ParetoChat: An LLM-Based Interface for Interactive Multi-Objective Optimization

Gokhan Ceyhan

cs.CLOct 16, 2026

ParetoChat: An LLM-Based Interface for Interactive Multi-Objective Optimization

Authors: Gokhan Ceyhan

Organizations: Just Eat Takeaway.com

Abstract

Multi-objective optimization models are often deployed in settings where decision makers (DMs) must balance some conflicting criteria. In practice, however, stakeholders must translate their qualitative preferences between different criteria into numerical weights, priorities, or reference points required by optimization methods, which can be difficult to specify and interpret. This paper proposes ParetoChat, an LLM (large language model)-based expert-agent interface for interactive multi-objective optimization. The agent translates natural-language user input into structured scalarization parameters, invokes an optimization system, presents candidate solutions, and iteratively elicits feedback. We describe a multi-agent architecture that separates input processing, multi-criteria decision-making (MCDM) expertise, solution presentation, and feedback processing. We then present a simulation study using an LLM-based DM agent and benchmark ParetoChat against interactive methods implemented in DESDEO, including reference-point and NIMBUS methods. The computational experiments on multi-objective binary knapsack and set-partitioning instances show that ParetoChat can guide the search efficiently toward solutions that match the DM's preferences. An application to historical courier-order assignment instances illustrates how users can explore objective extremes and intermediate trade-offs through natural-language requests. The results indicate that LLM agents may provide a practical interaction layer between business stakeholders and optimization tools.

Figures & tables

Panel of Figure 1 — Figure 1: ParetoChat acts as a natural-language interaction layer between business users and optimization systems.

Panel of Figure 2 — Figure 2: ParetoChat’s multi-agent architecture

User preference	Referenced solutions	Scalarization type	Scalarization parameters
Find a balanced solution across both objectives.	None	Weighted-sum	$w=(0.5,0.5)$
Improve delivery time, but do not let cost increase too much.	$z=(1000,60)$	Augmented epsilon constraint	$q=2$ , $\epsilon=1100$ , $\rho=10^{-4}$
Cost is most important, then delivery time.	None	Lexicographic	$priority_{cost}$ =1, $priority_{delivery\_time}$ =2
Show me something between these two saved options.	$z^{1}=(1000,60)$ , $z^{2}=(1200,40)$	Weighted-sum in a bounded region	$w=(0.5,0.5)$ , $1000\leq z_{1}\leq 1200$ , $40\leq z_{2}\leq 60$
Try to reach 30 minutes delivery time while keeping other metrics reasonable.	None	Achievement scalarizing function	$z^{r}=(1200,30)$ , $w=(0.5,0.5)$ , $\rho=10^{-4}$

Table 1: Examples of user preferences and likely structured scalarization outputs from the MCDM expert agent for a bi-objective minimization problem.

Cost (Euros)	Delivery time (mins)
101000.0	30.0
100000.0	30.0
25000.0	34.0
25000.0	34.8
15000.0	35.0
14000.0	35.0

Table 2: Feasible points for the example problem

Panel of Figure 4 — Figure 4: Feasible points for the example problem. The points presented by ParetoChat during the user session are marked with hollow red squares together with their display sequence.

Round 1	Round 2
User Find a solution that balances both objectives equally.	User Nice save it and find a solution that improves the delivery time somewhere around 30 minutes.
ParetoChat Based on your request to find a solution that balances both objectives equally, I found a candidate solution for you. To achieve this balance, I used the weighted-sum method. This assigns equal importance, or a weight of 50%, to both the cost and delivery-time objectives. The resulting solution has the following objective values. Cost: 9,000.0 Delivery Time: 36.0 What do you think of this solution? Would you like to save it?	ParetoChat Of course! Here is a presentation of the solution found based on your latest request. Based on your request to find a solution with a delivery time around 30 minutes, I have found a new solution for you. To achieve this, I used a reference point -based method. This means I searched for a solution where the delivery time is as close as possible to your target of 30 minutes. Here is the solution I found: Cost: 25,000.0 Delivery Time: 34.0

Table 3: A real conversation with ParetoChat on the example problem.

Panel of Figure 5 — Figure 5: The architecture of our evaluation framework based on an AI-based DM

Panel of Figure 6 — Figure 6: Indifference curves of the nonlinear value function in ( 15 ) for two normalized objectives with $z^{I}=(1,1)$ . The solid, dashed, and dotted curves represent $V=-0.0625$ , $V=-0.2025$ , and $V=-0.4225$ , respectively. Preference increases toward the ideal point marked by the red star.

