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Abstract: In this paper, we consider a flow shop scheduling problem under different conditions. The model is formulated in a form of mixed binary integer programming. The primary goal of this paper is to develop operation schedules that specify the completion time of operations. The objective function of our model is formulated as a minimization of the makespan, the weighted mean flow-time or the weighted mean tardiness. There are several constraints which are involved in our modeling such as the due dates of jobs, the jobs ready times, etc. For these objective functions and constraints, seven mixed binary integer programming models are proposed. We demonstrate the implementation of our proposed models using different numerical examples. As a case study, we apply the proposed models for an information systems development (ISD) center to schedule the ISD projects using some real data. [Copyright &y& Elsevier]

Abstract: This paper proposes an interactive approach for solving bi-level integer multi-objective fractional programming problem. At the first phase of the solution approach, we begin by finding the convex hull of its original set of constraints using the cutting-plane algorithm then the two level decision makers use the Charnes and Cooper transformation to convert the fractional objective functions to equivalent linear functions. At the second phase, the algorithm simplifies the equivalent problem by transforming it into separate multi-objective decision-making problem and solving it by using the ε-constraint method. In addition, the theoretical results are illustrated with the help of a numerical example. [Copyright &y& Elsevier]

Abstract: In this paper we study the permutation flow shop scheduling problem with order acceptance and weighted tardiness (PFSS-OAWT) faced by firms that have a number of candidate orders to be selected and scheduled on a flow shop production line. The objective is to maximize the total net profit with weighted tardiness penalties. We formulate the PFSS-OAWT problem as an integer programming (IP) model. A heuristic algorithm named Simulated Annealing Based on Partial Optimization (SABPO) is developed for solving the IP model and obtaining near-optimal solutions. Computational studies are carried out on solving 160 problem instances with different scales (small, medium, large, and very large). The experimental results show that the SABPO algorithm exhibits good optimality for small-sized problems and robustness for medium/large-sized problems compared with benchmarks. [Copyright &y& Elsevier]

Abstract: In this paper, we deal with the maximum diversity problem (MDP), which asks to select a specified number of elements from a given set so that the sum of distances between the selected elements is as large as possible. We develop an iterated tabu search (ITS) algorithm for solving this problem. We also present a steepest ascent algorithm, which is well suited in application settings where solutions of satisfactory quality are required to be provided very quickly. Computational results for problem instances involving up to 5000 elements show that the ITS algorithm is a very attractive alternative to the existing approaches. In particular, we demonstrate the outstanding performance of ITS on the MDP instances taken from the literature. For 69 such instances, new best solutions were found. [Copyright &y& Elsevier]

Abstract: Many combinatorial optimization problems are known to be NP-complete. A common point of view is that finding fast algorithms for such problems using a polynomial number of processors is unlikely. However, facts of this kind are usually established for “worst” case situations, and in practice many instances of NP-complete problems are successfully solved in polynomial time by such traditional combinatorial optimization techniques such as dynamic programming, branch-and-bound. New opportunities for an effective solution of combinatorial problems emerged with the advent of parallel machines. In this paper, we describe an algorithm which generates an optimal solution for the 0/1 integer knapsack problem on DNA computing. [Copyright &y& Elsevier]

Abstract: In this paper, based on microfluidic systems, we propose a DNA algorithm for solving the special 0–1 integer programming problem, which has n variables and m constraint terms. In our method, capillary electrophoresis (CE) is used to transfer and separate DNA strands, and the solutions are distinguished by analyzing the fluorescence imaging obtained by laser-induced fluorescence (LIF). Under the control of CE workstation, DNA strands with different lengths are separated and transferred according to an advanced program. This method has advantages such as low cost, low error, short operation time, and simple experimental steps. Moreover, there is no need to reconstruct probes and the size of biochip is linearly increased with the complexity of the problem. [Copyright &y& Elsevier]

Abstract: In this paper, we first show a DNA representation of a ternary number with digit set {−1,0,1}, which features its address and each bit position. Based on this DNA representation, operations for value assigning and bit position shifting are proposed. The algorithm of DNA computing for adding two ternary integers is presented. The algorithm works in O(m) steps for adding two ternary integers of m bits. [Copyright &y& Elsevier]

Abstract: In this paper, we develop a new filled function method to solve nonlinear integer programming problem. It is shown that any local minimizer of the new filled function constructed from a current local minimizer is either a better local minimizer of the original integer programming problem or a vertex of its constrained domain. Hence a better local minimizer can be obtained just by local search scheme for the new filled function. An algorithm based on the nice properties of the new filled function is proposed for locating the global minimizer of the original integer programming problem. Several numerical examples are presented to show the efficiency of the algorithm. [Copyright &y& Elsevier]

Many practical problems often lead to large nonconvex nonlinear programming problems that have many equality constraints. The global optimization algorithms of these problems have received much attention over the last few years. Generally, stochastic algorithms are suitable for these problems, but not efficient when there are too many equality constraints. Therefore, a global optimization algorithm for solving these problems is proposed in this paper. The new algorithm, based on a feasible set strategy, uses a stochastic algorithm and a deterministic local algorithm. The convergence of the algorithm is analyzed. This algorithm is applied to practical problem, and the numerical results illustrate the accuracy and efficiency of the algorithm. [Copyright &y& Elsevier]