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The characterization of strong valid inequalities for integer and mixed-integer programs is more of an artistic task than a systematic methodology, requiring inspiration that can sometimes be elusive. Frequently, this task is facilitated by…
The Traveling Thief Problem (TTP) is a multi-component optimization problem that captures the interplay between routing and packing decisions by combining the classical Traveling Salesperson Problem (TSP) and the Knapsack Problem (KP). The…
The search heuristics Tabu search and Simulated annealing are commonly used meta-heuristics. The two heuristics have different ways of ensuring diversification. The heuristics can be implemented for solving the stowage planning problem. The…
The optimal transmission switching problem (OTSP) is an established problem of changing a power grid's topology to obtain an improved operation by controlling the switching status of transmission lines. This problem was proven to be…
This paper presents a novel and efficient heuristic framework for approximating the solutions to the multiple traveling salesmen problem (m-TSP) and other variants on the TSP. The approach adopted in this paper is an extension of the…
Markov decision problems (MDPs) provide the foundations for a number of problems of interest to AI researchers studying automated planning and reinforcement learning. In this paper, we summarize results regarding the complexity of solving…
The single-track railway train timetabling problem (TTP) is an important and complex problem. This article proposes an integrated Monte Carlo Tree Search (MCTS) computing framework that combines heuristic methods, unsupervised learning…
This paper introduces OptimizedDP, a high-performance software library for several common grid-based dynamic programming (DP) algorithms used in control theory and robotics. Specifically, OptimizedDP provides functions to numerically solve…
The key to reconciling the polynomial-time intractability of many machine learning tasks in the worst case with the surprising solvability of these tasks by heuristic algorithms in practice seems to be exploiting restrictions on real-world…
Solving math word problems is the task that analyses the relation of quantities and requires an accurate understanding of contextual natural language information. Recent studies show that current models rely on shallow heuristics to predict…
Understanding the behaviour of heuristic search methods is a challenge. This even holds for simple local search methods such as 2-OPT for the Traveling Salesperson problem. In this paper, we present a general framework that is able to…
Fitting geometric models onto outlier contaminated data is provably intractable. Many computer vision systems rely on random sampling heuristics to solve robust fitting, which do not provide optimality guarantees and error bounds. It is…
Synthetic Benchmark Problems (SBPs) are commonly used to evaluate the performance of metaheuristic algorithms. However, these SBPs often contain various unrealistic properties, potentially leading to underestimation or overestimation of…
Memetic algorithms are techniques that orchestrate the interplay between population-based and trajectory-based algorithmic components. In particular, some memetic models can be regarded under this broad interpretation as a group of…
In this paper we introduce a new problem in the field of production planning which we call the Production Leveling Problem. The task is to assign orders to production periods such that the load in each period and on each production resource…
Many real-world optimization problems consist of multiple tightly coupled subproblems whose solutions must be coordinated to achieve high overall performance. However, existing large language model driven automated heuristic design…
In the past three decades, a large number of metaheuristics have been proposed and shown high performance in solving complex optimization problems. While most variation operators in existing metaheuristics are empirically designed, this…
Dynamic Programming (DP) and Constraint Programming (CP) are well-established paradigms for solving combinatorial optimization problems. Usually, these two approaches are used separately. This paper aims to show that the two can be combined…
Optimization problems is one of the most challenging applications of quantum computers, as well as one of the most relevants. As a consequence, it has attracted huge efforts to obtain a speedup over classical algorithms using quantum…
Metaheuristics are known to be strong in solving large-scale instances of computationally hard problems. However, their efficiency still needs exploration in the context of instance structure, scale and numerical properties for many of…