Combinatorial Optimization Problems in Applied Sciences

Dear Colleagues,

Applied sciences are defined as disciplines that apply existing scientific knowledge to develop practical applications such as technologies and inventions. In contrast to basic or pure sciences, which aim to expand knowledge to explain phenomena in the natural world, applied sciences aim to use this knowledge to address real-world problems and needs.

Note that independent of the field or application context, practical problems often involve multiple variables and objectives. Notable examples include the following:

• Engineering and Computer Science: structures, materials, flows, cost/risk minimization, profit/accuracy maximization, scheduling optimization, waste reduction, coverage maximization, computer-assisted design/planning/interaction, human–robot interaction, smart manufacturing, machine learning and algorithms.
• Medicine and Pharmacology: optimal chemical design, computer-assisted diagnosis, human–robot and remote assistance, health monitoring and prevention, development of new medications, and analysis of drug interactions.
• Agriculture and Environmental Sciences: resilient crop yields, sustainable farming practices, waste reduction, sustainable design of fertilizers, pollution minimization, and green technologies.

Because many practical problems can be translated into optimization tasks, combinatorial optimization has become a crucial tool to propose suitable and best solutions for these problems. For applied sciences, combinatorial optimization has improved solutions for the following problems:

• Economics and Logistics: the traveling salesman problem, knapsack problem, vehicle routing problem, protein folding, supply chain management, forecasting, and simulation.
• Intelligent Systems: feature selection, model architecture search, hyperparameter tuning, neural network design, adaptive heuristics/metaheuristics, big data analysis, computer-assisted diagnosis, and medical imaging interpretation.
• Social and Environmental Wellbeing: optimization of traffic light timing to reduce congestions and emissions, humanitarian logistics, distribution planning to reduce emissions, water, and carbon footprint reduction.

Note that all combinatorial problems involve strong mathematical foundations for modelling, analysis, and assessment. For example:

• Problems are modelled through mathematical constructs such as graphs, matrices, and functions;
• The design of solving algorithms is guided by the mathematical analysis of the combinatorial problem, leading to the determination of N-hard and NP-complete complexities, which are not likely to be solved to optimality;
• Reduction in the complexity of difficult problems through advanced approaches such as mathematical “relaxations”. Hence, combinatorial approaches must be supported by mathematical foundations to ensure their suitability for modelling and solving practical problems.

Aim:

The present Special Issue elaborates on these advances by providing a benchmark of current and original combinatorial optimization applications on social and environmental problems, including (but not limited to) healthcare, pollution/waste reduction, innovation in small- and medium-sized enterprises, humanitarian logistics, and labor planning. As a benchmark, it is encouraged that accepted works include all details of the designed combinatorial optimization algorithm, including the mathematical modelling of the practical problem and foundations of the algorithm itself, and implementation of programming codes for knowledge sharing within the community.

Prof. Dr. Santiago Omar Caballero-Morales
Guest Editor

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• mathematical modelling
• combinatorial optimization
• algorithms