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- Why is it absolutely necessary, while attempting to solve issues involving linear programming, to give the object function a larger weight than the constraints?Consider a problem with four variables, {A,B,C,D}. Each variable has domain {1,2,3}. The constraints on the problem are that A > B, B < C, A = D, C ¹ D. Perform variable elimination to remove variable B. Explain the process and show your work.Why is it of the utmost importance, when solving issues involving linear programming, to give the object function a larger weight than the constraints?
- Write algorithm for the continually growing set of linear approximations of the constraints simply makes a better and better outer approximation of the original nonlinear constraints.Bootstrapping procedure to achieve initial feasibility of a convex constrained region. INPUTS: NotSat: the set of inequality constraints having convex region effectsArc consistency in constrained satisfaction problems Suppose that we have three variables X1, X2 and X3, which are defined on the same domain of {1, 2, 3}. Two binary constraints for these three variables are defined according to the following: 1. Is X1 arc-consistent with respect to X2? And is X1 arc-consistent with respect to X3? and why? In addition, is X3 arc-consistent with respect X1 if the constraints between R1 and R3 are undirected (i.e., R31 is defined as {(X3, X1), [(2, 1),(1, 2),(1, 3),(3, 3)]} that switches the element order of every two-tuple of R13)? and why? 2. Suppose that, after some inference, the domain of X1 is reduced as {2, 3} and the constrains in R12 and R13 for X1 = 1 are removed accordingly. To be more specific, (1, 2) is removed from R13 due to reducing the domain of X1. Now is X1 still arc-consistent with respect to X2? And is X1 arc-consistent with respect to X3? and why? In addition, is X3 still arc-consistent with respect X1 if the constraints between…
- Describe the significance that why object function is more important than the constraints in the linear programming problems?Show how a single ternary constraint such as “A + B = C” can be turned into three binaryconstraints by using an auxiliary variable. You may assume finite domains. (Hint: Consider a newvariable that takes on values that are pairs of other values, and consider constraints such as “X is thefirst element of the pair Y .”) Next, show how constraints with more than three variables can betreated similarly. Finally, show how unary constraints can be eliminated by altering the domains ofvariables. This completes the demonstration that any CSP can be transformed into a CSP with onlybinary constraints.Explain the significance that why object function is more important than the constraints in the linear programming problems?
- Recognize overlapping from disjoint constraints.Select the correct answer ( there could be more than one correct option ) : 1- The unbounded optimization problem searches for the global extreme of a function on the part of domain. 2-The unbounded optimization problem searches for the global extreme of a function (on the entire domain). 3- The unbounded optimization problem searches for the extreme of a function subject to the constraints.A problem with optimization is specified:The input is one instance as a prerequisite.Postconditions: The result is one of the acceptable solutions in this situation, with the best (minimum or maximum, as appropriate) success metric. (The outputted solution need not be original.)