Oleg Shcherbina

A comparison of complete global optimization solvers

Abstract.Results are reported of testing a number of existing state of the art solvers for global constrained optimization and constraint satisfaction on a set of over 1000 test problems in up to 1000 variables, collected from the literature.The test problems are available online in AMPL and were translated into the input formats of the various solvers using routines from the COCONUT environment. These translators are available online, too.

Nonserial Dynamic Programming and Tree Decomposition in Discrete Optimization

Solving discrete optimization problems (DOP) can be a rather hard task. Many real DOPs contain a huge number of variables and/or constraints that make the models intractable for currently available solvers. There are few approaches for solving DOPs: tree search approaches (e.g., branch and bound), relaxation and decomposition methods. Large DOPs can be solved due to their special structure. Among decomposition approaches we can mention poorly known local decomposition algorithms using the special block matrix structure of constraints and half-forgotten nonserial dynamic programming algorithms which can exploit sparsity in the dependency graph of a DOP.

Modeling recreational systems using optimization techniques and information technologies

Due to intrinsic complexity and sophistication of decision problems in tourism and recreation, respective decision making processes can not be implemented without making use of modern computer technologies and operations research approaches. In this paper, we review research works on modeling recreational systems.

Graph-Based Local Elimination Algorithms in Discrete Optimization

The aim of this chapter is to provide a review of structural decomposition methods in discrete optimization and to give a unified framework in the form of local elimination algorithms (LEA). This chapter is organized as follows. Local elimination algorithms for discrete optimization (DO) problems (DOPs) with constraints are considered; a classification of dynamic programming computational procedures is given. We introduce Elimination Game and Elimination tree. Application of bucket elimination algorithm from constraint satisfaction (CS) to solving DOPs is done. We consider different local elimination schemes and related notions. Clustering that merges several variables into single meta-variable defines a promising approach to solve DOPs. This allows to create a quotient (condensed) graph and apply a local block elimination algorithm. In order to describe a block elimination process, we introduce Block Elimination Game. We discuss the connection of aforementioned local elimination algorithmic schemes and a way of transforming the directed acyclic graph (DAG) of computational LEA procedure to the tree decomposition.

Benchmarking ordering techniques for nonserial dynamic programming

Five ordering algorithms for the nonserial dynamic programming algorithm for solving sparse discrete optimization problems are compared in this paper. The benchmarking reveals that the ordering of the variables has a significant impact on the run-time of these algorithms. In addition, it is shown that different orderings are most effective for different classes of problems. Finally, it is shown that, amongst the algorithms considered here, heuristics based on maximum cardinality search and minimum fill-in perform best for solving the discrete optimization problems considered in this paper.

Computer-based system of tourism and recreational systems study and optimization.

This article discusses a methodology for development and validation of a comprehensive computer-based system of tourism and recreational systems study and optimization (CBSTRS) that is based on mathematical modeling of the recreational system and its processes, to assist planners in evaluating alternative scenarios and planning options. This allows empowering the organizational front-line by giving people systems with which they can solve their own problems, as distinct from the traditional approach of having specialists solve problems and then deliver solutions to the problem owners. The CBSTRS is a model-based decision support system (DSS) designed to work with data describing tourism and recreational systems, or, in other words, the CBSTRS is a database system with data describing recreational systems as well as a set of operations and mathematical models for working with the data. Proposed technology integrates common database operations such as query and statistical analysis with the unique possibility for mathematical modeling and analysis benefits offered by the system. These abilities distinguish the CBSTRS from usual information systems and make it valuable to a wide range of public and private enterprises for modeling and analyzing planning strategies for recreational systems.

Postoptimal Analysis in Nonserial Dynamic Programming

Usually, discrete optimization problems (DOPs) from applications have a special structure, and the matrices of constraints for large-scale problems have a lot of zero elements (sparse matrices). One of the promising ways to exploit sparsity in the interaction graph of the DOP is nonserial dynamic programming (NSDP), which allows to compute a solution in stages such that each of them uses results from previous stages. The drawback of NSDP methods consists on exponential time and space complexity that is exponential in the induced width of the DOP’s interaction graph. This causes an expediency and an urgency of development of tools that could help to cope with this difficulty. In this paper is shown that NSDP algorithm generates a family of related DOPs that differ from each other in their right-hand sides. For solving this family of related problems postoptimal and sensitivity analysis methods are proposed.