Combinatorial optimization through statistical instance-based learning

Question

1. What have the authors contributed in "Combinatorial optimization through statistical instance-based learning" ?

2. What are the future works mentioned in the paper "Combinatorial optimization through statistical instance-based learning" ?

3. What is the first step of the iterative process shown in Fig. 1?

4. How many iterations were performed on each problem instance?

Accepted Answer

In this paper, the authors present a heuristic methodology which employs the instance-based machine learning paradigm.. Experimental results are discussed concerning two well known problems, namely the knapsack problem and the set partitioning problem.

Accepted Answer

Some directions for further research are drawn from questions that arise quite naturally.. As an aspect of future work, extended experimentation on a variety of optimization problems is expected to reveal valuable statistical features, strongly informative and representative of the corresponding search spaces.

Accepted Answer

The first step of the iterative process shown in Fig. 1 is a preprocessing procedure, which adapts the KR approximator to the training set, in order to achieve higher prediction accuracy with respect to the underlying training set E .

Accepted Answer

Twelve iterations, of 5 minutes each, were performed on each problem instance after the construction of the initial training set.

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The absence of such a constraint contributes to the enrichment of the training set with feasible solutions of varying qualities, which contribute to a more detailed picture of the search space.

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As the proposed methodology is supposed to solve problems that enclose properties in a rather statistical than precisely defined manner, training data collected during the solving process are expected to be inconsistent.

Accepted Answer

In order to avoid cases where the LOOCV test would decide large values for k, and thus, slowing down the KR approximator, the size of the training set was kept stable to, at most, 25 training examples.

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The kernel function to be used at each iteration of the search schema is determined dynamically by LOOCV, from a repertoire of available kernel functions.

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The overall running time of the iterative part of their methodology was arranged to last for 3600 seconds, so that summed to the initial training set construction time equals to 4200 seconds.

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Because the 1s in each column are decided via a uniform distribution, the mentioned property is slightly depressed by the satisfiability of the problem constraints.

Accepted Answer

At every search step, the heuristic function chooses the assignment which brings the features vector of the extended path closer to specific features vectors of the best known solutions.

Accepted Answer

Each training example for the KR approximation scheme is a pair of a solution descriptive vector ~F , known as the features vector, and the respective objective function valueobj(~F ).

Accepted Answer

Solutions previously found by the proposed methodology are utilized as training examples, for evaluation of partial solutions on each search state.

Accepted Answer

Each of these clusters is meant to be used as a separate training set, for searching the corresponding sections of the searchspace in a locally exhaustive manner.

Accepted Answer

During the construction of a potential solution, the system simultaneously constructs a path towards the bottom of the search tree.

Combinatorial optimization through statistical instance-based learning

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Most frequently asked questions

1. What have the authors contributed in "Combinatorial optimization through statistical instance-based learning" ?

2. What are the future works mentioned in the paper "Combinatorial optimization through statistical instance-based learning" ?

3. What is the first step of the iterative process shown in Fig. 1?

4. How many iterations were performed on each problem instance?

5. What is the effect of the absence of a constraint?

6. What is the purpose of the proposed methodology?

7. How many training examples were used to avoid cases where the LOOCV test would decide large values?

8. What is the kernel function used at each iteration of the search schema?

9. How long did the iterative part of the methodology last?

10. Why is the property of the knapsack problem slightly depressed?

11. What is the heuristic function used to choose the assignment?

12. What is the training example for the KR approximation scheme?

13. What are the examples used for evaluation of partial solutions?

14. how many clusters are used for searching the corresponding sections of the searchspace?

15. What is the heuristic function used to construct a path?

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References

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