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With the pervasiveness of Stochastic Shortest-Path (SSP) problems in high-risk industries, such as last-mile autonomous delivery and supply chain management, robust planning algorithms are crucial for ensuring successful task completion…
A general-purpose C++ software program called $\mathbb{CGPOPS}$ is described for solving multiple-phase optimal control problems using adaptive Gaussian quadrature collocation. The software employs a Legendre-Gauss-Radau direct orthogonal…
Mixed Integer Programming (MIP) is NP-hard, and yet modern solvers often solve large real-world problems within minutes. This success can partially be attributed to heuristics. Since their behavior is highly instance-dependent, relying on…
Contour integration schemes are a valuable tool for the solution of difficult interior eigenvalue problems. However, the solution of many large linear systems with multiple right hand sides may prove a prohibitive computational expense. The…
We propose conformal predictive programming (CPP), a framework to solve chance constrained optimization problems, i.e., optimization problems with constraints that are functions of random variables. CPP utilizes samples from these random…
Current state-of-the-art solvers for mixed-integer programming (MIP) problems are designed to perform well on a wide range of problems. However, for many real-world use cases, problem instances come from a narrow distribution. This has…
We give a simple combinatorial algorithm to deterministically approximately count the number of satisfying assignments of general constraint satisfaction problems (CSPs). Suppose that the CSP has domain size $q=O(1)$, each constraint…
Cutting and Packing problems are occurring in different industries with a direct impact on the revenue of businesses. Generally, the goal in Cutting and Packing is to assign a set of smaller objects to a set of larger objects. To solve…
Since the adoption of large language models (LLMs) for text evaluation has become increasingly prevalent in the field of natural language processing (NLP), a series of existing works attempt to optimize the prompts for LLM evaluators to…
The traveling salesman problem (TSP) and the graph partitioning problem (GPP) are two important combinatorial optimization problems with many applications. Due to the NP-hardness of these problems, heuristic algorithms are commonly used to…
In this study, the periodic train timetabling problem is formulated using a time-space graph formulation. Three solution methods are proposed and compared where solutions are built by what we define as a dive-and-cut-and-price procedure. An…
It is well known that the variable ordering can be critical to the efficiency or even tractability of the cylindrical algebraic decomposition (CAD) algorithm. We propose new heuristics inspired by complexity analysis of CAD to choose the…
This paper considers stochastic optimization problems whose objective functions involve powers of random variables. For example, consider the classic Stochastic lp Load Balancing Problem (SLBp): There are $m$ machines and $n$ jobs, and…
The three-dimensional bin packing problem (3D-BPP) plays an important role in city logistics and manufacturing environments, due to its direct relevance to operational cost. Most existing literature have investigated the conventional…
Sampling-based planning algorithm is a powerful tool for solving planning problems in high-dimensional state spaces. In this article, we present a novel approach to sampling in the most promising regions, which significantly reduces…
Mean-variance portfolio optimization problems often involve separable nonconvex terms, including penalties on capital gains, integer share constraints, and minimum position and trade sizes. We propose a heuristic algorithm for such problems…
We develop algorithms capable of tackling robust black-box optimisation problems, where the number of model runs is limited. When a desired solution cannot be implemented exactly the aim is to find a robust one, where the worst case in an…
This paper proposes a problem-independent GRASP metaheuristic using the random-key optimizer (RKO) paradigm. GRASP (greedy randomized adaptive search procedure) is a metaheuristic for combinatorial optimization that repeatedly applies a…
A financial portfolio contains assets that offer a return with a certain level of risk. To maximise returns or minimise risk, the portfolio must be optimised - the ideal combination of optimal quantities of assets must be found. The number…
Fixed parameter tractable algorithms for bounded treewidth are known to exist for a wide class of graph optimization problems. While most research in this area has been focused on exact algorithms, it is hard to find decompositions of…