Consider the following biobjective integer knapsack problem (BOIKP): maximize f(x) = [f1(x) = 8x1 + 9x2 + 3x3, f2(x) = 3
Posted: Thu May 05, 2022 7:35 pm
Consider the following biobjective integer knapsack problem
(BOIKP):
maximize f(x) = [f1(x) = 8x1 + 9x2 + 3x3, f2(x) = 3x1 + 2x2 +
10x3]
subject to 2x1 + 2x2
+ 3x3 ≤ 6
x1, x2, x3 ≥ 0, integer.
NOTE: All Pareto outcomes for this problem
have integer components.
(a). Use the weighted-sum method and/or the epsilon constraint
method and design an optimization process to compute all Pareto
outcomes to this problem. Present the optimization process in the
form of a multi-step procedure (pseudocode or flowchart) and
explain why this process guarantees to find all Pareto
outcomes.
Please answer (a).
(BOIKP):
maximize f(x) = [f1(x) = 8x1 + 9x2 + 3x3, f2(x) = 3x1 + 2x2 +
10x3]
subject to 2x1 + 2x2
+ 3x3 ≤ 6
x1, x2, x3 ≥ 0, integer.
NOTE: All Pareto outcomes for this problem
have integer components.
(a). Use the weighted-sum method and/or the epsilon constraint
method and design an optimization process to compute all Pareto
outcomes to this problem. Present the optimization process in the
form of a multi-step procedure (pseudocode or flowchart) and
explain why this process guarantees to find all Pareto
outcomes.
Please answer (a).