5 research outputs found
Restructuring in Combinatorial Optimization
The paper addresses a new class of combinatorial problems which consist in
restructuring of solutions (as structures) in combinatorial optimization. Two
main features of the restructuring process are examined: (i) a cost of the
restructuring, (ii) a closeness to a goal solution. This problem corresponds to
redesign (improvement, upgrade) of modular systems or solutions. The
restructuring approach is described and illustrated for the following
combinatorial optimization problems: knapsack problem, multiple choice problem,
assignment problem, spanning tree problems. Examples illustrate the
restructuring processes.Comment: 11 pages, 12 figure
Course on System Design (structural approach)
The article describes a course on system design (structural approach) which
involves the following: issues of systems engineering; structural models; basic
technological problems (structural system modeling, modular design,
evaluation/comparison, revelation of bottlenecks, improvement/upgrade,
multistage design, modeling of system evolution); solving methods
(optimization, combinatorial optimization, multicriteria decision making);
design frameworks; and applications. The course contains lectures and a set of
special laboratory works. The laboratory works consist in designing and
implementing a set of programs to solve multicriteria problems
(ranking/selection, multiple choice problem, clustering, assignment). The
programs above are used to solve some standard problems (e.g., hierarchical
design of a student plan, design of a marketing strategy). Concurrently, each
student can examine a unique applied problem from his/her applied domain(s)
(e.g., telemetric system, GSM network, integrated security system, testing of
microprocessor systems, wireless sensor, corporative communication network,
network topology). Mainly, the course is targeted to developing the student
skills in modular analysis and design of various multidisciplinary composite
systems (e.g., software, electronic devices, information, computers,
communications). The course was implemented in Moscow Institute of Physics and
Technology (State University).Comment: 22 pages, 14 figure
Improvement/Extension of Modular Systems as Combinatorial Reengineering (Survey)
The paper describes development (improvement/extension) approaches for
composite (modular) systems (as combinatorial reengineering). The following
system improvement/extension actions are considered: (a) improvement of systems
component(s) (e.g., improvement of a system component, replacement of a system
component); (b) improvement of system component interconnection
(compatibility); (c) joint improvement improvement of system components(s) and
their interconnection; (d) improvement of system structure (replacement of
system part(s), addition of a system part, deletion of a system part,
modification of system structure). The study of system improvement approaches
involve some crucial issues: (i) scales for evaluation of system components and
component compatibility (quantitative scale, ordinal scale, poset-like scale,
scale based on interval multiset estimate), (ii) evaluation of integrated
system quality, (iii) integration methods to obtain the integrated system
quality. The system improvement/extension strategies can be examined as
seleciton/combination of the improvement action(s) above and as modification of
system structure. The strategies are based on combinatorial optimization
problems (e.g., multicriteria selection, knapsack problem, multiple choice
problem, combinatorial synthesis based on morphological clique problem,
assignment/reassignment problem, graph recoloring problem, spanning problems,
hotlink assignment). Here, heuristics are used. Various system
improvement/extension strategies are presented including illustrative numerical
examples.Comment: 24 pages, 28 figures, 14 tables. arXiv admin note: text overlap with
arXiv:1212.173
Towards Integrated Glance To Restructuring in Combinatorial Optimization
The paper focuses on a new class of combinatorial problems which consists in
restructuring of solutions (as sets/structures) in combinatorial optimization.
Two main features of the restructuring process are examined: (i) a cost of the
restructuring, (ii) a closeness to a goal solution. Three types of the
restructuring problems are under study: (a) one-stage structuring, (b)
multi-stage structuring, and (c) structuring over changed element set.
One-criterion and multicriteria problem formulations can be considered. The
restructuring problems correspond to redesign (improvement, upgrade) of modular
systems or solutions. The restructuring approach is described and illustrated
(problem statements, solving schemes, examples) for the following combinatorial
optimization problems: knapsack problem, multiple choice problem, assignment
problem, spanning tree problems, clustering problem, multicriteria ranking
(sorting) problem, morphological clique problem. Numerical examples illustrate
the restructuring problems and solving schemes.Comment: 31 pages, 34 figures, 10 table
Towards combinatorial clustering: preliminary research survey
The paper describes clustering problems from the combinatorial viewpoint. A
brief systemic survey is presented including the following: (i) basic
clustering problems (e.g., classification, clustering, sorting, clustering with
an order over cluster), (ii) basic approaches to assessment of objects and
object proximities (i.e., scales, comparison, aggregation issues), (iii) basic
approaches to evaluation of local quality characteristics for clusters and
total quality characteristics for clustering solutions, (iv) clustering as
multicriteria optimization problem, (v) generalized modular clustering
framework, (vi) basic clustering models/methods (e.g., hierarchical clustering,
k-means clustering, minimum spanning tree based clustering, clustering as
assignment, detection of clisue/quasi-clique based clustering, correlation
clustering, network communities based clustering), Special attention is
targeted to formulation of clustering as multicriteria optimization models.
Combinatorial optimization models are used as auxiliary problems (e.g.,
assignment, partitioning, knapsack problem, multiple choice problem,
morphological clique problem, searching for consensus/median for structures).
Numerical examples illustrate problem formulations, solving methods, and
applications. The material can be used as follows: (a) a research survey, (b) a
fundamental for designing the structure/architecture of composite modular
clustering software, (c) a bibliography reference collection, and (d) a
tutorial.Comment: 102 pages, 66 figures, 67 table