Problem	Tool	Pareto size	Tool calls	Eval. sols	Optimal	Rank norm.	Rel. value gap	AIDM time (s)	Tool time (s)
2OBKP	NIMBUS	162.4 (35.1)	6.6 (1.9)	14.0 (5.1)	22	0.9765 (0.0936)	0.0096 (0.0439)	77.57 (23.99)	24.73 (7.24)
	RPM		7.1 (2.0)	13.3 (3.9)	7	0.9207 (0.0878)	0.0282 (0.0350)	74.19 (19.08)	23.42 (6.32)
	ParetoChat		6.2 (1.0)	5.3 (1.2)	15	0.9613 (0.0769)	0.0084 (0.0157)	59.54 (17.39)	216.88 (53.97)
3OBKP	NIMBUS	4927.6 (2010.3)	7.3 (1.5)	17.8 (7.2)	0	0.8812 (0.1080)	0.0636 (0.0522)	95.98 (18.65)	29.13 (6.31)
	RPM		6.5 (2.0)	18.1 (4.0)	7	0.9844 (0.0248)	0.0160 (0.0186)	82.02 (20.29)	29.01 (8.22)
	ParetoChat		7.5 (1.5)	6.1 (1.5)	1	0.9074 (0.1065)	0.0415 (0.0374)	73.68 (14.70)	278.50 (59.77)

Table 4: Simulation results with a linear value function (Eq. 14 )

Problem	Tool	Pareto size	Tool calls	Eval. sols	Optimal	Rank norm.	Rel. value gap	AIDM time (s)	Tool time (s)
2OBKP	NIMBUS	162.4 (35.1)	8.8 (1.5)	18.8 (5.6)	15	0.9627 (0.0975)	0.0018 (0.0042)	96.90 (20.71)	34.50 (6.38)
	RPM		7.5 (1.7)	15.0 (4.3)	16	0.9759 (0.0506)	0.0008 (0.0013)	73.86 (17.04)	25.38 (5.40)
	ParetoChat		7.6 (2.0)	6.6 (2.1)	9	0.8925 (0.1523)	0.0071 (0.0151)	63.75 (26.57)	296.29 (105.68)
3OBKP	NIMBUS	4927.6 (2010.3)	8.6 (1.9)	20.9 (6.4)	0	0.9226 (0.0992)	0.0153 (0.0167)	104.01 (25.17)	34.88 (8.15)
	RPM		8.1 (1.9)	25.0 (7.1)	4	0.9749 (0.0461)	0.0071 (0.0114)	104.26 (33.96)	36.13 (7.88)
	ParetoChat		7.7 (1.3)	6.6 (1.2)	1	0.8350 (0.1558)	0.0329 (0.0315)	62.31 (11.00)	300.98 (50.72)

Table 5: Simulation results with a nonlinear value function (Eq. 15 )

Problem	Solver calls	Eval. sols	Optimal	Rank norm.	Rel. value gap	AIDM time (s)	Tool time (s)
3OBKP	13.4 (2.4)	10.9 (2.3)	9	0.966 (0.059)	0.017 (0.020)	118.0 (27.9)	663.4 (148.2)
4OBKP	14.1 (1.9)	10.9 (2.3)	7	0.978 (0.034)	0.036 (0.037)	112.3 (24.6)	672.1 (121.0)

Table 6: Simulation results for ParetoChat with the modified AIDM prompt and a linear value function (Eq. 14 )

Figure 7: Example courier-order assignments. In Assignment 1, an idle courier is assigned two orders: the first order will be delivered before the second is picked up. In Assignment 2, orders are pooled, meaning that the second order will be picked up before the first is delivered. In Assignment 3, the courier is already delivering an order and is assigned a new order to pick up after completing the current delivery.

Trial Number	User input	Generated scalarization	PD	DD	PU
1	Find a balancing solution	Weighted sum: $w_{\mathrm{PU}}=1.0$ , $w_{\mathrm{DD}}=1.0$ , $w_{\mathrm{PD}}=1.0$	0	166	340
2	Now minimize delivery delay	Lexicographic: $p_{\mathrm{DD}}=1$ , $p_{\mathrm{PU}}=2$ , $p_{\mathrm{PD}}=2$	0	144	381
3	Now minimize pickup duration	Weighted sum: $w_{\mathrm{PU}}=1.0$ , $w_{\mathrm{DD}}=0.1$ , $w_{\mathrm{PD}}=0.1$	9	368	286
4	Find a solution between 2 and 3	Weighted sum: $w_{\mathrm{PU}}=0.47$ , $w_{\mathrm{DD}}=0.44$ , $w_{\mathrm{PD}}=0.09$	0	177	329
5	Find a solution between 3 and 4	Weighted sum: $w_{\mathrm{PU}}=0.668$ , $w_{\mathrm{DD}}=0.245$ , $w_{\mathrm{PD}}=0.086$	9	204	314
6	Find a solution between 3 and 5	Weighted sum: $w_{\mathrm{PU}}=0.834$ , $w_{\mathrm{DD}}=0.1725$ , $w_{\mathrm{PD}}=0.093$	9	230	307

