I. Litvinchev - Academia.edu (original) (raw)

Papers by I. Litvinchev

Computational Mathematics and Mathematical Physics, Apr 1, 1993

Data Analysis and Optimization for Engineering and Computing Problems

EAI Endorsed Trans. Energy Web, 2020

An approach for designing topologically optimized parts is proposed. It is used for manufacturing... more An approach for designing topologically optimized parts is proposed. It is used for manufacturing support-free structures by Direct Metal Laser Sintering (DMLS). This integral approach allows obtaining parts taking into account their strength properties. It combines weak sensitivity to the direction of printing with the simplicity of the subsequent post-processing. A circular packing model is proposed to optimize the part geometry subject to the DMLS constraints. A fast heuristic algorithm is developed to solve the corresponding optimization problem. A prototype obtained by this optimized design approach is presented.

Advances in Intelligent Systems and Computing, 2019

The paper considers a packing problem of arbitrary shaped objects into an optimized container (OP... more The paper considers a packing problem of arbitrary shaped objects into an optimized container (OPP) formulated as a knapsack problem. Mathematical model of OPP in the form of a knapsack problem (KP) is provided. A new approach of reducing the knapsack problem (KP) to a sequence of the open dimension problems (ODP) is proposed. The key idea of the approach is based on the homothetic transformations of the container. The approach is most efficient for optimization packing problems into containers of complex geometry.

Advances in Intelligent Systems and Computing, 2019

Packing convex 3D objects inside a convex container with balancing conditions is considered. The ... more Packing convex 3D objects inside a convex container with balancing conditions is considered. The convex container is divided into subcontainers by a given number of supporting boards. The problem has applications in space engineering for rocketry design and takes into account both geometric (object orientations, minimum and/or maximum allowable distances between objects, combinatorial characteristics of the object arrangements inside subcontainers) and mechanical constraints (equilibrium, moments of inertia, stability). A general nonlinear optimization model is introduced and a solution strategy is provided. Numerical results are presented to illustrate the approach.

In this paper a mixed-integer linear programming (MILP) model is studied for the bi-objective pub... more In this paper a mixed-integer linear programming (MILP) model is studied for the bi-objective public R&D projects portfolio problem. The proposed approach provides an acceptable compromise between the impact and the number of supported projects. Lagrangian relaxation techniques are considered to get easy computable bounds for the objectives. The experiments show that a solution can be obtained in less than a minute for instances comprising of up to 25,000 project proposals. This brings significant improvement to the previous approaches that efficiently manage instances of a few hundred projects.

A placement problem of irregular 2D&3D objects in a domain (container) of minimum area (volume), ... more A placement problem of irregular 2D&3D objects in a domain (container) of minimum area (volume), that related to the field of Packing and Cutting problems is considered. Placement objects may be continuously translated and rotated. A general nonlinear programming model of the problem is presented employing the phi-function technique. We propose a decomposition algorithm that generalizes previously published compaction algorithms of searching for local optimal solutions for some packing and cutting problems. Our decomposition algorithm reduces the optimization placement problem to a sequence of nonlinear programming subproblems of considerably smaller dimension.

Journal of Computer and Systems Sciences International, 2017

Modified Lagrangian bounds are proposed for the generalized assignment problem. The approach is b... more Modified Lagrangian bounds are proposed for the generalized assignment problem. The approach is based on a double decomposable structure of the formulation. A family of greedy heuristics is considered to get Lagrangian based feasible solutions. Numerical results for problem instances with number of agents close to number of tasks are provided.

Data Analysis and Optimization for Engineering and Computing Problems

EAI Endorsed Transactions on Energy Web

IFAC-PapersOnLine

Abstract A packing problem for irregular 3D objects approximated by polyhedra is presented. The o... more Abstract A packing problem for irregular 3D objects approximated by polyhedra is presented. The objects have to be packed into a cuboid of minimum height under continuous rotations, translations and minimum allowable distances between objects. The problem has various applications and arises, e.g. in additive manufacturing. Containment, distance and non-overlapping constraints are described using the phi-function technique. The irregular packing problem is formulated in the form of nonlinear programming problem. A solution algorithm is proposed based on a fast starting point algorithm and efficient local optimization procedure.

Journal of Global Optimization

Packing ellipses with arbitrary orientation into a convex polygonal container which has a given s... more Packing ellipses with arbitrary orientation into a convex polygonal container which has a given shape is considered. The objective is to find a minimum scaling (homothetic) coefficient for the polygon still containing a given collection of ellipses. New phi-functions and quasi phi-functions to describe non-overlapping and containment constraints are introduced. The packing problem is then stated as a continuous nonlinear programming problem. A solution approach is proposed combining a new starting point algorithm and a new modification of the LOFRT procedure (J Glob Optim 65(2):283–307, 2016) to search for locally optimal solutions. Computational results are provided to demonstrate the efficiency of our approach. The computational results are presented for new problem instances, as well as for instances presented in the recent paper (http://www.optimization-online.org/DB_FILE/2016/03/5348.pdf, 2016).

