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

Composition of Modular Telemetry System with Interval Multiset Estimates

The paper describes combinatorial synthesis approach with interval multset estimates of system elements for modeling, analysis, design, and improvement of a modular telemetry system. Morphological (modular) system design and improvement are considered as composition of the telemetry system elements (components) configuration. The solving process is based on Hierarchical Morphological Multicriteria Design (HMMD): (i) multicriteria selection of alternatives for system components, (ii) synthesis of the selected alternatives into a resultant combination (while taking into account quality of the alternatives above and their compatibility). Interval multiset estimates are used for assessment of design alternatives for telemetry system elements. Two additional systems problems are examined: (a) improvement of the obtained solutions, (b) aggregation of the obtained solutions into a resultant system configuration. The improvement and aggregation processes are based on multiple choice problem with interval multiset estimates. Numerical examples for an on-board telemetry subsystem illustrate the design and improvement processes.Comment: 9 pages, 9 figures, 6 table

Combinatorial framework for planning in geological exploration

The paper describes combinatorial framework for planning of geological exploration for oil-gas fields. The suggested scheme of the geological exploration involves the following stages: (1) building of special 4-layer tree-like model (layer of geological exploration): productive layer, group of productive layers, oil-gas field, oil-gas region (or group of the fields); (2) generations of local design (exploration) alternatives for each low-layer geological objects: conservation, additional search, independent utilization, joint utilization; (3) multicriteria (i.e., multi-attribute) assessment of the design (exploration) alternatives and their interrelation (compatibility) and mapping if the obtained vector estimates into integrated ordinal scale; (4) hierarchical design ('bottom-up') of composite exploration plans for each oil-gas field; (5) integration of the plans into region plans and (6) aggregation of the region plans into a general exploration plan. Stages 2, 3, 4, and 5 are based on hierarchical multicriteria morphological design (HMMD) method (assessment of ranking of alternatives, selection and composition of alternatives into composite alternatives). The composition problem is based on morphological clique model. Aggregation of the obtained modular alternatives (stage 6) is based on detection of a alternatives 'kernel' and its extension by addition of elements (multiple choice model). In addition, the usage of multiset estimates for alternatives is described as well. The alternative estimates are based on expert judgment. The suggested combinatorial planning methodology is illustrated by numerical examples for geological exploration of Yamal peninsula.Comment: 14 pages, 15 figures, 11 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 Bin Packing (preliminary problem survey, models with multiset estimates)

The paper described a generalized integrated glance to bin packing problems including a brief literature survey and some new problem formulations for the cases of multiset estimates of items. A new systemic viewpoint to bin packing problems is suggested: (a) basic element sets (item set, bin set, item subset assigned to bin), (b) binary relation over the sets: relation over item set as compatibility, precedence, dominance; relation over items and bins (i.e., correspondence of items to bins). A special attention is targeted to the following versions of bin packing problems: (a) problem with multiset estimates of items, (b) problem with colored items (and some close problems). Applied examples of bin packing problems are considered: (i) planning in paper industry (framework of combinatorial problems), (ii) selection of information messages, (iii) packing of messages/information packages in WiMAX communication system (brief description).Comment: 39 pages, 18 figures, 14 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

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

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

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

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