This paper presents a new approach to solving the optimal unit location problem in a stochastic emergency service system that takes into account state transitions and unit availabilities. The goal is to minimize the system-wide mean response time, which is formulated as a combinatorial optimization problem. We show that this problem is NP-hard and develop lower and upper bounds for the optimal solution using a special case of the classic p-median problem. To solve the problem, we develop a Bayesian optimization algorithm that we show converges to the optimal solution with a sublinear regret rate. Through numerical experiments and a study utilizing real data from the St. Paul, Minnesota emergency response system, we demonstrate that our model consistently and efficiently converges to the optimal solution. This is in contrast to the performance of the p-median, which deteriorates with increased utilizations. Our solution can potentially serve as a practical tool for emergency unit deployment decisions and is applicable in large cities.

Bayesian Optimization (BO) is a well-established approach for solving expensive black-box optimization tasks. However, the selection of its underlying probabilistic surrogate model remains an important yet challenging problem. We introduce a novel Gaussian Process (GP)-based BO approach adopting spectral mixture kernels, derived from spectral densities which are scale-location mixtures of Cauchy and Gaussian distributions. It preserves the sample efficiency of BO, whist boosting expressiveness and flexibility of the GP surrogate. We further bound the maximal information gain of spectral mixture kernels in terms of operator spectra, and demonstrate that it is possible to approximate conventional kernels and their compositions using them. Finally, We empirically validate that our BO method outperforms current baselines on a variety of synthetic and real-world examples.

Conducted an extensive literature review on Automatic Heuristic Design, analyzing cutting-edge methodologies such as EoH (Evolution of Heuristics) and ReEvo (Recursive Evolution) to identify optimization strategies.

Designed and implemented novel inventory and ordering policies by leveraging Base Stock, Capped Base Stock, and Constant Order as initial strategies, enhancing decision-making efficiency in supply chain model.

Developed data-driven heuristics through systematic experimentation, improving algorithmic performance in dynamic inventory management scenarios.

Consider the problem of multi-product dynamic pricing with contextual information, where a seller is faced with a large number products which are described by high-dimensional feature vectors, and customers with unknown heterogeneous price sensitivities.

Propose a pricing policy that uses a regularized maximum likelihood function to estimate the parameters of the choice model and subsequently sets the best prices based on the obtained estimates.

Benchmark the performance using the classic regret minimization framework where the regret is defined as the expected revenue loss against a clairvoyant policy that knows the parameters of the choice model in advance, and establish a lower bound and upper bound on the regret.