***** Adam Letchford *****

Some Thoughts on Duality in Continuous and Discrete Optimisation

Duality is a fundamental concept in optimisation. In the first half of this talk, I will give a gentle introduction to duality in continuous and discrete optimisation. Examples will include (i) classic linear programming duality; (ii) Lagrangian duality for nonlinear programming; (iii) duality for conic optimisation; and (iv) Lagrangian, surrogate and subadditive duality for integer programming. In the second half of the talk, I will review and discuss various ways in which duality can be of practical use. Examples will include (i) sensitivity analysis; (ii) the design of exact or heuristic algorithms for various problems; and (iii) theorem-proving. The last of these three applications may be surprising to some.

***** Boglárka G-Tóth *****

Advanced Hybrid Quantum Optimization Frameworks

This talk introduces quantum optimization methods, focusing on the ground state search problem of the Ising Hamiltonian via Variational Quantum Algorithms (VQAs). To enhance the performance and reliability of VQAs in solving binary linear programming problems, we propose and evaluate two novel operational frameworks exploiting the structure of linear programs and relevant aspects of their physical encodings in a quantum computer.
Specifically, we show classically integrated hybrid quantum optimization algorithms that utilize these aspects in two different ways: a constraint generation routine, which aims to provide high-quality solutions quickly, and a complete branch-and-bound scheme that decomposes the original problem with respect to the physical structure and is measurable by metrics like the primal-dual integral.

***** Claudia Archetti *****

Exact approaches for colorful components problems based on representative formulations

Carmine Sorgente, Martina Cerulli, Claudia Archetti, Diego Delle Donne

In a node-colored graph, a colorful component is a connected subgraph in which no two nodes share the same color. Colorful components problems are graph modification problems that aim to transform a node-colored graph into a collection of colorful components by deleting edges. We consider three variants of colorful components problems that have been studied in the literature: the MOP, MCC, and MEC problems. For them, we propose new integer programming formulations based on representative nodes, where each component is identified by a representative, eliminating the symmetry inherent in classical assignment-based models. Moreover, we introduce a novel flow-based modeling approach to enforce component connectivity through additional variables and constraints. To further improve computational efficiency, we also develop a preprocessing procedure that reduces the number of variables in the representative formulations. Computational experiments demonstrate that the proposed models, particularly those using flow-based connectivity constraints, significantly outperform the current state-of-the-art approach, solving all benchmark instances to optimality within negligible computational time.

***** Dick den Hertog *****

Optimization for a Better World

This keynote explores the transformative role of optimization in helping non-governmental organizations (NGOs) and non-profit organizations (NPOs) accelerate progress toward the United Nations Sustainable Development Goals (SDGs). Through the work of the Analytics for a Better World Institute, cutting-edge optimization methods are developed and applied to address some of society’s most pressing humanitarian and environmental challenges.
Drawing on real-world collaborations with NGOs and NPOs, the keynote will demonstrate how optimization can substantially enhance social impact. One featured example is a collaboration with The Ocean Cleanup, where advanced optimization models are used to determine how cleanup vessels should be deployed and routed to maximize the removal of plastic from the world’s oceans, thereby increasing the effectiveness of large-scale efforts to combat marine pollution.
The keynote will also present a range of projects that use geospatial optimization to improve access to healthcare and other essential services. These include optimizing the locations of primary healthcare facilities in Timor-Leste, determining the optimal placement of stroke centers in Vietnam, planning COVID-19 testing centers in Nepal, and identifying suitable locations for water wells in Sudan. These initiatives have been conducted in partnership with organizations such as the World Bank, the World Health Organization, Amref Health Africa, and the American Red Cross.
Beyond showcasing the societal impact of these applications, the keynote will discuss the novel methodological and computational challenges they have generated. Many of these challenges remain open research questions, creating exciting opportunities for future advances in optimization and analytics for social good.

***** Gabriele Eichfelder *****

Beyond a Single Optimum: Trade-offs and Insights in Multiobjective Optimization

This talk gives an introduction to multiobjective optimization. We present fundamental concepts and basic solution approaches, and highlight the additional challenges that arise when moving from one objective to several objectives. In particular, we discuss why the numerical solution of multiobjective problems requires new ideas and present several ingredients that are useful for designing effective solution approaches.

***** Tom Van Woensel *****

Two-Echelon Vehicle Routing Problems: A short review, some models and directions for future research

In the two-echelon vehicle routing problem (2E-VRP), the distribution network is split into two echelons. Different vehicles are operated on the first and second echelon to maintain economies of scale and adhere to any vehicle restrictions that may be present in either echelon. Intermediate facilities are located at the borders of the echelons to facilitate the consolidation and transshipment of goods between echelons. Examples of two-echelon distribution systems include express delivery, grocery and hypermarket products distribution, multi-modal freight transportation, city logistics, and ecommerce and home delivery services. In recent years, the body of literature on the 2E-VRP has expanded significantly. Many research papers have appeared in the scientific literature so far, which underlines both the academic and practical relevance of 2E-VRPs. In this review, we structure and revise all literature on the 2E-VRP. Mathematical formulations and benchmark datasets used to test and to evaluate new algorithms are reviewed and discussed.