The optimization of Multidimensional Knapsacks with Family-Split Penalties has been introduced in the literature as a variant more classical Knapsack and Multi-Knapsack problems. This problem deals set items partitioned families, when single item is picked to maximize utility, then all its family must be picked. Items from same can assigned different knapsacks, this situation split penalties ar...

Some of industrial and real life problems are difficult to be solved by traditional methods, because they need exponential number calculations. As an example, we can mention decision-making problems. They defined as optimization Ant Colony Optimization (ACO) is between the best that solves combinatorial The method mimics behavior ants in nature, when look for a food. One algorithm parameters ca...

In this paper, we consider the multi-band robust knapsack problem which generalizes the Γ-robust knapsack problem by subdividing the single deviation band into several smaller bands. We state a compact ILP formulation and develop two dynamic programming algorithms based on the presented model where the first has a complexity linear in the number of items and the second has a complexity linear i...

this paper introduces an indirect adaptive fuzzy sliding mode controller as a power system stabilizer for damping local and inter-area modes of oscillations of multi-machine power systems. this controller is designed based on the combination of sliding mode controller and the fuzzy logic systems. the fuzzy systems are used to approximate the unknown functions of power system model. generator sp...

In this paper, we define the notion of (dual) multi-fuzzy normedspaces and describe some properties of them. We then investigate Ulam-Hyers stability of Jensen's functional equation for mappings from linear spaces into  multi-fuzzy normed spaces. We establish an asymptotic behavior of the Jensen equation in the framework of multi-fuzzy normed spaces.

This paper presents a new heuristic algorithm for the MultipleChoice Multi-Dimension Knapsack Problem (MMKP) in PRAM model. MMKP is a variant of the classical 0-1 knapsack problem, has a knapsack with multidimensional capacity constraints, groups of items, each item having a utility value and multidimensional resource constraints. The problem is to maximize the total value of the items in the k...

Multi Expression Programming (MEP) is a Genetic Programming variant that uses linear chromosomes for solution encoding. A unique feature of MEP is its ability of encoding multiple solutions of a problem in a single chromosome. In this paper we use Multi Expression Programming for evolving digital circuits for a well-known NP-Complete problem: the knapsack (subset sum) problem. Numerical experim...

In this note, we revise the problem of axial anomaly in framework very special relativity following Fujikawa's path integral approach. We show nonperturbatively that no VSR contribution is present measure $(3+1)$-dimensional spacetime. Furthermore, extend our results to $(1+1)$ dimensions, as well two-dimesional curved

We study the problem of predicting a set or list of options under knapsack constraint. The quality of such lists are evaluated by a submodular reward function that measures both quality and diversity. Similar to DAgger (Ross et al., 2010), by a reduction to online learning, we show how to adapt two sequence prediction models to imitate greedy maximization under knapsack constraint problems: CON...