On combinatorial optimization for dominating sets (literature survey, new models)

The paper focuses on some versions of connected dominating set problems: basic problems and multicriteria problems. A literature survey on basic problem formulations and solving approaches is presented. The basic connected dominating set problems are illustrated by simplifyed numerical examples. New integer programming formulations of dominating set problems (with multiset estimates) are suggested.

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.

Time-interval balancing in multi-processor scheduling of composite modular jobs (preliminary description)

The article describes a special time-interval balancing in multi-processor scheduling of composite modular jobs. This scheduling problem is close to just-in-time planning approach. First, brief literature surveys are presented on just-in-time scheduling and due-data/due-window scheduling problems. Further, the problem and its formulation are proposed for the time-interval balanced scheduling of composite modular jobs. The illustrative real world planning example for modular home-building is described. Here, the main objective function consists in a balance between production of the typical building modules (details) and the assembly processes of the building(s) (by several teams). The assembly plan has to be modified to satisfy the balance requirements. The solving framework is based on the following: (i) clustering of initial set of modular detail types to obtain about ten basic detail types that correspond to main manufacturing conveyors; (ii) designing a preliminary plan of assembly for buildings; (iii) detection of unbalanced time periods, (iv) modification of the planning solution to improve the schedule balance. The framework implements a metaheuristic based on local optimization approach. Two other applications (supply chain management, information transmission systems) are briefly described.

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.

Towards balanced clustering - part 1 (preliminaries)

The article contains a preliminary glance at balanced clustering problems. Basic balanced structures and combinatorial balanced problems are briefly described. A special attention is targeted to various balance/unbalance indices (including some new versions of the indices): by cluster cardinality, by cluster weights, by inter-cluster edge/arc weights, by cluster element structure (for element multi-type clustering). Further, versions of optimization clustering problems are suggested (including multicriteria problem formulations). Illustrative numerical examples describe calculation of balance indices and element multi-type balance clustering problems (including example for design of student teams).

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.

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).

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.

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).

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.