New Possibilities for Constructing Heuristic Solutions to Problems of Electromagnetic Diffraction

The paper formulates the foundations of a recently developed approach, named the method of fundamental components, intended for constructing heuristic solutions in problems of electromagnetic diffraction, for the first time. The difference between the new method and the known heuristic approaches lies in the application of an adjustment procedure that increases the accuracy. The possibility of the mentioned method for obtaining new results is illustrated with the help of the author’s previously published works. The advantages of the new method in constructing high-speed solvers and in the physical interpretation of numerical solutions are shown.

Heuristic Approaches With Reinforced Parameter Tuning for the Car Sequencing Problems With Block Batches

Motivated by the practical supply chain management of the automobile industry, we study the car sequencing problem (CSP) that minimize the conflicts arising from scheduling cars into an assembly line. The CSP is a well established problem, subject to the paint batching constraints to reduce the the costs for color changes and capacity constraints in the assembly shop to level the usage of the options. However, the existing approaches to this problem do not take into account the block batches, which desires a consecutive production batch of cars requiring a certain option. This requirement often occurs when specialized labor time window is short in the customized car production scenario, and renders additional complexities to the traditional car sequencing problem. In this paper, we propose a novel model to deals with these constraints and simultaneously generate the sequencing and replenishment decisions. In addition to our model formulation, we develop two math-heuristic approaches to solve the propose large-scale car sequencing problem. The selected heuristics are based on relax-and-fix procedures, fix-and-optimize procedures and variable neighborhood search. To solve the large-sized instances (commercial solvers, i.e., Cplex, cannot provide a feasible solution within 1 hour), we design and implement a reinforced parameter tuning mechanism to dynamically select the parameter values, so as to speed up the search process. The proposed models and heuristics are tested on compatible instances from the benchmark in the literature (CSPLib), as well as large-sized instances generated from real-world cases. We report on extensive computational experiments, and provide basic managerial insights into the planning process.

Attacking the linear congruential generator on elliptic curves via lattice techniques

In this paper we study the linear congruential generator on elliptic curves from the cryptographic point of view. We show that if sufficiently many of the most significant bits of the composer and of three consecutive values of the sequence are given, then one can recover the seed and the composer (even in the case where the elliptic curve is private). The results are based on lattice reduction techniques and improve some recent approaches of the same security problem. We also estimate limits of some heuristic approaches, which still remain much weaker than those known for nonlinear congruential generators. Several examples are tested using implementations of ours algorithms.

On Explaining Random Forests with SAT

Random Forest (RFs) are among the most widely used Machine Learning (ML) classifiers. Even though RFs are not interpretable, there are no dedicated non-heuristic approaches for computing explanations of RFs. Moreover, there is recent work on polynomial algorithms for explaining ML models, including naive Bayes classifiers. Hence, one question is whether finding explanations of RFs can be solved in polynomial time. This paper answers this question negatively, by proving that computing one PI-explanation of an RF is D^P-hard. Furthermore, the paper proposes a propositional encoding for computing explanations of RFs, thus enabling finding PI-explanations with a SAT solver. This contrasts with earlier work on explaining boosted trees (BTs) and neural networks (NNs), which requires encodings based on SMT/MILP. Experimental results, obtained on a wide range of publicly available datasets, demonstrate that the proposed SAT-based approach scales to RFs of sizes common in practical applications. Perhaps more importantly, the experimental results demonstrate that, for the vast majority of examples considered, the SAT-based approach proposed in this paper significantly outperforms existing heuristic approaches.