Optimization DY0-001 Practice Questions (Page 4)

Questions 16–20

1. 16application · medium

   A logistics company needs to find the optimal route for a delivery truck that must visit 15 different locations and return to the warehouse. The goal is to minimize total travel distance. The operations team is considering different algorithmic approaches. Which technique is most directly applicable to this type of constrained optimization problem?

   • ANewton's method, because it uses second-order derivatives to converge quickly to the optimal route.
   • BGradient descent, because it can efficiently find the minimum of the distance function.
   • CLinear programming, because the distance is a linear function of the route.
   • DA genetic algorithm, because it can explore a large discrete solution space and find a good, though not necessarily perfect, route.
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2. 17expert · hard

   A data scientist is working on a constrained optimization problem where the objective function is not differentiable. The constraints are simple bounds on the variables. The team needs a method that can handle the non-differentiability and is known to work well for this type of problem. Which technique is most appropriate?

   • ASubgradient method, because it generalizes gradient descent to non-differentiable convex functions and can handle bound constraints.
   • BSimplex method, because it is designed for non-differentiable problems.
   • CNewton's method, because it uses second-order derivatives to converge faster.
   • DGradient descent, because it is the standard method for all optimization problems.
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4. 18foundation · easy

   Which of the following is an example of an inequality constraint?

   • Ax = 5
   • Bx + y = z
   • Cx + y = 10
   • Dx^2 + y^2 ≤ 25
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5. 19application · medium

   A hospital is optimizing its staff scheduling. The objective is to minimize overtime costs. The constraints are that each nurse must work at least 3 shifts per week, no nurse can work more than 5 shifts per week, and there must be at least 2 nurses on duty at all times. Which of the following best describes this optimization problem?

   • AA constrained problem, but only because of the minimum staffing requirement, not the shift limits.
   • BAn unconstrained problem where the goal is to find the schedule that minimizes overtime costs.
   • CA constrained problem with both lower-bound and upper-bound constraints on the decision variables.
   • DAn unconstrained problem because the objective is to minimize costs, which is the only factor to consider.
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6. 20foundation · easy

   Which of the following is a common technique for unconstrained optimization?

   • APenalty method
   • BSimplex method
   • CGradient descent
   • DBranch and bound
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