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This article presents an improved genetic algorithm with two-level approximation (GATA) to optimize the distribution and size of stiffeners simultaneously. A novel optimization model of stiffeners, including two kinds of design variables, is established. The first level approximation problem transforms the original implicit problem to an explicit problem which involves the topology and size variables. Then, a genetic algorithm (GA) addresses the mixed variables. The individuals in the GA are coded by topology variables, and when calculating an individual's fitness, the second level approximation problem is embedded to optimize the size variables. Considering the stiffeners' optimization, several aspects of the initial GATA are updated, including the relationship between two kinds of variables, the weight and its sensitivity calculation and the GA strategy, to optimize the stiffeners' size and distribution simultaneously. Numerical examples show that the improved GATA is effective in optimizing the stiffened shells' topology and size variables simultaneously. [ABSTRACT FROM AUTHOR]

This article addresses permutation flowshop scheduling problems with simple linear deterioration. The objectives are to minimize logarithm of the makespan, total logarithm of the completion time, total weighted logarithm of the completion time, and the sum of the quadratic job logarithms of the completion times. Approximation algorithms and their worst-case bounds are presented and analysed. Branch-and-bound algorithms are also proposed to solve the problems optimally. Computational experiments are performed to illustrate the algorithms. [ABSTRACT FROM AUTHOR]

This article presents a novel method to compute averaged Hausdorff () approximations of the Pareto fronts of multi-objective optimization problems. The underlying idea is to utilize directly the scalar optimization problem that is induced by theperformance indicator. This method can be viewed as a certain set based scalarization approach and can be addressed both by mathematical programming techniques and evolutionary algorithms (EAs). In this work, the focus is on the latter where a first single objective EA for suchapproximations is proposed. Finally, the strength of the novel approach is demonstrated on some bi-objective benchmark problems with different shapes of the Pareto front. [ABSTRACT FROM PUBLISHER]

This work studies a scheduling problem where each job must be either accepted and scheduled to complete within its specified due window, or rejected altogether. Each job has a certain processing time and contributes a certain profit if accepted or penalty cost if rejected. There is a set of renewable resources, and no resource limit can be exceeded at any time. Each job requires a certain amount of each resource when processed, and the objective is to maximize total profit. A mixed-integer programming formulation and three approximation algorithms are presented: a priority rule heuristic, an algorithm based on the metaheuristic for randomized priority search and an evolutionary algorithm. Computational experiments comparing these four solution methods were performed on a set of generated benchmark problems covering a wide range of problem characteristics. The evolutionary algorithm outperformed the other methods in most cases, often significantly, and never significantly underperformed any method. [ABSTRACT FROM PUBLISHER]

This article addresses the flow shop scheduling problem to minimize the sum of the completion times. On the basis of the properties in job sequencing, the triangular shortest processing time (TSPT) first and dynamic triangular shortest processing time first heuristics are designed to solve the static and dynamic versions of this problem, respectively. Moreover, an improvement scheme is provided for these heuristics to enhance the quality of the original solutions. For further numerical evaluation of the heuristics, two new lower bounds with performance guarantees are presented for the two versions of the problem. At the end of the article, a series of numerical experiments is conducted to demonstrate the effectiveness of the algorithms. [ABSTRACT FROM AUTHOR]

Common deficiencies found in previous studies that modelled quay crane scheduling with non-crossing constraints (QCSNC) in port container terminals are identified. Remedies for the problems are proposed to prevent the occurrence of unrealistic optimal solutions for QCSNC. Additionally, two approximation schemes for QCSNC are studied. The first one is called the best partition (BP) method, which can be solved by dynamic programming (DP) with time complexity of O(mn2). A more efficient algorithm is designed to improve the original DP by adopting binary search. Next, based on BP and an exact algorithm for QCSNC (with pseudo-polynomial computational time), the second approximation scheme, called the enhanced best partition (EBP) method, is proposed to achieve a better estimation of the optimal makespan for QCSNC. The results of numerical experiments show that EBP is an effective approximation scheme for the problem of QCSNC. [ABSTRACT FROM AUTHOR]