Small size instances Sample Clauses

Small size instances. A first overview of the results for the set of 90 small instances is displayed in Figure 3. On the left side, the bar chart (a) presents results with respect to the efficiency criteria. For each algorithm, it shows the percentage of instances for which the algorithm terminates within the time limit (3600 seconds). The average running time (in seconds) for these instances is shown in parentheses. On the right side, the bar chart (b) summarizes results in terms of the effectiveness criteria. It shows the percentage of instances for which each algorithm A obtains the best overall solution (∆QA = 0). The first bar in Figure 3(b), marked “RL”, shows the percentage of instances for which the contract-duration relaxed model yields a feasible (and hence, optimal) solution in the first phase of the relax-and-repair heuristic (see Section 7). For each algorithm A, the average gap GA over the set of instances for which A finds the best solution is shown in parentheses. On the other hand, when A does not find the best solution, the average relative difference ∆QA to the best-known value is displayed in parentheses. Another overview of the results is provided in Figure 4 and Figure 5, which display the performance profile of each algorithm for the criteria FA, BA, GA, and ∆QA. The performance profile can be viewed as the empirical distribution function of the performance criterion of interest (▇▇▇▇▇ & Mor´e, 2002). More precisely, for an algorithm A, a criterion CA, and a value x on the horizontal axis, the performance profile indicates the percentage of instances for which CA ≤ x. The profiles allow for easy visualization and comparison of the performance of different algorithms over a range of instances (in the present case, the collection of 90 small instances).
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