Combinatorial Optimization and Its Real-World Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E: Applied Mathematics".

Deadline for manuscript submissions: 28 February 2027 | Viewed by 1272

Special Issue Editor


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Guest Editor
Department of Economics and Business Studies, University of Genoa, 16126 Genoa, Italy
Interests: heuristic methods to solve combinatorial optimization problems; optimization models and methods in distributive logistics
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Special Issue Information

Dear Colleagues,

Building on the success of our first edition, this Mathematics Special Issue will continue the exploration of cutting-edge advances in combinatorial optimization and its real-world applications across diverse fields—from logistics and healthcare to manufacturing and service industries.

As modern decision-making problems grow increasingly complex, often involving large-scale NP-hard challenges with vast numbers of variables and constraints, there is a pressing need for

  • Innovative models (e.g., mixed-integer linear programming, Boolean formulations);
  • Efficient heuristics that balance solution quality with reduced computation times;
  • Energy-aware algorithms to minimize computational resources;
  • Practical case studies demonstrating successful implementation.

We invite contributions that address such challenges, offering theoretical insights or applied solutions to advance the field. Topics of interest include, but are not limited to, the following:

  • Optimization techniques for large models;
  • Heuristic and metaheuristic design;
  • Real-world applications with measurable impact.

Join us in shaping the next generation of combinatorial optimization tools. We look forward to receiving your submissions!

Prof. Dr. Anna Sciomachen
Guest Editor

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Keywords

  • optimization
  • mixed-integer linear programming
  • large-size models
  • Boolean problems
  • heuristics
  • metaheuristics
  • energy-efficient algorithms
  • case studies

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Published Papers (2 papers)

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Research

30 pages, 10197 KB  
Article
Gromov–Wasserstein Meets Combinatorial Optimization: A Scalable Solver for the Capacitated Quadratic Assignment Problem
by Iman Seyedi, Antonio Candelieri, Enza Messina and Francesco Archetti
Mathematics 2026, 14(11), 1972; https://doi.org/10.3390/math14111972 - 3 Jun 2026
Abstract
The Capacitated Quadratic Assignment Problem (CQAP) arises in logistics and network design, requiring the allocation of tasks to agents under quadratic interaction costs and capacity constraints. Classical exact solvers become computationally infeasible for large-scale instances, while heuristic methods such as Genetic Algorithms suffer [...] Read more.
The Capacitated Quadratic Assignment Problem (CQAP) arises in logistics and network design, requiring the allocation of tasks to agents under quadratic interaction costs and capacity constraints. Classical exact solvers become computationally infeasible for large-scale instances, while heuristic methods such as Genetic Algorithms suffer from scalability limitations and sensitivity to local optima, leaving a gap for principled scalable approximations. In this paper, we address CQAP using the Gromov–Wasserstein (GW) framework, derived from Optimal Transport (OT) theory. In particular, we propose a multi-initialization GW strategy (GW_MultiInit) that mitigates the local optima problem inherent to non-convex GW optimization and scales efficiently to large problem sizes. Computational experiments on synthetic CQAP instances show that GW_MultiInit consistently achieves solutions close to the exact optimum for small- and medium-scale problems, and outperforms heuristic baselines such as the genetic algorithm at large scale in both runtime and solution quality across the benchmarks tested. To validate generalizability, we further evaluate GW_MultiInit On 17 QAPLIB benchmark instances adapted to the CQAP setting, GW_MultiInit achieves the best approximate result on 15 out of 17 instances with an average optimality gap of 0.34%, demonstrating strong generalizability beyond synthetic data. Additional comparisons with Entropic GW and Fused GW highlight practical trade-offs between accuracy, speed, and parameter sensitivity, offering guidelines for real-world deployment. Our results suggest that GW-based methods, and GW_MultiInit in particular, offer a promising and scalable approach for CQAP and related large-scale assignment problems within the problem scales examined. Full article
(This article belongs to the Special Issue Combinatorial Optimization and Its Real-World Applications)
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25 pages, 4516 KB  
Article
Mathematical Programming for Optimal Evacuation in Industrial Facilities
by Carmine Cerrone, Massimo Paolucci and Anna Sciomachen
Mathematics 2026, 14(4), 632; https://doi.org/10.3390/math14040632 - 11 Feb 2026
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Abstract
This paper presents an optimization framework for determining safe and efficient evacuation paths in complex industrial facilities. The proposed approach models the evacuation process through a timed flow network that captures both the structural characteristics of the layout and the temporal evolution of [...] Read more.
This paper presents an optimization framework for determining safe and efficient evacuation paths in complex industrial facilities. The proposed approach models the evacuation process through a timed flow network that captures both the structural characteristics of the layout and the temporal evolution of emergency conditions. The formulation accommodates real-time updates, enabling dynamic re-routing when certain areas or connections become inaccessible. Computational experiments on large-scale instances demonstrate the scalability of the model and its ability to provide complete evacuation plans under increasing demand. The results confirm predictable relationships between population size, time horizon, and evacuation completion, supporting its use as a decision support tool for both strategic planning and operational response. Full article
(This article belongs to the Special Issue Combinatorial Optimization and Its Real-World Applications)
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