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In container terminal yards, the Container Rehandling Problem (CRP) involves rearranging containers between stacks under specific operational rules, and it is a pivotal optimization challenge in intelligent container scheduling systems.…
Submodular functions and their optimization have found applications in diverse settings ranging from machine learning and data mining to game theory and economics. In this work, we consider the constrained maximization of a submodular…
We consider chance-constrained binary knapsack problems, where the weights of items are independent random variables with the means and standard deviations known. The chance constraint can be reformulated as a second-order cone constraint…
In robotics, methods and softwares usually require optimizations of hyperparameters in order to be efficient for specific tasks, for instance industrial bin-picking from homogeneous heaps of different objects. We present a developmental…
The paper focuses on a new class of combinatorial problems which consists in restructuring of solutions (as sets/structures) in combinatorial optimization. Two main features of the restructuring process are examined: (i) a cost of the…
Problems involving the efficient arrangement of simple objects, as captured by bin packing and makespan scheduling, are fundamental tasks in combinatorial optimization. These are well understood in the traditional online and offline cases,…
Bin Packing with Minimum Color Fragmentation (BPMCF) is an extension of the Bin Packing Problem in which each item has a size and a color and the goal is to minimize the sum of the number of bins containing items of each color. In this…
In two-dimensional geometric knapsack problem, we are given a set of n axis-aligned rectangular items and an axis-aligned square-shaped knapsack. Each item has integral width, integral height and an associated integral profit. The goal is…
We study optimal policy learning under combined budget and minimum coverage constraints. We show that the problem admits a knapsack-type structure and that the optimal policy can be characterized by an affine threshold rule involving both…
In the Colored Bin Packing problem a sequence of items of sizes up to $1$ arrives to be packed into bins of unit capacity. Each item has one of $c\geq 2$ colors and an additional constraint is that we cannot pack two items of the same color…
We consider robust combinatorial optimization problems where the decision maker can react to a scenario by choosing from a finite set of $k$ solutions. This approach is appropriate for decision problems under uncertainty where the…
We present filling as a new type of spatial subdivision problem that is related to covering and packing. Filling addresses the optimal placement of overlapping objects lying entirely inside an arbitrary shape so as to cover the most…
In many submodular optimization applications, datasets are naturally partitioned into disjoint subsets. These scenarios give rise to submodular optimization problems with partition-based constraints, where the desired solution set should be…
We consider the Ordered Open End Bin Packing problem. Items of sizes in $(0,1]$ are presented one by one, to be assigned to bins in this order. An item can be assigned to any bin for which the current total size strictly below $1$. This…
A popular approach in combinatorial optimization is to model problems as integer linear programs. Ideally, the relaxed linear program would have only integer solutions, which happens for instance when the constraint matrix is totally…
The following online bin packing problem is considered: Items with integer sizes are given and variable sized bins arrive online. A bin must be used if there is still an item remaining which fits in it when the bin arrives. The goal is to…
We present a centralized algorithmic framework for solving multi-robot path planning problems in general, two-dimensional, continuous environments while minimizing globally the task completion time. The framework obtains high levels of…
We consider set covering problems where the underlying set system satisfies a particular replacement property w.r.t. a given partial order on the elements: Whenever a set is in the set system then a set stemming from it via the replacement…
We give new approximation algorithms for the submodular joint replenishment problem and the inventory routing problem, using an iterative rounding approach. In both problems, we are given a set of $N$ items and a discrete time horizon of…
We consider a general class of binary packing problems with a convex quadratic knapsack constraint. We prove that these problems are APX-hard to approximate and present constant-factor approximation algorithms based upon three different…