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

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

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

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

Aggregation of Composite Solutions: strategies, models, examples

The paper addresses aggregation issues for composite (modular) solutions. A systemic view point is suggested for various aggregation problems. Several solution structures are considered: sets, set morphologies, trees, etc. Mainly, the aggregation approach is targeted to set morphologies. The aggregation problems are based on basic structures as substructure, superstructure, median/consensus, and extended median/consensus. In the last case, preliminary structure is built (e.g., substructure, median/consensus) and addition of solution elements is considered while taking into account profit of the additional elements and total resource constraint. Four aggregation strategies are examined: (i) extension strategy (designing a substructure of initial solutions as "system kernel" and extension of the substructure by additional elements); (ii) compression strategy (designing a superstructure of initial solutions and deletion of some its elements); (iii) combined strategy; and (iv) new design strategy to build a new solution over an extended domain of solution elements. Numerical real-world examples (e.g., telemetry system, communication protocol, student plan, security system, Web-based information system, investment, educational courses) illustrate the suggested aggregation approach.Comment: 72 pages, 116 figures, 35 table