# From Portfolio Solvers to Agentic Solvers

Roberto Amadini, Simone Gazza

► To cite this version:

Roberto Amadini, Simone Gazza. From Portfolio Solvers to Agentic Solvers. LLM-Solve, Tias Guns; Serdar Kadioglu; Stefan Szeider; Dimos Tsouros, Aug 2025, Glasgow, United Kingdom, United Kingdom. pp.569 - 585, 10.5281/zenodo.17640236. hal-05446738

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# From Portfolio Solvers to Agentic Solvers

Roberto Amadini ✉ ID

University of Bologna, Italy
OPTIMA ARC Centre, Melbourne, Australia

Simone Gazza ✉ ID

University of Bologna, Italy
OPTIMA ARC Centre, Melbourne, Australia

## Abstract

This paper explores the shift from traditional portfolio solvers to agentic solvers, enabled by Large Language Models (LLMs) to support autonomous and collaborative behavior across solving systems. Beyond per-instance algorithm selection, agentic solvers can dynamically adapt strategies, refine solutions, and reformulate models. LLMs act as orchestrators, enhancing flexibility, scalability, and adaptivity.

This work was submitted on 21 June 2025 and accepted on 25 June 2025 for the LLM-Solve Workshop [15] at CP/SAT/SoCS 2025 [1].

**2012 ACM Subject Classification** Computing methodologies → Intelligent agents; Theory of computation → Constraint and logic programming; Computing methodologies → Information extraction

**Keywords and phrases** Agentic solver, Constraint Programming, LLM

Artificial Intelligence (AI), especially Machine Learning (ML) and Large Language Models (LLMs), has made remarkable strides. Yet, many real-world problems—such as scheduling, planning, or routing—remain NP-hard, where neither ML nor LLMs can reliably produce optimal or even correct solutions. To tackle such problems, various methods have been developed, from heuristics and approximate to complete, exact approaches. These rely on constraint-solving technologies like SAT, SMT, MIP, ASP, and others. While numerous solvers exist, they often depends heavily on the specific instance being solved.

This challenge motivates the *Algorithm Selection (AS)* problem [6, 12, 11]. Introduced by Rice in 1976 [16], AS is modernly addressed using *supervised ML* on a *per instance* basis, i.e., based on instance features. This approach, called *portfolio solving*, has shown strong results across different domains [10, 18, 3, 5, 4, 7, 8]. Yet, after early success in the 2010s including two AS competitions [14], interest has waned. High development effort, limited adaptivity, and the rise of end-to-end ML have shifted focus to AutoML and Algorithm Configuration.

In this position paper, we propose revitalizing portfolio solving within the emerging Agentic AI paradigm [2]. The idea is to have *agentic solvers* that exhibit autonomy, initiative, and coordination, reasoning with both static knowledge and live feedback. This approach aims to enhance generality and responsiveness while reducing the reliance on extensive training phases, offering a modular framework that goes beyond traditional portfolio methods.

The core of an agentic solver is a *central coordinator* that we currently envision based on a LLM. Similarly to AS and portfolio-based techniques, the coordinator *dynamically* selects the most appropriate solver(s), e.g., based on SAT, CP, MIP, or meta-heuristics, according to the characteristics of the problem at hand. However, unlike those approaches, the coordinator also engages in *proactive* problem's and solvers' manipulation, leading to greater flexibility, adaptability, and autonomy in the solving process.

Unlike standard AS techniques, which typically require a heavy and supervised training phase to match problem features with solver performance, the LLM can operate in an *unsupervised* manner by leveraging its pre-trained internal knowledge. When needed, the model can be fine-tuned on domain-specific data or extended through *Retrieval-Augmented*

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<figure><img src="image_3.png" /><figcaption>Figure 1 The agentic solver structure as currently envisioned.</figcaption></figure>

*Generation* (RAG [13]), which enables modular access to external knowledge at inference time. This allows the system to incorporate feedback from past solving experiences, improving performance over time through iterative refinement and context accumulation.

The central coordinator is capable of executing multiple solvers in parallel, comparing intermediate outcomes, initiating problem reformulations to better suite a different solving technology [9], and adjusting solver parameters or configurations as needed. It can also *autonomously* query external knowledge sources (such as the world-wide-web) to enhance its problem-solving capabilities, surpassing the static limitations of classical portfolio solvers.

A sketch of an agentic solver architecture is shown in Fig. 1. The user interacts via the LLM's prompt, while the coordinator's knowledge base is stored in the RAG. Other information (such as performances) can be stored in the RAG too, to improve future outcomes. Suggestions and feedbacks can be provided by the LLM itself or by the user.

Several challenges emerge with this new paradigm. Communication overhead and latency between solvers and the LLM—particularly when accessed via external APIs—may impact efficiency but can be mitigated by running local, optimized models. A second concern is the reliability of the LLM’s decisions [17], as large models are known to hallucinate, or anyway they are not designed to guarantee the output soundness. This can be addressed through both formal verification and feedback mechanisms that help refine future behavior.

Finally, the explainability of solver orchestration remains essential; ensuring that the coordinator can justify its decisions in an interpretable way is critical to fostering trust and enabling validation.

## Acknowledgments

This work is partly supported by the project FREEDA (CUP: I53D23003550006), funded by the frameworks PRIN (MUR, Italy) and Next Generation EU. The work is also partly supported by: PNRR - M4C2 - Investimento 1.3, Partenariato Esteso PE00000013 - “FAIR - Future Artificial Intelligence Research” - Spoke 8 “Pervasive AI”;

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