Mathematical Problems in Engineering

A packing (layout) problem for a number of clusters (groups) composed of convex objects (e.g., ci... more A packing (layout) problem for a number of clusters (groups) composed of convex objects (e.g., circles, ellipses, or convex polygons) is considered. The clusters have to be packed into a given rectangular container subject to nonoverlapping between objects within a cluster. Each cluster is represented by the convex hull of objects that form the cluster. Two clusters are said to be nonoverlapping if their convex hulls do not overlap. A cluster is said to be entirely in the container if so is its convex hull. All objects in the cluster have the same shape (different sizes are allowed) and can be continuously translated and rotated. The objective of optimized packing is constructing a maximum sparse layout for clusters subject to nonoverlapping and containment conditions for clusters and objects. Here the term sparse means that clusters are sufficiently distant one from another. New quasi-phi-functions and phi-functions to describe analytically nonoverlapping, containment and distance ...

Wireless Networks

The paper studies packing ellipses in a rectangular container of minimum area. The problem has va... more The paper studies packing ellipses in a rectangular container of minimum area. The problem has various applications in production, logistics, industrial design. New phi-functions are proposed to state containment constraints and quasi-phi-functions are used for analytical description of non-overlapping constraints. A mathematical model for the packing problem is stated as a nonlinear programming problem. Two algorithms to find feasible starting points for identical and non-identical ellipses are proposed. The optimization procedure is used as a compaction algorithm to search for local optimal solutions. Computational results are provided to show the efficiency of the proposed approach.

Applied and computational mathematics

In the two-stage capacitated facility location problem a single product is produced at some plant... more In the two-stage capacitated facility location problem a single product is produced at some plants in order to satisfy customer demands. The product is transported from these plants to some depots and then to the customers. The capacities of the plants and depots are limited. The aim is to select cost minimizing locations from a set of potential plants and depots. This cost includes fixed cost associated with opening plants and depots, and variable cost associated with both transportation stages. In this work a Lagrangian relaxation is analyzed and a Lagrangian heuristic producing feasible solutions is presented. The results of a computational study are reported.

USSR Computational Mathematics and Mathematical Physics, 1989

USSR Computational Mathematics and Mathematical Physics, 1987

ABSTRACT A method of expansion is given which does not utilize the block-separable structure of t... more ABSTRACT A method of expansion is given which does not utilize the block-separable structure of the problem and which is based on aggregation of the variables. The monotonicity of the iterative process with respect to a functional is proved. The possibility of aggregation of the constraints is considered.

USSR Computational Mathematics and Mathematical Physics, 1990

Computational Mathematics and Mathematical Physics

Computational Mathematics and Mathematical Physics, Apr 1, 1993

Data Analysis and Optimization for Engineering and Computing Problems

EAI Endorsed Trans. Energy Web, 2020

An approach for designing topologically optimized parts is proposed. It is used for manufacturing... more An approach for designing topologically optimized parts is proposed. It is used for manufacturing support-free structures by Direct Metal Laser Sintering (DMLS). This integral approach allows obtaining parts taking into account their strength properties. It combines weak sensitivity to the direction of printing with the simplicity of the subsequent post-processing. A circular packing model is proposed to optimize the part geometry subject to the DMLS constraints. A fast heuristic algorithm is developed to solve the corresponding optimization problem. A prototype obtained by this optimized design approach is presented.

Advances in Intelligent Systems and Computing, 2019

The paper considers a packing problem of arbitrary shaped objects into an optimized container (OP... more The paper considers a packing problem of arbitrary shaped objects into an optimized container (OPP) formulated as a knapsack problem. Mathematical model of OPP in the form of a knapsack problem (KP) is provided. A new approach of reducing the knapsack problem (KP) to a sequence of the open dimension problems (ODP) is proposed. The key idea of the approach is based on the homothetic transformations of the container. The approach is most efficient for optimization packing problems into containers of complex geometry.

Advances in Intelligent Systems and Computing, 2019

Packing convex 3D objects inside a convex container with balancing conditions is considered. The ... more Packing convex 3D objects inside a convex container with balancing conditions is considered. The convex container is divided into subcontainers by a given number of supporting boards. The problem has applications in space engineering for rocketry design and takes into account both geometric (object orientations, minimum and/or maximum allowable distances between objects, combinatorial characteristics of the object arrangements inside subcontainers) and mechanical constraints (equilibrium, moments of inertia, stability). A general nonlinear optimization model is introduced and a solution strategy is provided. Numerical results are presented to illustrate the approach.

In this paper a mixed-integer linear programming (MILP) model is studied for the bi-objective pub... more In this paper a mixed-integer linear programming (MILP) model is studied for the bi-objective public R&D projects portfolio problem. The proposed approach provides an acceptable compromise between the impact and the number of supported projects. Lagrangian relaxation techniques are considered to get easy computable bounds for the objectives. The experiments show that a solution can be obtained in less than a minute for instances comprising of up to 25,000 project proposals. This brings significant improvement to the previous approaches that efficiently manage instances of a few hundred projects.

