Complete Solution of a Constrained Tropical Optimization Problem with Application to Location Analysis
نویسنده
چکیده
We present a multidimensional optimization problem that is formulated and solved in the tropical mathematics setting. The problem consists in minimizing a nonlinear objective function defined on vectors in a finite-dimensional semimodule over an idempotent semifield by means of a conjugate transposition operator, subject to the constraints in the form of linear vector inequalities. A complete direct solution to the problem under fairly general assumptions is given in a compact vector form suitable for both further analysis and practical implementation. We apply the general result to solve multidimensional minimax single facility location problems with Chebyshev distance and with inequality constraints imposed on the feasible location area. Key-Words: idempotent semifield, tropical mathematics, minimax optimization problem, single facility location problem, Chebyshev distance. MSC (2010): 65K10, 15A80, 65K05, 90C48, 90B85
منابع مشابه
Bi-objective optimization of multi-server intermodal hub-location-allocation problem in congested systems: modeling and solution
A new multi-objective intermodal hub-location-allocation problem is modeled in this paper in which both the origin and the destination hub facilities are modeled as an M/M/m queuing system. The problem is being formulated as a constrained bi-objective optimization model to minimize the total costs as well as minimizing the total system time. A small-size problem is solved on the GAMS software t...
متن کاملDirect solution to constrained tropical optimization problems with application to project scheduling
We examine a new optimization problem formulated in the tropical mathematics setting as a further extension of certain known problems. The problem is to minimize a nonlinear objective function, which is defined on vectors over an idempotent semifield by using multiplicative conjugate transposition, subject to inequality constraints. As compared to the known problems, the new one has a more gene...
متن کاملUsing tropical optimization to solve constrained minimax single-facility location problems with rectilinear distance
We consider a constrained minimax single-facility location problem with addends on the plane with rectilinear distance. The problem is first formulated in a standard form, and then represented in terms of tropical mathematics as a constrained optimization problem. We apply methods and results of tropical optimization to obtain direct, explicit solutions to the optimization problem. The results ...
متن کاملA constrained tropical optimization problem: complete solution and application example
A multidimensional optimization problem is considered, which is formulated in terms of tropical mathematics as to minimize a nonlinear objective function subject to linear inequality constraints. The optimization problem is motivated by a problem in project scheduling when an optimal schedule is given by minimizing the flow time of activities in a project under various activity precedence const...
متن کاملCONSTRAINED BIG BANG-BIG CRUNCH ALGORITHM FOR OPTIMAL SOLUTION OF LARGE SCALE RESERVOIR OPERATION PROBLEM
A constrained version of the Big Bang-Big Crunch algorithm for the efficient solution of the optimal reservoir operation problems is proposed in this paper. Big Bang-Big Crunch (BB-BC) algorithm is a new meta-heuristic population-based algorithm that relies on one of the theories of the evolution of universe namely, the Big Bang and Big Crunch theory. An improved formulation of the algorithm na...
متن کامل