Related papers: Robust Extensible Bin Packing and Revisiting the C…
In this work, we study a single-machine scheduling problem that aims at minimizing the total cost of a schedule subject to start-time dependent costs. This framework naturally captures scenarios where costs fluctuate throughout the day,…
In this paper we consider the discounted 0-1 knapsack problem (DKP), which is an extension of the classical knapsack problem where a set of items is decomposed into groups of three items. At most one item can be chosen from each group and…
In practise, it is often desirable to provide the decision-maker with a rich set of diverse solutions of decent quality instead of just a single solution. In this paper we study evolutionary diversity optimization for the knapsack problem…
The Bin Packing Problem (BPP) has attracted enthusiastic research interest recently, owing to widespread applications in logistics and warehousing environments. It is truly essential to optimize the bin packing to enable more objects to be…
We study the geometric knapsack problem in which we are given a set of $d$-dimensional objects (each with associated profits) and the goal is to find the maximum profit subset that can be packed non-overlappingly into a given…
We consider several extensions of the fractional bin packing problem, a relaxation of the traditional bin packing problem where the objects may be split across multiple bins. In these extensions, we introduce load-balancing constraints…
We close three open problems in the separation complexity of valid inequalities for the knapsack polytope. Specifically, we establish that the separation problems for extended cover inequalities, (1,k)-configuration inequalities, and weight…
When uncertainty meets costly information gathering, a fundamental question emerges: which data points should we probe to unlock near-optimal solutions? Sparsification of stochastic packing problems addresses this trade-off. The existing…
We present new approximation schemes for bin packing based on the following two approaches: (1) partitioning the given problem into mostly identical sub-problems of constant size and then construct a solution by combining the solutions of…
Optimization problems with uncertain black-box constraints, modeled by warped Gaussian processes, have recently been considered in the Bayesian optimization setting. This work introduces a new class of constraints in which the same…
In the current work we introduce a novel estimation of distribution algorithm to tackle a hard combinatorial optimization problem, namely the single-machine scheduling problem, with uncertain delivery times. The majority of the existing…
We study the computational complexity of multi-stage robust optimization problems. Such problems are formulated with alternating min/max quantifiers and therefore naturally fall into a higher stage of the polynomial hierarchy. Despite this,…
Robust optimization has been established as a leading methodology to approach decision problems under uncertainty. To derive a robust optimization model, a central ingredient is to identify a suitable model for uncertainty, which is called…
Following the work of Anily et al., we consider a variant of bin packing, called "bin packing with general cost structures" (GCBP) and design an asymptotic fully polynomial time approximation scheme (AFPTAS) for this problem. In the classic…
The 0/1 knapsack problem is weakly NP-hard in that there exist pseudo-polynomial time algorithms based on dynamic programming that can solve it exactly. There are also the core branch and bound algorithms that can solve large randomly…
Packing problems are in general NP-hard, even for simple cases. Since now there are no highly efficient algorithms available for solving packing problems. The two-dimensional bin packing problem is about packing all given rectangular items,…
We consider the maximization problem of monotone submodular functions under an uncertain knapsack constraint. Specifically, the problem is discussed in the situation that the knapsack capacity is not given explicitly and can be accessed…
In the present paper, a robust approach to a special class of convex feasibility problems is considered. By techniques of convex and variational analysis, conditions for the existence of robust feasible solutions and related error bounds…
Knapsack problem (KP) is a representative combinatorial optimization problem that aims to maximize the total profit by selecting a subset of items under given constraints on the total weights. In this study, we analyze a generalized version…
We extend Robust Optimization to fractional programming, where both the objective and the constraints contain uncertain parameters. Earlier work did not consider uncertainty in both the objective and the constraints, or did not use Robust…