arXiv subjects

Andrea Raith

Publications and source records attributed to Andrea Raith.

6 recordsLinked to original sources

arXiv2025

Resource Constrained Pathfinding with A* and Negative Weights

Constrained pathfinding is a well-studied, yet challenging network optimisation problem that can be seen in a broad range of real-world applications. Pathfinding with multiple resource limits, which is known as the Resource Constrained Shortest Path Problem (RCSP), aims to plan a cost-optimum path subject to limited usage of resources. Given the recent advances in constrained and multi-criteria search with A*, this paper introduces a new resource constrained search framework on the basis of A* to tackle RCSP in large networks, even in the presence of negative cost and negative resources. We empirically evaluate our new algorithm on a set of large instances and show up to two orders of magnitude faster performance compared to state-of-the-art RCSP algorithms in the literature.

cs.AI↗

arXiv2025

Parallelizing Multi-objective A* Search

The Multi-objective Shortest Path (MOSP) problem is a classic network optimization problem that aims to find all Pareto-optimal paths between two points in a graph with multiple edge costs. Recent studies on multi-objective search with A* (MOA*) have demonstrated superior performance in solving difficult MOSP instances. This paper presents a novel search framework that allows efficient parallelization of MOA* with different objective orders. The framework incorporates a unique upper bounding strategy that helps the search reduce the problem's dimensionality to one in certain cases. Experimental results demonstrate that the proposed framework can enhance the performance of recent A*-based solutions, with the speed-up proportional to the problem dimension.

cs.AI↗

arXiv2024

Resource Constrained Pathfinding with Enhanced Bidirectional A* Search

The classic Resource Constrained Shortest Path (RCSP) problem aims to find a cost optimal path between a pair of nodes in a network such that the resources used in the path are within a given limit. Having been studied for over a decade, RCSP has seen recent solutions that utilize heuristic-guided search to solve the constrained problem faster. Building upon the bidirectional A* search paradigm, this research introduces a novel constrained search framework that uses efficient pruning strategies to allow for accelerated and effective RCSP search in large-scale networks. Results show that, compared to the state of the art, our enhanced framework can significantly reduce the constrained search time, achieving speed-ups of over to two orders of magnitude.

cs.AI↗

arXiv2024

Benders Decomposition for Bi-objective Linear Programs

In this paper, we develop a new decomposition technique for solving bi-objective linear programming problems. The proposed methodology combines the bi-objective simplex algorithm with Benders decomposition and can be used to obtain a complete set of extreme efficient solutions, and the corresponding set of extreme non-dominated points, for a bi-objective linear program. Using a Benders-like reformulation, the decomposition approach decouples the problem into a bi-objective master problem and a bi-objective subproblem, each of which is solved using the bi-objective parametric simplex algorithm. The master problem provides candidate extreme efficient solutions that the subproblem assesses for feasibility and optimality. As in standard Benders decomposition, optimality and feasibility cuts are generated by the subproblem and guide the master problem solve. This paper discusses bi-objective Benders decomposition from a theoretical perspective, proves the correctness of the proposed reformulation and addresses the need for so-called weighted optimality cuts. Furthermore, we present an algorithm to solve the reformulation and discuss its performance for three types of bi-objective optimisation problems.

math.OC↗

arXiv2024

Pareto local search for a multi-objective demand response problem in residential areas with heat pumps and electric vehicles

In future energy systems characterized by significant shares of fluctuating renewable energy sources, there is a need for a fundamental change in electricity consumption. The energy system requires the ability to adapt to the intermittent electricity generation of renewable energy sources. This can be achieved by integrating flexible electrical loads, such as electric heating devices and electric vehicles, in combination with efficient control methods. In this paper, we introduce the Pareto local search method PALSS with heuristic search operations to solve the multi-objective optimization problem of a residential area with different types of flexible loads. PALSS shifts the flexible electricity load with the objective of minimizing the electricity cost and peak load while maintaining the inhabitants' comfort in favorable ranges. Further, we include reinforcement learning into the heuristic search operations in the approach RELAPALSS and use the dichotomous method for obtaining all Pareto-optimal solutions of the multi-objective optimization problem with conflicting goals. The methods are evaluated in simulations with different configurations of the residential area. The results show that PALSS and RELAPALSS strongly outperform the two multi-objective evolutionary algorithms NSGA-II and SPEA-II from the literature and the conventional control approach. The inclusion of reinforcement learning in RELAPALSS leads to additional improvements. Our study reveals the need for multi-objective optimization methods to utilize renewable energy sources in residential areas.

eess.SY↗

arXiv2017

Multi-objective minmax robust combinatorial optimization with cardinality-constrained uncertainty

In this paper we develop two approaches to find minmax robust efficient solutions for multi-objective combinatorial optimization problems with cardinality-constrained uncertainty. First, we extend an algorithm of Bertsimas and Sim (2003) for the single-objective problem to multi-objective optimization. We propose also an enhancement to accelerate the algorithm, even for the single-objective case, and we develop a faster version for special multi-objective instances. Second, we introduce a deterministic multi-objective problem with sum and bottleneck functions, which provides a superset of the robust efficient solutions. Based on this, we develop a label setting algorithm to solve the multi-objective uncertain shortest path problem. We compare both approaches on instances of the multi-objective uncertain shortest path problem originating from hazardous material transportation.

math.OC↗