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We propose a new algorithm for fixed‐charge network flow problems based on ghost image (GI) processes as proposed in Glover (1994) and adapted to fixed‐charge transportation problems in Glover et al. (2005). Our GI algorithm iteratively modifies an idealized representation of the problem embodied in a parametric GI, enabling all steps to be performed with a primal network flow algorithm operating...
We introduce a new class of assignment‐based neighborhoods for symmetric and asymmetric traveling salesman problems that exhibits a combinatorial leverage property, by which a tour can be generated in polynomial time that dominates an exponential number of other tours. The ejection chain perspective motivating the new neighborhoods differs from that underlying the most general assignment‐based neighborhoods...
The Quadratic Unconstrained Binary Optimization problem (QUBO) has become a unifying model for representing a wide range of combinatorial optimization problems, and for linking a variety of disciplines that face these problems. A new class of quantum annealing computer that maps QUBO onto a physical qubit network structure with specific size and edge density restrictions is generating a growing interest...
Ejection chain methods, which include the classical Lin–Kernighan (LK) procedure and the Stem‐and‐Cycle (S&C) reference structure, have been the source of the currently leading algorithms for large scale symmetric traveling salesman problems (STSP). Although these methods proved highly effective in generating large neighborhoods for symmetric instances, their potential application to the asymmetric...
In this study, we present a new tabu search algorithm for the quadratic assignment problem (QAP) that utilizes an embedded neighborhood construction called an ejection chain. Our ejection chain approach provides a combinatorial leverage effect, where the size of the neighborhood grows multiplicatively while the effort of finding a best move in the neighborhood grows only additively. Our results illustrate...
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