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We propose a dead-end control algorithm for the exact solution of NP-hard combinatorial optimization problems. The efficiency of the algorithm is demonstrated by examples of solving the set-partition and 0-1 knapsack problems. The paper also shows that the use of the idea of dead-end controls when implementing the dynamic programming method can considerably reduce the number of problem state variables at each optimization step. A comparative analysis of the proposed method with known algorithms for solving these problems is carried out. [ABSTRACT FROM AUTHOR]

This paper formalizes a novel model that is able to use both interval representations, parameterizations, partial memberships and multi-polarity. These are differing modalities of uncertain knowledge that are supported by many models in the literature. The new structure that embraces all these features simultaneously is called interval-valued multi-polar fuzzy soft set (IVmFSS, for short). An enhanced combination of interval-valued m-polar fuzzy (IVmF) sets and soft sets produces this model. As such, the theory of IVmFSSs constitutes both an interval-valued multipolar-fuzzy generalization of soft set theory; a multipolar generalization of interval-valued fuzzy soft set theory; and an interval-valued generalization of multi-polar fuzzy set theory. Some fundamental operations for IVmFSSs, including intersection, union, complement, "OR", "AND", are explored and investigated through examples. An algorithm is developed to solve decision-making problems having data in interval-valued m-polar fuzzy soft form. It is applied to two numerical examples. In addition, three parameter reduction approaches and their algorithmic formulation are proposed for IVmFSSs. They are respectively called parameter reduction based on optimal choice, rank based parameter reduction, and normal parameter reduction. Moreover, these outcomes are compared with existing interval-valued fuzzy methods; relatedly, a comparative analysis among reduction approaches is investigated. Two real case studies for the selection of best site for an airport construction and best rotavator are studied. [ABSTRACT FROM AUTHOR]

This paper substantiates the urgency of developing theoretical foundations, methods, and algorithms for cryptographic protection of color image pixels using problem-oriented multifunctional data structuring and representing codes of color image pixels in the Rademacher, Chrestenson, Rademacher–Chrestenson, Haar–Chrestenson, and Galois systems and investigates the possibility of increasing the operating speed of algorithms for transforming, processing, and recognizing digital images using the modular arithmetic of residue number systems based on the mathematics of arithmetic operations of a non-positional residue number system. [ABSTRACT FROM AUTHOR]

The following paper describes a method for solving certain non-convex minimization problems. These problems contain properties where the feasible region may be represented as a union of convex cones. This set of cones is generated by the intersection of finitely many half-spaces passing through a defined origin. Globally the problem is non-convex, but it is locally convex within the interior of the generated cones whereas the objective function tends to infinity elsewhere. The following algorithm results in a polyhedral representation of all of the cones and an interior point in each of them. In order to solve the problem globally, a convex optimization algorithm is required to be initialized at each interior point and to converge to the local minimum over the corresponding cone. The best of these solutions is the global optimum. A study of the time complexity is presented herewith along with a detailed computational analysis. [ABSTRACT FROM AUTHOR]

The m-machine no-wait flowshop scheduling problem, with the objective of minimizing total completion time subject to the constraint that makespan has to be less than or equal to a certain value, is addressed in this paper. First, an algorithm is proposed to find an upper bound on the makespan in case the upper bound is not given or unknown. Given the upper bound on makespan, a proposed algorithm ( PAL) with five versions L (1, 5, 10, 15, and 20) and a genetic algorithm ( GA) are utilized for solving the problem. Furthermore, a dominance relation is established for the case of four machines. The five versions of PAL and GA are evaluated on randomly generated problems with different number of jobs and number of machines. Computational experiments show that the errors of PA10, PA15, and PA20 are much smaller than that of GA while the CPU times of PA10, PA15, and PA20 are significantly smaller than that of GA. Therefore, the algorithms PA10, PA15, and PA20 are superior to the GA algorithm. [ABSTRACT FROM AUTHOR]

The tool switching problem is used to determine a job sequence and the tools to be loaded on a machine with the objective of minimising the total number of tool switches. In this paper, in order to develop a practical and efficient approach to solving this problem, a beam-search-based algorithm is introduced to formulate the solution space of the problem. The performance of the heuristic algorithm is compared with the heuristic developed by Bard. The proposed algorithm is then tested on some random test problems. The results show that the beam-search-based algorithm performs well in terms of computational efficiency and solution quality. [ABSTRACT FROM AUTHOR]

For any odd t ≥ 9 , we present a polynomial-time algorithm that solves the 3-colouring problem, and finds a 3-colouring if one exists, in P t -free graphs of odd girth at least t - 2 . In particular, our algorithm works for (P 9 , C 3 , C 5) -free graphs, thus making progress towards determining the complexity of 3-colouring in P t -free graphs, which is open for t ≥ 8 . [ABSTRACT FROM AUTHOR]

We propose and axiomatically analyze a class of rational solutions to simple allocation problems where a policy-maker allocates an endowment $$E$$ among $$n$$ agents described by a characteristic vector c. We propose a class of recursive rules which mimic a decision process where the policy-maker initially starts with a reference allocation of $$E$$ in mind and then uses the data of the problem to recursively adjust his previous allocation decisions. We show that recursive rules uniquely satisfy rationality, c-continuity, and other-c monotonicity. We also show that a well-known member of this class, the Equal Gains rule, uniquely satisfies rationality, c-continuity, and equal treatment of equals. [ABSTRACT FROM AUTHOR]

The purpose of this research is to develop two manpower supply planning models and a solution algorithm for mass rapid transit carriage maintenance under mixed deterministic and stochastic demands. These models are formulated as mixed integer programs that are characterized as NP-hard. We employ problem decomposition techniques, coupled with the CPLEX mathematical programming solver, to develop an algorithm that is capable of efficiently solving the problems. The models and the method used currently in actual operations are evaluated by a simulation-based evaluation method. Finally, we perform a case study using real operating data from a Taiwan MRT maintenance facility. The preliminary results are good, showing that the models could be useful for planning carriage maintenance manpower supply. [ABSTRACT FROM AUTHOR]