Course detail
Computing Methods in Logistics Optimization Problems
FSI-SOU-A Acad. year: 2027/2028 Summer semester
The course introduces mathematical and computational methods for solving optimization problems, with particular emphasis on logistics, planning, and operational decision-making. Students are introduced to selected exact, deterministic, and stochastic optimization algorithms, their implementation, and their applications to practical problems. The main emphasis is on identifying the structure of optimization problems, selecting suitable solution methods, and experimentally evaluating the quality of the obtained solutions.
The first part covers one-dimensional and multidimensional continuous optimization, gradient-based methods, Newton-type methods, derivative-free and stochastic approaches, and population-based algorithms. This is followed by constrained optimization, penalty reformulations, the augmented Lagrangian method, interior-point methods, the simplex method, and selected approaches to integer optimization.
The second part focuses on heuristic and metaheuristic algorithms particularly suitable for combinatorial optimization problems. Topics include local search, iterated local search, GRASP, variable neighborhood search, tabu search, simulated annealing, evolutionary algorithms, and ant colony optimization. The course also introduces multiobjective optimization algorithms, including NSGA-II and MOEA/D, as well as modular algorithm implementations and automatic algorithm configuration.
Computer-assisted exercises focus on implementing and experimentally analyzing selected methods, using available optimization libraries, and applying them to representative logistics problems such as routing, scheduling, assignment, and other decision-making tasks. Students compare solution quality, computational requirements, and the reliability of different optimization approaches.
Language of instruction
English
Number of ECTS credits
6
Supervisor
Department
Entry knowledge
Students are expected to have a basic understanding of mathematical optimization, including optimization problem formulation, objective functions, decision variables, constraints, and fundamental principles of numerical optimization methods.
Required mathematical knowledge includes fundamentals of linear algebra, differential calculus of functions of one and several variables, probability theory, and mathematical statistics.
Basic programming skills are required, including familiarity with functions, data structures, conditional statements, and loops, and the ability to implement, execute, and test simple algorithms. Previous knowledge of specific logistics optimization algorithms is not required.
Rules for evaluation and completion of the course
Course-unit credit requirements: active participation in seminars, mastering the subject matter, and semester project acceptance.
Examination: Written exam focused on the successful implementation of the discussed methods accompanied by oral discussion of the results.
Attendance at seminars is required as well as active participation. Passive or missing students are required to work out additional assignments.
Aims
Upon successful completion of the course, students will be able to:
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Formulate and classify selected logistics optimization problems by identifying decision variables, objective functions, and constraints, and justify the selection of suitable optimization approaches based on problem structure.
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Apply and compare selected continuous optimization methods, including gradient-based methods, Newton-type methods, direct methods, and stochastic optimization approaches, and assess their suitability for problems with different objective function and constraint properties.
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Apply and evaluate selected constrained optimization and integer programming techniques, including penalty methods, the augmented Lagrangian method, interior-point methods, the simplex method, and the principles of branch-and-bound.
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Design, implement, and analyze selected local-search-based heuristics and metaheuristics, particularly for combinatorial logistics problems, and assess the influence of solution representations and neighborhood structures on algorithm performance.
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Implement or appropriately use selected population-based, evolutionary, swarm-based, and multiobjective optimization algorithms, and compare their performance in terms of solution quality and computational requirements.
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Design and conduct reproducible computational experiments with selected optimization algorithms, evaluate their results using appropriate performance measures, employ available algorithmic frameworks, and assess the benefits of automatic parameter configuration.
Study aids
Study materials include lecture notes, assignments for computer-based exercises, sample implementations of optimization algorithms, and test tasks. These materials are made available via the university's e-learning platform.
The study programmes with the given course
Programme N-LAN-A: Logistics Analytics, Master's, compulsory
Type of course unit
Lecture
26 hours, optionally
Syllabus
1. Introduction to optimization algorithms and 1D optimization
2. Descend direction methods, Grandient methods, Newton-type methods
3. Direct and stochastic optimization methods
4. Population-based methods for continuous problems
5. Penalty reformulations, Augmented Lagrangian
6. Interior point methods, barrier method, two-phase methods
7. Simplex method in matrix form, Integer and combinatorial optimization – Branch and Bound method, Gomory cuts
8. Local Search, Iterated Local Search, GRASP
9. Variable Neigborhood Search, Tabu Search, Simulated Annealing
10. Evolutionary Algorithms, Genetic Algorithms
11. Swarm Intelligence methods, Ant Colony Optimization
12. Multiobjective methods, NSGA-II, MOEA/D
13. Available software implementations, modular frameworks, automatic algorithm design (IRACE), modern approaches
Computer-assisted exercise
26 hours, compulsory
Syllabus
Implementation and analysis of the following methods:
1. 1D optimization methods
2. Descend direction methods, Grandient methods, Newton-type methods
3. Direct and stochastic optimization methods
4. Population-based methods for continuous problems
5. Augmented Lagrangian
6. Interior point methods, barrier method, two-phase methods
7. Simplex method in matrix form, Branch and Bound method, Gomory cuts
8. Local Search, Iterated Local Search, GRASP
9. Variable Neighborhood Search, Tabu Search, Simulated Annealing
10. Evolutionary Algorithms, Genetic Algorithms
11. Swarm Intelligence methods, Ant Colony Optimization
12. Multiobjective methods, NSGA-II, MOEA/D
13. Utilization of modular frameworks