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The constrained-optimization problem (COP) is a significant generalization of the classic constraint-satisfaction problem (CSP) model. [1] COP is a CSP that includes an objective function to be optimized. Many algorithms are used to handle the optimization part.
A constraint optimization problem (COP) is a constraint satisfaction problem associated to an objective function. An optimal solution to a minimization (maximization) COP is a solution that minimizes (maximizes) the value of the objective function. During the search of the solutions of a COP, a user can wish for:
JaCoP is a constraint solver for constraint satisfaction problems. It is written in Java and it is provided as a Java library. JaCoP has an interface to the MiniZinc and AMPL modeling languages. Its main focus is on ease of use, modeling power, as well as efficiency. It has a large collection of global constraints implemented to facilitate ...
A multiple constrained problem could consider both the weight and volume of the books. (Solution: if any number of each book is available, then three yellow books and three grey books; if only the shown books are available, then all except for the green book.) The knapsack problem is the following problem in combinatorial optimization:
The classic model of Constraint Satisfaction Problem defines a model of static, inflexible constraints. This rigid model is a shortcoming that makes it difficult to represent problems easily. [ 33 ] Several modifications of the basic CSP definition have been proposed to adapt the model to a wide variety of problems.
JaCoP, an open source Java constraint solver. Koalog, a commercial Java-based constraint solver. logilab-constraint, an open source constraint solver written in pure Python with constraint propagation algorithms. Minion, an open-source constraint solver written in C++, with a small language for the purpose of specifying models/problems.
A general chance constrained optimization problem can be formulated as follows: (,,) (,,) =, {(,,)}Here, is the objective function, represents the equality constraints, represents the inequality constraints, represents the state variables, represents the control variables, represents the uncertain parameters, and is the confidence level.
An optimization problem is one of calculation of the extrema (maxima, minima or stationary points) of an objective function over a set of unknown real variables and conditional to the satisfaction of a system of equalities and inequalities, collectively termed constraints.