We consider Newton’s algorithm as well as a variant, the Gauss– Newton algorithm, to solve a system of nonlinear equations F (x) = 0, where x ∈ R , F : R → R. We use a line search method to ensure global convergence. The exact form of our algorithm depends on the rank of the Jacobian J(x) of F . Computational results on some standard test problems are presented, which show that the algorithm ma...

The author recently proposed a new class of knapsack type PKC referred to as K(II)ΣΠPKC [1]. In K(II)ΣΠPKC with old algorithm DA[I], Bob randomly constructs a very small subset of Alice’s set of public key whose order is very large, under the condition that the coding rate ρ satisfies 0.01 < ρ < 0.2. In K(II)ΣΠPKC, no secret sequence such as super-increasing sequence or shifted-odd sequence but...

In the current competitive conditions, all the manufacturers’ efforts are focused on increasing the customer satisfaction as well as reducing the production and delivery costs; thus, there is an increasing concentration on the structure and principles of supply chain (SC). Accordingly, the present research investigated simultaneous optimization of the total costs of a chain and customer satisfa...

In this paper, a hybrid meta-heuristic approach is proposed to optimize the mathematical model of a system with mixed repairable and non-repairable components. In this system, repairable and non-repairable components are connected in series. Redundant components and preventive maintenance strategies are applied for non-repairable and repairable components, respectively. The problem is formulate...

This paper  presents a new multi objective job shop scheduling with sequence-dependent setup times. The objectives are to minimize the makespan and sum of the earliness and tardiness of jobs in a time window. A mixed integer programming model is developed for the given problem that belongs to NP-hard class. In this case, traditional approaches cannot reach to an optimal solution in a reasonable...

A redundancy allocation problem (RAP) is a well-known NP-hard problem that involves the selection of elements and redundancy levels to maximize the system reliability under various system-level constraints. In many practical design situations, reliability apportionment is complicated because of the presence of several conflicting objectives that cannot be combined into a single-objective functi...

It is a known fact that the performance of optimization algorithms for NP-Hard problems vary from instance to instance. We observed the same trend when we comprehensively studied multiobjective evolutionary algorithms (MOEAs) on a six benchmark instances of discrete time-cost trade-off problem (DTCTP) in a construction project. In this paper, instead of using a single algorithm to solve DTCTP, ...

The following MOEA algorithms are briefly summarized and compared: • NPGA Niched Pareto Genetic Algorithm (1994) – NPGA II (2001) • NSGA Non-dominated Sorting Genetic Algorithm (1994) – NSGA II (2000) • SPEA Strength Pareto Evolutionary Algorithm (1998) – SPEA2 (2001) – SPEA2+ (2004) – ISPEA Immunity SPEA (2003) • PAES Pareto Archived Evolution Strategy (2000) – M-PAES Mimetic PAES (2000) • PES...

The non-dominated sorting genetic algorithm II (NSGA-II) is the most intensively used multi-objective evolutionary (MOEA) in real-world applications. However, contrast to several simple MOEAs analyzed also via mathematical means, no such study exists for NSGA-II so far. In this work, we show that runtime analyses are feasible NSGA-II. As particular results, prove with a population size larger t...