Quadratic knapsack problems

An Iterated Semi-Greedy Algorithm for the 0-1 Quadratic Knapsack Problem

“…The 0-1 Quadratic Knapsack Problem was introduced by Gallo, Hammer, and Simeone [2]. Let us assume that the knapsack's capacity is c and there are n candidate objects, that w i and p ii respectively are the weight and the profit of object i ∈ [n], and that p ij is the pairwise profit of two objects i ∈ [n] and j ∈ [n] (i = j).…”

A hybrid metaheuristic approach to solving the UBQP problem

“…Besides its theoretical significance as a canonical NP-hard problem [13], the UBQP is notable for its ability to formulate a wide range of important problems, including those from computer aided design [28], social psychology [21], traffic management [12,45], financial analysis [29,34], machine scheduling [1] and cellular radio channel allocation [10]. Moreover, the application potential of UBQP is much greater than might be imagined, due to the ability to incorporate quadratic infeasibility constraints into the objective function in an explicit manner.…”

Diversification-driven tabu search for unconstrained binary quadratic problems

“…The formulation UBQP is notable for its ability to represent a wide range of important problems, including those from social psychology (Harary (1953)), financial analysis (Laughunn (1970); McBride and Yormark (1980)), computer aided design (Krarup and Pruzan (1978)), traffic management (Gallo et al (1980); Witsgall (1975)), machine scheduling (Alidaee et al (1994)), cellular radio channel allocation (Chardaire and Sutter (1994)) and molecular conformation (Phillips and Rosen (1994)). Moreover, many combinatorial optimization problems pertaining to graphs such as determining maximum cliques, maximum cuts, maximum vertex packing, minimum coverings, maximum independent sets, maximum independent weighted sets are known to be capable of being formulated by the UBQP problem as documented in papers of Pardalos and Rodgers (1990), Pardalos and Xue (1994).…”