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SolverStudio is a free Excel plug-in developed at the University of Auckland [1] that supports optimization and simulation modelling in a spreadsheet using an algebraic modeling language. It is popular in education, [ 2 ] the public sector [ 3 ] and industry for optimization users because it uses industry-standard modelling languages and is ...
Most problems can be formulated in terms of a search space and target in several different ways. For example, for the traveling salesman problem a solution can be a route visiting all cities and the goal is to find the shortest route. But a solution can also be a path, and being a cycle is part of the target.
The primary data set used in cost distance analysis is the cost raster, sometimes called the cost-of-passage surface, [9] the friction image, [8] the cost-rate field, or cost surface. In most implementations, this is a raster grid , in which the value of each cell represents the cost (i.e., expended resources, such as time, money, or energy) of ...
Given a system transforming a set of inputs to output values, described by a mathematical function f, optimization refers to the generation and selection of the best solution from some set of available alternatives, [1] by systematically choosing input values from within an allowed set, computing the value of the function, and recording the best value found during the process.
The study of facility location problems (FLP), also known as location analysis, is a branch of operations research and computational geometry concerned with the optimal placement of facilities to minimize transportation costs while considering factors like avoiding placing hazardous materials near housing, and competitors' facilities.
Given a system minimize subject to ,, the reduced cost vector can be computed as , where is the dual cost vector. It follows directly that for a minimization problem, any non- basic variables at their lower bounds with strictly negative reduced costs are eligible to enter that basis, while any basic variables must have a reduced cost that is ...
A related problem is the minimum cost circulation problem, which can be used for solving minimum cost flow. The minimum cost circulation problem has no source and sink; instead it has costs and lower and upper bounds on each edge, and seeks flow amounts within the given bounds that balance the flow at each vertex and minimize the sum over edges ...
A solution of MOLP is defined to be a finite subset ¯ of efficient points that carries a sufficient amount of information in order to describe the upper image of MOLP. Denoting by S {\displaystyle S} the feasible set of MOLP, the upper image of MOLP is the set P := P [ S ] + R + q := { y ∈ R q : ∃ x ∈ S : y ≥ P x } {\displaystyle ...