Note on Combinatorial Engineering Frameworks for Hierarchical Modular Systems

The paper briefly describes a basic set of special combinatorial engineering frameworks for solving complex problems in the field of hierarchical modular systems. The frameworks consist of combinatorial problems (and corresponding models), which are interconnected/linked (e.g., by preference relation). Mainly, hierarchical morphological system model is used. The list of basic standard combinatorial engineering (technological) frameworks is the following: (1) design of system hierarchical model, (2) combinatorial synthesis ('bottom-up' process for system design), (3) system evaluation, (4) detection of system bottlenecks, (5) system improvement (re-design, upgrade), (6) multi-stage design (design of system trajectory), (7) combinatorial modeling of system evolution/development and system forecasting. The combinatorial engineering frameworks are targeted to maintenance of some system life cycle stages. The list of main underlaying combinatorial optimization problems involves the following: knapsack problem, multiple-choice problem, assignment problem, spanning trees, morphological clique problem.Comment: 11 pages, 7 figures, 3 table

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

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

Composite Strategy for Multicriteria Ranking/Sorting (methodological issues, examples)

The paper addresses the modular design of composite solving strategies for multicriteria ranking (sorting). Here a 'scale of creativity' that is close to creative levels proposed by Altshuller is used as the reference viewpoint: (i) a basic object, (ii) a selected object, (iii) a modified object, and (iv) a designed object (e.g., composition of object components). These levels maybe used in various parts of decision support systems (DSS) (e.g., information, operations, user). The paper focuses on the more creative above-mentioned level (i.e., composition or combinatorial synthesis) for the operational part (i.e., composite solving strategy). This is important for a search/exploration mode of decision making process with usage of various procedures and techniques and analysis/integration of obtained results. The paper describes methodological issues of decision technology and synthesis of composite strategy for multicriteria ranking. The synthesis of composite strategies is based on 'hierarchical morphological multicriteria design' (HMMD) which is based on selection and combination of design alternatives (DAs) (here: local procedures or techniques) while taking into account their quality and quality of their interconnections (IC). A new version of HMMD with interval multiset estimates for DAs is used. The operational environment of DSS COMBI for multicriteria ranking, consisting of a morphology of local procedures or techniques (as design alternatives DAs), is examined as a basic one.Comment: 24 pages, 28 figures, 5 table

Note on Evolution and Forecasting of Requirements: Communications Example

Combinatorial evolution and forecasting of system requirements is examined. The morphological model is used for a hierarchical requirements system (i.e., system parts, design alternatives for the system parts, ordinal estimates for the alternatives). A set of system changes involves changes of the system structure, component alternatives and their estimates. The composition process of the forecast is based on combinatorial synthesis (knapsack problem, multiple choice problem, hierarchical morphological design). An illustrative numerical example for four-phase evolution and forecasting of requirements to communications is described.Comment: 8 pages, 8 figures, 9 table

Towards Decision Support Technology Platform for Modular Systems

The survey methodological paper addresses a glance to a general decision support platform technology for modular systems (modular/composite alterantives/solutions) in various applied domains. The decision support platform consists of seven basic combinatorial engineering frameworks (system synthesis, system modeling, evaluation, detection of bottleneck, improvement/extension, multistage design, combinatorial evolution and forecasting). The decision support platform is based on decision support procedures (e.g., multicriteria selection/sorting, clustering), combinatorial optimization problems (e.g., knapsack, multiple choice problem, clique, assignment/allocation, covering, spanning trees), and their combinations. The following is described: (1) general scheme of the decision support platform technology; (2) brief descriptions of modular (composite) systems (or composite alternatives); (3) trends in moving from chocie/selection of alternatives to processing of composite alternatives which correspond to hierarchical modular products/systems; (4) scheme of resource requirements (i.e., human, information-computer); and (5) basic combinatorial engineering frameworks and their applications in various domains.Comment: 10 pages, 9 figures, 2 table

Discrete Route/Trajectory Decision Making Problems

The paper focuses on composite multistage decision making problems which are targeted to design a route/trajectory from an initial decision situation (origin) to goal (destination) decision situation(s). Automobile routing problem is considered as a basic physical metaphor. The problems are based on a discrete (combinatorial) operations/states design/solving space (e.g., digraph). The described types of discrete decision making problems can be considered as intelligent design of a route (trajectory, strategy) and can be used in many domains: (a) education (planning of student educational trajectory), (b) medicine (medical treatment), (c) economics (trajectory of start-up development). Several types of the route decision making problems are described: (i) basic route decision making, (ii) multi-goal route decision making, (iii) multi-route decision making, (iv) multi-route decision making with route/trajectory change(s), (v) composite multi-route decision making (solution is a composition of several routes/trajectories at several corresponding domains), and (vi) composite multi-route decision making with coordinated routes/trajectories. In addition, problems of modeling and building the design spaces are considered. Numerical examples illustrate the suggested approach. Three applications are considered: educational trajectory (orienteering problem), plan of start-up company (modular three-stage design), and plan of medical treatment (planning over digraph with two-component vertices).Comment: 25 pages, 34 figures, 16 table

Multiset Estimates and Combinatorial Synthesis

The paper addresses an approach to ordinal assessment of alternatives based on assignment of elements into an ordinal scale. Basic versions of the assessment problems are formulated while taking into account the number of levels at a basic ordinal scale [1,2,...,l] and the number of assigned elements (e.g., 1,2,3). The obtained estimates are multisets (or bags) (cardinality of the multiset equals a constant). Scale-posets for the examined assessment problems are presented. 'Interval multiset estimates' are suggested. Further, operations over multiset estimates are examined: (a) integration of multiset estimates, (b) proximity for multiset estimates, (c) comparison of multiset estimates, (d) aggregation of multiset estimates, and (e) alignment of multiset estimates. Combinatorial synthesis based on morphological approach is examined including the modified version of the approach with multiset estimates of design alternatives. Knapsack-like problems with multiset estimates are briefly described as well. The assessment approach, multiset-estimates, and corresponding combinatorial problems are illustrated by numerical examples.Comment: 30 pages, 24 figures, 10 table

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

On balanced clustering with tree-like structures over clusters

The article addresses balanced clustering problems with an additional requirement as a tree-like structure over the obtained balanced clusters. This kind of clustering problems can be useful in some applications (e.g., network design, management and routing). Various types of the initial elements are considered. Four basic greedy-like solving strategies (design framework) are considered: balancing-spanning strategy, spanning-balancing strategy, direct strategy, and design of layered structures with balancing. An extended description of the spanning-balancing strategy is presented including four solving schemes and an illustrative numerical example.Comment: 15 pages, 15 figures, 9 table