Accelerate Assessment Calculations for Quadratic Assignment Problem Solution

The Quadratic Assignment Problem (QAP) is widely recognized as an important combinatorial optimization problem. QAP finds extensive applications in practical scenarios such as facility placement, computer manufacturing, communication networks, and other areas. It solves real-world challenges by optimizing resource allocation in a way that minimizes costs or distances. The essence of the proposed approach is a systematic enumeration of possible permutations of elements using the next lexicographical permutation and heap’s methods. Rather than relying on random or heuristic-based initialization, we generate permutations in a predictable sequence. Moreover, this study proposes an efficient calculation approach that selectively calculates only the changes in elements resulting from the adjustment of permutations, thereby reducing the need to re-evaluate the entire cost function for each permutation and speeding up the search for optimal solutions. In addition, we employ a brute force algorithm, which evaluates all permutations and calculates the cost of each permutation, and an illustrative implementation of this approach using C++ program for QAP. The proposed approach demonstrates improved computational efficiency, reduces the search space, and opens avenues for further exploration of the use of optimization technologies in other combinatorial optimization problems for larger problem instances.