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The Facility Location Problem (FLP) is a well-studied optimization problem with applications in many real-world scenarios. Past literature has explored the solutions from different perspectives to tackle FLPs. These include investigating…

In order for an e-commerce platform to maximize its revenue, it must recommend customers items they are most likely to purchase. However, the company often has business constraints on these items, such as the number of each item in stock.…

This paper addresses the single-item single-stocking location non-stationary stochastic lot-sizing problem under a reorder point -- order quantity control strategy. The reorder points and order quantities are chosen at the beginning of the…

Preference Optimization (PO), is gaining popularity as an alternative choice of Proximal Policy Optimization (PPO) for aligning Large Language Models (LLMs). Recent research on aligning LLMs iteratively with synthetic or partially synthetic…

Direct Preference Optimization (DPO) have emerged as a popular method for aligning Large Language Models (LLMs) with human preferences. While DPO effectively preserves the relative ordering between chosen and rejected responses through…

As development of large language models (LLM) progresses, aligning them with human preferences has become increasingly important. We propose stepwise DPO (sDPO), an extension of the recently popularized direct preference optimization (DPO)…

Aligning large language models with human preferences is essential for improving interaction quality and safety by ensuring outputs better reflect human values. A promising strategy involves Reinforcement Learning from Human Feedback…

Evaluating preference optimization (PO) algorithms on LLM alignment is a challenging task that presents prohibitive costs, noise, and several variables like model size and hyper-parameters. In this work, we show that it is possible to gain…

Proximal policy optimization (PPO) has yielded state-of-the-art results in policy search, a subfield of reinforcement learning, with one of its key points being the use of a surrogate objective function to restrict the step size at each…

We investigate the Plackett-Luce (PL) model based listwise learning-to-rank (LTR) on data with partitioned preference, where a set of items are sliced into ordered and disjoint partitions, but the ranking of items within a partition is…

We consider single-machine scheduling problems that are natural generalizations or variations of the min-sum set cover problem and the min-sum vertex cover problem. For each of these problems, we give new approximation algorithms. Some of…

Many applications of large language models (LLMs), ranging from chatbots to creative writing, require nuanced subjective judgments that can differ significantly across different groups. Existing alignment algorithms can be expensive to…

In this paper, we introduce and study the Facility Location Problem with Aleatory Agents (FLPAA), where the facility accommodates n agents larger than the number of agents reporting their preferences, namely n_r. The spare capacity is used…

The facility location problem is a well-known challenge in logistics that is proven to be NP-hard. In this paper we specifically simulate the geographical placement of facilities to provide adequate service to customers. Determining…

We study a competitive facility location problem (CFLP), where two firms sequentially open new facilities within their budgets, in order to maximize their market shares of demand that follows a probabilistic choice model. This process is a…

Preferential Bayesian optimisation (PBO) deals with optimisation problems where the objective function can only be accessed via preference judgments, such as "this is better than that" between two candidate solutions (like in A/B tests or…

In this study we introduce a new method to solve the Dynamics Facility Layout Problems (DFLPs). To represent each layout, we use the slicing tree method integrated with our proposed heuristic to obtain promising initial solutions. Then, we…

Price differentiation is a common strategy in many markets. In this paper, we study a static multiproduct price optimization problem with demand given by a discrete mixed multinomial logit model. By considering a mixed logit model that…

The ability of LLMs to represent diverse perspectives is critical as they increasingly impact society. However, recent studies reveal that alignment algorithms such as RLHF and DPO significantly reduce the diversity of LLM outputs. Not only…

Preference optimization is widely used to align Large Language Models (LLMs) with preference feedback. However, most existing methods train on a single positive-negative pair per prompt, discarding additional supervision available in…