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Updated: May 27, 2025

Quadruple-Checkerboard: A Modification of the Three-Dimensional Checkerboard for Studying Drug Combinations

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On the Use of the Doubly Stochastic Matrix Models for the Quadratic Assignment Problem.

Valentino Santucci¹, Josu Ceberio²

¹University for Foreigners of Perugia, Perugia, 06123, Italy valentino.santucci@unistrapg.it.

Evolutionary Computation

|February 20, 2025

Summary

Doubly Stochastic Matrices (DSMs) offer an effective approach for solving complex permutation problems like the Quadratic Assignment Problem (QAP). Experiments show DSMs outperform other models in efficiency and computational performance for assignment and ordering tasks.

Keywords:

Doubly Stochastic Matrix Estimation of Distribution Algorithm Fourier transform.Ordering vs. Assignment Problems Quadratic Assignment Problem

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Area of Science:

Combinatorial Optimization
Computational Mathematics

Background:

Permutation problems are challenging in combinatorial optimization.
Existing methods for optimizing permutations vary significantly in their information utilization.

Purpose of the Study:

To propose and evaluate Doubly Stochastic Matrices (DSMs) within Estimation of Distribution Algorithms for permutation optimization.
To assess the effectiveness and efficiency of DSMs compared to other permutation models.

Main Methods:

Utilizing DSMs as a probabilistic model for permutations.
Developing efficient learning and sampling schemes for iterative probability model updates.
Conducting experiments on standard Quadratic Assignment Problem (QAP) benchmarks.

Main Results:

DSMs demonstrated superior effectiveness and computational efficiency over four other permutation models for the QAP.
DSMs show promise for assignment problems and ordering problems like the Linear Ordering Problem (LOP).

Conclusions:

DSMs are a valuable tool for assignment and ordering problems.
Potential applications of DSMs extend to other optimization paradigms like genetic algorithms and gradient search.