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In operations research, the Knapsack Problem (KP) is one of the classical optimization problems that has been widely studied. The KP has several variants and, in this paper, we address the binary KP, where for a given knapsack (with limited…

This work considers the problem of finding analytical expressions for the expected values of dis- tributed computing performance metrics when the underlying communication network has a complex structure. Through active probing tests a real…

Supervised classification techniques use training samples to find classification rules with small expected 0-1 loss. Conventional methods achieve efficient learning and out-of-sample generalization by minimizing surrogate losses over…

This research proposes a novel indicator-based hybrid evolutionary approach that combines approximate and exact algorithms. We apply it to a new bi-criteria formulation of the travelling thief problem, which is known to the Evolutionary…

Knapsack and Partition are two important additive problems whose fine-grained complexities in the $(1-\varepsilon)$-approximation setting are not yet settled. In this work, we make progress on both problems by giving improved algorithms. -…

We consider an expected-value ranking and selection (R&S) problem where all k solutions' simulation outputs depend on a common parameter whose uncertainty can be modeled by a distribution. We define the most probable best (MPB) to be the…

We establish optimal convergence rates for a decomposition-based scalable approach to kernel ridge regression. The method is simple to describe: it randomly partitions a dataset of size N into m subsets of equal size, computes an…

In the bi-objective branch-and-bound literature, a key ingredient is objective branching, i.e. to create smaller and disjoint sub-problems in the objective space, obtained from the partial dominance of the lower bound set by the upper bound…

The submodular knapsack problem (SKP), which seeks to maximize a submodular set function by selecting a subset of elements within a given budget, is an important discrete optimization problem. The majority of existing approaches to solving…

Chance-constrained optimization has emerged as a promising framework for managing uncertainties in power systems. This work advances its application to the DC Optimal Power Flow (DC-OPF) model, developing a novel approach to uncertainty…

The chance constrained travelling thief problem (chance constrained TTP) has been introduced as a stochastic variation of the classical travelling thief problem (TTP) in an attempt to embody the effect of uncertainty in the problem…

Prediction models are often employed in estimating parameters of optimization models. Despite the fact that in an end-to-end view, the real goal is to achieve good optimization performance, the prediction performance is measured on its own.…

Large-scale optimization problems that involve thousands of decision variables have extensively arisen from various industrial areas. As a powerful optimization tool for many real-world applications, evolutionary algorithms (EAs) fail to…

This paper proposes a hierarchical approximate-factor approach to analyzing high-dimensional, large-scale heterogeneous time series data using distributed computing. The new method employs a multiple-fold dimension reduction procedure using…

We investigate a class of chance-constrained combinatorial optimization problems. Given a pre-specified risk level $\epsilon \in [0,1]$, the chance-constrained program aims to find the minimum cost selection of a vector of binary decisions…

Spectral clustering is one of the most popular clustering methods. However, how to balance the efficiency and effectiveness of the large-scale spectral clustering with limited computing resources has not been properly solved for a long…

Quality diversity (QD) algorithms have been shown to be very successful when dealing with problems in areas such as robotics, games and combinatorial optimization. They aim to maximize the quality of solutions for different regions of the…

The Travelling Thief Problem (TTP) is a challenging combinatorial optimization problem that attracts many scholars. The TTP interconnects two well-known NP-hard problems: the Travelling Salesman Problem (TSP) and the 0-1 Knapsack Problem…

We examine the negative occupancy distribution and the coupon-collector distribution, both of which arise as distributions relating to hitting times in the extended occupancy problem. These distributions constitute a full solution to a…

Given n elements with nonnegative integer weights w1,..., wn and an integer capacity C, we consider the counting version of the classic knapsack problem: find the number of distinct subsets whose weights add up to at most the given…