32,500 research outputs found
Large Language Models for Supply Chain Optimization
Supply chain operations traditionally involve a variety of complex decision
making problems. Over the last few decades, supply chains greatly benefited
from advances in computation, which allowed the transition from manual
processing to automation and cost-effective optimization. Nonetheless, business
operators still need to spend substantial efforts in \emph{explaining} and
interpreting the optimization outcomes to stakeholders. Motivated by the recent
advances in Large Language Models (LLMs), we study how this disruptive
technology can help bridge the gap between supply chain automation and human
comprehension and trust thereof. We design \name{} -- a framework that accepts
as input queries in plain text, and outputs insights about the underlying
optimization outcomes. Our framework does not forgo the state-of-the-art
combinatorial optimization technology, but rather leverages it to
quantitatively answer what-if scenarios (e.g., how would the cost change if we
used supplier B instead of supplier A for a given demand?). Importantly, our
design does not require sending proprietary data over to LLMs, which can be a
privacy concern in some circumstances. We demonstrate the effectiveness of our
framework on a real server placement scenario within Microsoft's cloud supply
chain. Along the way, we develop a general evaluation benchmark, which can be
used to evaluate the accuracy of the LLM output in other scenarios
Denoising Autoencoders for fast Combinatorial Black Box Optimization
Estimation of Distribution Algorithms (EDAs) require flexible probability
models that can be efficiently learned and sampled. Autoencoders (AE) are
generative stochastic networks with these desired properties. We integrate a
special type of AE, the Denoising Autoencoder (DAE), into an EDA and evaluate
the performance of DAE-EDA on several combinatorial optimization problems with
a single objective. We asses the number of fitness evaluations as well as the
required CPU times. We compare the results to the performance to the Bayesian
Optimization Algorithm (BOA) and RBM-EDA, another EDA which is based on a
generative neural network which has proven competitive with BOA. For the
considered problem instances, DAE-EDA is considerably faster than BOA and
RBM-EDA, sometimes by orders of magnitude. The number of fitness evaluations is
higher than for BOA, but competitive with RBM-EDA. These results show that DAEs
can be useful tools for problems with low but non-negligible fitness evaluation
costs.Comment: corrected typos and small inconsistencie
Combinatorial Network Optimization with Unknown Variables: Multi-Armed Bandits with Linear Rewards
In the classic multi-armed bandits problem, the goal is to have a policy for
dynamically operating arms that each yield stochastic rewards with unknown
means. The key metric of interest is regret, defined as the gap between the
expected total reward accumulated by an omniscient player that knows the reward
means for each arm, and the expected total reward accumulated by the given
policy. The policies presented in prior work have storage, computation and
regret all growing linearly with the number of arms, which is not scalable when
the number of arms is large. We consider in this work a broad class of
multi-armed bandits with dependent arms that yield rewards as a linear
combination of a set of unknown parameters. For this general framework, we
present efficient policies that are shown to achieve regret that grows
logarithmically with time, and polynomially in the number of unknown parameters
(even though the number of dependent arms may grow exponentially). Furthermore,
these policies only require storage that grows linearly in the number of
unknown parameters. We show that this generalization is broadly applicable and
useful for many interesting tasks in networks that can be formulated as
tractable combinatorial optimization problems with linear objective functions,
such as maximum weight matching, shortest path, and minimum spanning tree
computations
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Developments in linear and integer programming
In this review we describe recent developments in linear and integer (linear) programming. For over 50 years Operational Research practitioners have made use of linear optimisation models to aid decision making and over this period the size of problems that can be solved has increased dramatically, the time required to solve problems has decreased substantially and the flexibility of modelling and solving systems has increased steadily. Large models are no longer confined to large computers, and the flexibility of optimisation systems embedded in other decision support tools has made on-line decision making using linear programming a reality (and using integer programming a possibility). The review focuses on recent developments in algorithms, software and applications and investigates some connections between linear optimisation and other technologies
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