In the generalized balanced optimization problem (GBaOP) the objective value $${\max_{e \in S}{|c(e)-k\max(S)|}}$$ is minimized over all feasible subsets S of E = {1, . . . , m}. We show that the algorithm proposed in Punnen and Aneja (Oper Res Lett 32:27–30, 2004 ) can be modified to ensure...

Although greedy algorithms are important, nowadays it is well assumed that the solutions they obtain can be used as a starting point for more sophisticated methods. This paper describes an evolutionary approach which is based on genetic algorithms (GA). A constructive heuristic, so-called fuzzy...

This article describes how the 0/1 Multiple Knapsack Problem (MKP), a generalization of popular 0/1 Knapsack Problem, is NP-hard and harder than simple Knapsack Problem. Solution of MKP involves two levels of choice – one for selecting an item to be placed and the other for selecting the...

The traveling thief problem (TTP) is a benchmark problem that consists of two well-known problems, the traveling salesman problem (TSP) and the knapsack problem (KP). It was defined to imitate complex real-world applications that comprise different interdependent sub-problems. Various approaches...