Abstract In the operations research (OR) literature several highly efficient solution methods for the Quadratic Knapsack Problem (QKP) have been documented. However, these solution approaches are not readily available for industrial applications. In this short paper, we demonstrate that OR practitioners must be careful in their use of general-purpose integer programming software such as Gurobi when solving QKPs. We verify the very positive impact of fine-tuning parameters when solving QKPs with Gurobi.

Abstract New estimations on settling-time for fixed-time stabilization of nonlinear systems are derived. By using the new proposed results on fixed-time stable and designing proper effective event-triggered control (ETC), fixed-time stabilization (FTS) for a kind of delayed neural networks is investigated. The new estimations on settling-time for fixed-time stabilization can be used to discussed other systems, such as complex networks, multi-agent systems and so on. At last, example simulations are given to corroborate the effectiveness of the derived results.

Abstract This paper presents a class of novel recurrent neural network approaches for a distributed partitioned optimization scenario, where the objective function is separable, strongly convex, and possibly nonsmooth, with the computation of a part of the solution being distributed to a vertex for execution. In our proposed algorithmic framework, the block splitting method allows the solution to be partitioned among vertices according to the divisible structure of the problem, so that each neuron only holds a local memory of the decision variable rather than the memory of the entire decision variable. A local timer is installed for each neuron. If a neuron is triggered by its own timer and a neighbor timer, it will reach an activated state and then update and transmit its own variable information. This asynchronous evolution strategy with time helps to save computational resources. The proposed algorithm is distributed and scalable, with the computation of a single neuron not depending on the size of the vertex network, and the convergence of the algorithm can be guaranteed.

Abstract In order to give machines, the interpretable thinking ability of mathematicians, the automatic derivation engine for advanced mathematics symbolic systems was explored to develop, which could update machines from the shallow thinking ability, such as natural language understanding and elementary mathematical numerical computation, to deep thinking, such as equivalent derivation for symbolic systems. This article proposed the complex logic algorithm design and development method with the frameworks as the core components. Starting with problem-resolving examples, the initial idea, basic data structure, and programming features of this new method were introduced in detail. However, this article proposed the integrated development environment for this method, as well as the main scheduling algorithm, core process algorithm, workflow dynamic display algorithm, execution status monitoring algorithm, generalization processing method, etc. The new method could be applicable to intelligent system development tasks that needed to gradually accumulate instance experience and had practical significance for the complex logic algorithms development, visualization software design, reduction complexity for software test and maintenance, and software reliability improvement. This article used the application problem solved by partial differential equations as an example to explain this method from the whole process, such as lexical analysis, semantic analysis, symbolic system establishment, and equivalent derivation to result validation, demonstrating the new dynamism and potential for logic derivation-based classical artificial intelligence methods.