Matematik 1A erbjuder stöd för att koppla samman matematik med karaktÀrsÀmnen, samt av i vilken utstrÀckning sÄdant stöd Àr autentiskt. Undersökningen bestÄr av analys av totalt fyra uppgifter hÀmtade frÄn tvÄ olika lÀroböcker i matematik. Bedömningen av uppgifternas autenticitet görs med avseende pÄ en modifierad version av ett ramverk som anvÀnts av Skolverket för att skapa instruktioner till hur man konstruerar autentiska uppgifter. Arbetets omfattning Àr mycket begrÀnsat, varför inga sÀkra besked kan ges. Undersökningen tyder pÄ att det i lÀroböcker för Matematik 1A görs försök att sammankoppla matematiken med karaktÀrsÀmnen, men att det finns brister i frÄga om autenticitet av sÄdan sammankoppling
VerklighetsnÀra matematik : en studie av infÀrgning och autenticitet av uppgifter i lÀroböcker i matematik
LÀroplaner i matematik för gymnasiet tar upp att matematik ska kopplas till karaktÀrsÀmnen. SÀrskilt tydligt Àr det i lÀroplanen för Matematik 1a, som lÀses av alla elever pÄ yrkesprogram. Skolverket har i en modul med titeln "Undervisa matematik pÄ yrkesprogram" förtydligat vad som önskas i frÄga om att koppla samman matematik med karaktÀrsÀmnen. Speciellt finns ett fokus pÄ att uppgifter bör vara autentiska. LÀrare lÄter ofta undervisningen utgÄ frÄn en lÀrobok i matematik, snarare Àn frÄn lÀroplanen. Det Àr dÀrför viktigt att lÀroböcker har god överensstÀmmelse med lÀroplanen. Det föreliggande arbetet Àr en undersökning av huruvida lÀroböcker för Matematik 1A erbjuder stöd för att koppla samman matematik med karaktÀrsÀmnen, samt av i vilken utstrÀckning sÄdant stöd Àr autentiskt. Undersökningen bestÄr av analys av totalt fyra uppgifter hÀmtade frÄn tvÄ olika lÀroböcker i matematik. Bedömningen av uppgifternas autenticitet görs med avseende pÄ en modifierad version av ett ramverk som anvÀnts av Skolverket för att skapa instruktioner till hur man konstruerar autentiska uppgifter. Arbetets omfattning Àr mycket begrÀnsat, varför inga sÀkra besked kan ges. Undersökningen tyder pÄ att det i lÀroböcker för Matematik 1A görs försök att sammankoppla matematiken med karaktÀrsÀmnen, men att det finns brister i frÄga om autenticitet av sÄdan sammankoppling
Combinatorial Optimization : Three Applications
Combinatorial optimization is a diverse area of mathematics. It concerns optimization on feasible regions defined by discrete sets, graphs, hypergraphs, matroids, etc. . . which all have a large number of applications. They occur in virtually all domains of human activity since humans always want to do things easier, faster, consume less resources, etc. . . This thesis concerns three applied problems within combinatorial optimization. The first paper generalizes previous optimal upper bounds on the minimum Euclidean distance for phase-shift keying (PSK) block codes, that are explicit in the parameters alphabet size, block length and code size. There is a strong connection between high minimum Euclidean distance and good error-correcting capabilities. The bounds are generalized in several respects, such as from codes on symmetric PSK to codes on asymmetric PSK. They are also generalized to other types of noise than Gaussian, allowing more efficient block codes when noise is non-Gaussian. We provide examples of codes on asymmetric PSK that have higher minimum Euclidean distance than any comparable codes on symmetric PSK.Several classes of codes are shown to be optimal among codes on symmetric PSK since their Euclidean distance coincides with the bound. The second paper considers a parallel computer system with m identical computers,where we study optimal performance precaution for one possible computer crash. We anticipate that some computer may crash, and restrict the cost in such a situation. How costly is such a precaution when no crash occurs? We set a restriction that the completion time of a parallel program after a crash is at most a factor r + 1 larger than if we use an optimal allocation with m - 1 computers. This is an r-dependent restriction of the set of allocations of a program. Then the worst-case ratio of the optimal r-dependent completion time in the case of no crash and the unrestricted optimal completion time defines a function f(r,m). In the paper we establish upper and lower bounds of the worst-case cost function f(r,m) and characterize worst-case programs. The third paper considers the problem of Map Matching (MM), i.e. matching time and location measurements of a vehicle to a route in a road network. The paper presents a probabilistic algorithm for MM based on a second order hidden Markov model (HMM), as opposed to first order HMMs which are usually used. This allows a more detailed analysis of the data while preserving algorithmic complexity O(n). Both measurement densities and transition probabilities are determined with respect to Kolmogorov's third axiom, which in this context implies that the probabilities are additive over a partition of a road segment
Combinatorial Optimization - Three Applications
Combinatorial optimization is a diverse area of mathematics. It concerns
optimization on feasible regions defined by discrete sets, graphs, hypergraphs,
matroids, etc. . . which all have a large number of applications. They occur in
virtually all domains of human activity since humans always want to do things
easier, faster, consume less resources, etc. . . This
thesis concerns three applied problems within combinatorial optimization.
