We consider cooperative traveling salesman games with non-negative asymmetric costs satisfying the triangle inequality. We construct a stable cost allocation with budget balance guarantee equal to the Held-Karp integrality gap for the asymmetric traveling salesman problem, using the parsimonious property and a previously unknown connection to linear production games. We also show that our techniques … Read more
We study the computational question whether a given polytope or spectrahedron $S_A$ (as given by the positive semidefiniteness region of a linear matrix pencil $A(x)$) is contained in another one $S_B$. First we classify the computational complexity, extending results on the polytope/poly\-tope-case by Gritzmann and Klee to the polytope/spectrahedron-case. For various restricted containment problems, NP-hardness … Read more
We completely characterize deterministic strategy-proof and group strategy-proof mechanisms on single-sinked public policy domain. The single-sinked domain can be used to model any allocation problem where a single output must be chosen in an interval with the assumption that agents’ preferences have a single most loathful point (the sink) in the interval, and the preferences … Read more
This paper presents a new hybridization of VNS and path-relinking on a particle swarm framework for the permutational fowshop scheduling problem with total flowtime criterion. The operators of the proposed particle swarm are based on path-relinking and variable neighborhood search methods. The performance of the new approach was tested on the bechmark suit of Taillard, … Read more
We present a novel multi-population biased random-key genetic algorithm (BRKGA) for the 2D and 3D bin packing problem. The approach uses a maximal-space representation to manage the free spaces in the bins. The proposed algorithm uses a decoder based on a novel placement procedure within a multi-population genetic algorithm based on random keys. The BRKGA … Read more
In this paper, we study the hop-constrained survivable network design problem with reliable edges. Given a graph with non-negative edge weights and node pairs Q, the hop-constrained survivable network design problem consists of constructing a minimum weight set of edges so that the induced subgraph contains at least K edge-disjoint paths containing at most L … Read more
Recently there has been intensive interest on approximation of the NP-hard submodular maximization problem due to their theoretical and practical significance. In this work, we extend this line of research by focusing on the simultaneous approximation of multiple submodular function maximization. We address existence and nonexistence results for both deterministic and randomized approximation when the … Read more
Many combinatorial optimization problems have natural formulations as submodular minimization problems over well-studied combinatorial structures. A standard approach to these problems is to linearize the objective function by introducing new variables and constraints, yielding an extended formulation. We propose two new approaches for constrained submodular minimization problems. The first is a linearization approach that requires … Read more
We study scheduling as a means to address the increasing energy concerns in manufacturing enterprises. In particular, we consider a flow shop scheduling problem with a restriction on peak power consumption, in addition to the traditional time-based objectives. We investigate both mathematical programming and combinatorial approaches to this scheduling problem, and test our approaches with … Read more
We consider the decision problem asking whether a partial rational symmetric matrix with an all-ones diagonal can be completed to a full positive semidefinite matrix of rank at most $k$. We show that this problem is $\NP$-hard for any fixed integer $k\ge 2$. Equivalently, for $k\ge 2$, it is $\NP$-hard to test membership in the … Read more