A placement problem of irregular 2D&3D objects in a domain (container) of minimum area (volume), ... more A placement problem of irregular 2D&3D objects in a domain (container) of minimum area (volume), that related to the field of Packing and Cutting problems is considered. Placement objects may be continuously translated and rotated. A general nonlinear programming model of the problem is presented employing the phi-function technique. We propose a decomposition algorithm that generalizes previously published compaction algorithms of searching for local optimal solutions for some packing and cutting problems. Our decomposition algorithm reduces the optimization placement problem to a sequence of nonlinear programming subproblems of considerably smaller dimension.

Journal of Computer and Systems Sciences International, 2017

Modified Lagrangian bounds are proposed for the generalized assignment problem. The approach is b... more Modified Lagrangian bounds are proposed for the generalized assignment problem. The approach is based on a double decomposable structure of the formulation. A family of greedy heuristics is considered to get Lagrangian based feasible solutions. Numerical results for problem instances with number of agents close to number of tasks are provided.

Data Analysis and Optimization for Engineering and Computing Problems

EAI Endorsed Transactions on Energy Web

IFAC-PapersOnLine

Abstract A packing problem for irregular 3D objects approximated by polyhedra is presented. The o... more Abstract A packing problem for irregular 3D objects approximated by polyhedra is presented. The objects have to be packed into a cuboid of minimum height under continuous rotations, translations and minimum allowable distances between objects. The problem has various applications and arises, e.g. in additive manufacturing. Containment, distance and non-overlapping constraints are described using the phi-function technique. The irregular packing problem is formulated in the form of nonlinear programming problem. A solution algorithm is proposed based on a fast starting point algorithm and efficient local optimization procedure.

Journal of Global Optimization

Packing ellipses with arbitrary orientation into a convex polygonal container which has a given s... more Packing ellipses with arbitrary orientation into a convex polygonal container which has a given shape is considered. The objective is to find a minimum scaling (homothetic) coefficient for the polygon still containing a given collection of ellipses. New phi-functions and quasi phi-functions to describe non-overlapping and containment constraints are introduced. The packing problem is then stated as a continuous nonlinear programming problem. A solution approach is proposed combining a new starting point algorithm and a new modification of the LOFRT procedure (J Glob Optim 65(2):283–307, 2016) to search for locally optimal solutions. Computational results are provided to demonstrate the efficiency of our approach. The computational results are presented for new problem instances, as well as for instances presented in the recent paper (http://www.optimization-online.org/DB_FILE/2016/03/5348.pdf, 2016).

Mathematical Problems in Engineering

A packing (layout) problem for a number of clusters (groups) composed of convex objects (e.g., ci... more A packing (layout) problem for a number of clusters (groups) composed of convex objects (e.g., circles, ellipses, or convex polygons) is considered. The clusters have to be packed into a given rectangular container subject to nonoverlapping between objects within a cluster. Each cluster is represented by the convex hull of objects that form the cluster. Two clusters are said to be nonoverlapping if their convex hulls do not overlap. A cluster is said to be entirely in the container if so is its convex hull. All objects in the cluster have the same shape (different sizes are allowed) and can be continuously translated and rotated. The objective of optimized packing is constructing a maximum sparse layout for clusters subject to nonoverlapping and containment conditions for clusters and objects. Here the term sparse means that clusters are sufficiently distant one from another. New quasi-phi-functions and phi-functions to describe analytically nonoverlapping, containment and distance ...

Wireless Networks

The paper studies packing ellipses in a rectangular container of minimum area. The problem has va... more The paper studies packing ellipses in a rectangular container of minimum area. The problem has various applications in production, logistics, industrial design. New phi-functions are proposed to state containment constraints and quasi-phi-functions are used for analytical description of non-overlapping constraints. A mathematical model for the packing problem is stated as a nonlinear programming problem. Two algorithms to find feasible starting points for identical and non-identical ellipses are proposed. The optimization procedure is used as a compaction algorithm to search for local optimal solutions. Computational results are provided to show the efficiency of the proposed approach.

Applied and computational mathematics

In the two-stage capacitated facility location problem a single product is produced at some plant... more In the two-stage capacitated facility location problem a single product is produced at some plants in order to satisfy customer demands. The product is transported from these plants to some depots and then to the customers. The capacities of the plants and depots are limited. The aim is to select cost minimizing locations from a set of potential plants and depots. This cost includes fixed cost associated with opening plants and depots, and variable cost associated with both transportation stages. In this work a Lagrangian relaxation is analyzed and a Lagrangian heuristic producing feasible solutions is presented. The results of a computational study are reported.

USSR Computational Mathematics and Mathematical Physics, 1989

USSR Computational Mathematics and Mathematical Physics, 1987

ABSTRACT A method of expansion is given which does not utilize the block-separable structure of t... more ABSTRACT A method of expansion is given which does not utilize the block-separable structure of the problem and which is based on aggregation of the variables. The monotonicity of the iterative process with respect to a functional is proved. The possibility of aggregation of the constraints is considered.

USSR Computational Mathematics and Mathematical Physics, 1990

Computational Mathematics and Mathematical Physics