Table 7: ParetoChat interaction history for solving the courier-order assignment problem - Instance 1

Panel of Figure 9 — Figure 9: Visualizations of the objective values and trade-offs among the trial solutions generated during the ParetoChat interaction for Instance 1. Objective values in the scatter plot and parallel-coordinate plot are normalized using min–max scaling.

Trial Number	User input	Generated scalarization	PD	DD	PU
1	Find a solution that minimizes pickup duration	Lexicographic: $p_{\mathrm{PU}}=1$ , $p_{\mathrm{DD}}=2$ , $p_{\mathrm{PD}}=2$	105	1629	336
2	Find a solution that minimizes delivery delay	Weighted sum: $w_{\mathrm{DD}}=0.8$ , $w_{\mathrm{PU}}=0.1$ , $w_{\mathrm{PD}}=0.1$	4	288	633
3	Minimize delivery delay further. What is the minimum you can achieve?	Weighted sum: $w_{\mathrm{DD}}=0.8$ , $w_{\mathrm{PU}}=0.1$ , $w_{\mathrm{PD}}=0.1$	4	288	633
4	Minimize delivery delay further. What is the minimum you can achieve?	Weighted sum: $w_{\mathrm{DD}}=0.9$ , $w_{\mathrm{PU}}=0.05$ , $w_{\mathrm{PD}}=0.05$	4	285	668
5	Now minimize delivery delay using lexicographic method.	Lexicographic: $p_{\mathrm{DD}}=1$ , $p_{\mathrm{PU}}=2$ , $p_{\mathrm{PD}}=3$	10	285	668
6	Now minimize pickup delay	Lexicographic: $p_{\mathrm{PD}}=1$ , $p_{\mathrm{PU}}=2$ , $p_{\mathrm{DD}}=2$	0	2034	853

Table 8: ParetoChat interaction history for solving the courier-order assignment problem - Instance 2

Panel of Figure 10 — Figure 10: Visualizations of the objective values and trade-offs among the trial solutions generated during the ParetoChat interaction for Instance 2. Objective values in the scatter plot and parallel-coordinate plot are normalized using min–max scaling. Solutions from Trials 3 and 5 are omitted because Trial 3 duplicates Trial 2 and Trial 5 is dominated by Trial 4.

Multi-Objective Optimization

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Let's Have a Conversation: Designing and Evaluating LLM Agents for Interactive Optimization

Joshua Drossman, Alexandre Jacquillat, Sébastien Martin

Operations Research Center and Sloan School of Management, Massachusetts Institute of Technology, Cambridge, MA. · Kellogg School of Management, Northwestern University, Evanston, IL

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Optimization is as much about modeling the right problem as solving it. Identifying the right objectives, constraints, and trade-offs demands extensive interaction between researchers and stakeholders. Large language models can empower decision-makers with optimization capabilities through interactive optimization agents that can propose, interpret and refine solutions. However, it is fundamentally harder to evaluate a conversation-based interaction than traditional one-shot approaches. This paper proposes a scalable and replicable methodology for evaluating optimization agents through conversations. We build LLM-powered decision agents that role-play diverse stakeholders, each governed by an internal utility function but communicating like a real decision-maker. We generate thousands of conversations in a school scheduling case study. Results show that one-shot evaluation is severely limiting: the same optimization agent converges to much higher-quality solutions through conversations. Then, this paper uses this methodology to demonstrate that tailored optimization agents, endowed with domain-specific prompts and structured tools, can lead to significant improvements in solution quality in fewer interactions, as compared to general-purpose chatbots. These findings provide evidence of the benefits of emerging solutions at the AI-optimization interface to expand the reach of optimization technologies in practice. They also uncover the impact of operations research expertise to facilitate interactive deployments through the design of effective and reliable optimization agents.

Abstract

Multi-Objective Optimization

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