The first paper generalizes previous optimal upper bounds on the minimum
Euclidean distance for phase-shift keying (PSK) block codes, that are explicit
in the parameters alphabet size, block length and code size. There is a strong
connection between high minimum Euclidean distance and good error-correcting
capabilities. The bounds are generalized in
several respects, such as from codes on symmetric PSK to codes on asymmetric
PSK. They are also generalized to other types of noise than Gaussian, allowing
more efficient block
codes when noise is non-Gaussian. We provide examples of codes on asymmetric
PSK that have higher minimum Euclidean distance than any comparable codes on
symmetric PSK.Several classes of codes are shown to be optimal among codes on
symmetric PSK since their Euclidean distance coincides with the bound.
The second paper considers a parallel computer system with m identical
computers,where we study optimal performance precaution for one possible
computer crash. We anticipate that some computer may crash, and restrict the
cost in such a situation. How costly is such a precaution when no crash occurs?
We set a restriction that the completion time of a parallel program after a
crash is at most a factor r + 1 larger than if we use an optimal allocation
with m - 1 computers. This is an r-dependent restriction of the set of
allocations of a program. Then the worst-case ratio of the optimal r-dependent
completion time in the case of no crash and the unrestricted optimal completion
time defines a function
f(r,m). In the paper we establish upper and lower bounds of the worst-case cost
function f(r,m) and characterize worst-case programs.
The third paper considers the problem of Map Matching (MM), i.e. matching time
and location measurements of a vehicle to a route in a road network. The paper
presents a
probabilistic algorithm for MM based on a second order hidden Markov model
(HMM), as opposed to first order HMMs which are usually used. This allows a
more detailed analysis
of the data while preserving algorithmic complexity O(n). Both measurement
densities and transition probabilities are determined with respect to
Kolmogorov's third axiom, which in
this context implies that the probabilities are additive over a partition of a
road segment
Bounds on the Performance of PSK Block Codes
In wireless communication, the minimum Euclidean distance between codewords is
a major factor for the ability to correct errors in messages, and it is of
interest to maximize the minimum Euclidean distance.
The thesis improves previously established general upper bounds on minimum
Euclidean distance of phase shift keying block codes. There are no requirements
on structure of codes, as the bound depends only on alphabet size, word length
and code size. Prior to this thesis, bounds found by use of a method of Elias,
had been improved by generalization of Elias' method. The method used here is
an attempt to optimize that generalization
Optimal Computer Crash Performance Precaution
Distributed Computing and NetworkingFor a parallel computer system with m identical computers, we study optimal performance precaution for one possible computer crash. We want to calculate the cost of crash precaution in the case of no crash. We thus define a tolerance level r meaning that we only tolerate that the completion time of a parallel program after a crash is at most a factor r + 1 larger than if we use optimal allocation on m - 1 computers. This is an r-dependent restriction of the set of allocations of a program. Then, what is the worst-case ratio of the optimal r-dependent completion time in the case of no crash and the unrestricted optimal completion time of the same parallel program? We denote the maximal ratio of completion times f(r, m) - i.e., the ratio for worst-case programs. In the paper we establish upper and lower bounds of the worst-case cost function f (r, m) and characterize worst-case programs
In press: Generalized upper bounds on the minimum distance of PSK block codes
This paper generalizes previous optimal upper bounds on the minimum Euclidean
distance for phase shift
keying (PSK) block codes, that are explicit in three parameters: alphabet size,
block length and code size.
The bounds are primarily generalized from codes over symmetric PSK to codes
over asymmetric PSK
and also to general alphabet size. Furthermore, block codes are optimized in
the presence of other types of
noise than Gaussian, which induces also non-Euclidean distance measures. In
some instances, codes over
asymmetric PSK prove to give higher Euclidean distance than any code over
symmetric PSK with the
same parameters. We also provide certain classes of codes that are optimal
among codes over symmetric PSK
Optimal computer crash performance precaution
For a parallel computer system withmidentical computers, we study optimal
performance precaution for one possible computer crash. We want to calculate
the cost of crash precaution in the case of no crash. We thus define a
tolerance level r meaning that we only tolerate that the completion time of a
parallel program after a crash is at most a factor r + 1 larger than if we use
optimal allocation on m - 1 computers. This is an r-dependent restriction of
the set of allocations of a program. Then, what is the worst-case ratio of the
optimal r-dependent completion time in the case of no crash and the
unrestricted optimal completion time of the same parallel program? We denote
the maximal ratio of completion times f(r, m) - i.e., the ratio for worst-case
programs. In the paper we establish upper and lower bounds of the worst-case
cost function f(r, m) and characterize worst-case programs