A bi-objective approach for shortest-path network interdiction

In the literature, solution approaches to the shortest-path network interdiction problem have been developed for optimizing a single figure-of-merit of the network configuration when considering limited amount of resources available to interdict network links. This paper presents a newly developed evolutionary algorithm that allows approximating the optimal Pareto set of network interdiction strategies when considering bi-objective shortest path problems. Thus, the paper considers the concurrent optimization of two objectives: (1) maximization of shortest-path length and (2) minimization of interdiction strategy cost. Also, the paper considers the transformation of the first objective into the minimization of the most reliable path reliability. To solve these multi-objective optimization problems, an evolutionary algorithm has been developed. This algorithm is based on Monte Carlo simulation, to generate potential network interdiction strategies, graph theory to analyze strategies’ shortest path or most reliable path and, an evolutionary search driven by the probability that a link will appear in the optimal Pareto set. Examples for different sizes of networks and network behavior are used throughout the paper to illustrate and validate the approach.     

A genetic algorithm for a bi-objective capacitated arc routing problem

The capacitated arc routing problem (CARP) is a very hard vehicle routing problem for which the objective—in its classical form—is the minimization of the total cost of the routes. In addition, one can seek to minimize also the cost of the longest trip.In this paper, a multi-objective genetic algorithm is presented for this more realistic CARP. Inspired by the second version of the Non-dominated sorted genetic algorithm framework, the procedure is improved by using good constructive heuristics to seed the initial population and by including a local search procedure. The new framework and its different flavour is appraised on three sets of classical CARP instances comprising 81 files.Yet designed for a bi-objective problem, the best versions are competitive with state-of-the-art metaheuristics for the single objective CARP, both in terms of solution quality and computational efficiency: indeed, they retrieve a majority of proven optima and improve two best-known solutions.     

A branch-and-cut algorithm for two-level survivable network design problems

This paper approaches the problem of designing a two-level network protected against single-edge failures. The problem simultaneously decides on the partition of the set of nodes into terminals and hubs, the connection of the hubs through a backbone network (first network level), and the assignment of terminals to hubs and their connection through access networks (second network level). We consider two survivable structures in both network levels. One structure is a two-edge connected network, and the other structure is a ring. There is a limit on the number of nodes in each access network, and there are fixed costs associated with the hubs and the access and backbone links. The aim of the problem is to minimize the total cost. We give integer programming formulations and valid inequalities for the different versions of the problem, solve them using a branch-and-cut algorithm, and discuss computational results. Some of the new inequalities can be used also to solve other problems in the literature, like the plant cycle location problem and the hub location routing problem.     

Fault-tolerant ring embedding in a star graph with both link andnode failures

The star graph interconnection network has been recognized as an attractive alternative to the hypercube network. Previously, the star graph has been shown to contain a Hamiltonian cycle. In this paper, we consider an injured star graph with some faulty links and nodes. We show that even with f_e⩽n-3 faulty links, a Hamiltonian cycle still can be found in an n-star, and that with f_v⩽n-3 faulty nodes, a ring containing at most 4f_v nodes less than that in a Hamiltonian cycle can be found (i.e. the ring contains at least n!-4f_v nodes). In general, in an n-star with f_e faulty links and f_v faulty nodes, where f_e+f_v⩽n-3, our embedding is able to establish a ring containing at least n!-4f_v nodes     

Two‐node‐connected star problem

In this study, a two‐node‐connected star problem (2NCSP) is introduced. We are given a simple graph and internal and external costs for each link of the graph. The goal is to find the minimum‐cost spanning subgraph, where the core is two‐node‐connected and the remaining external nodes are connected to the core. First, we show that the 2NCSP belongs to the class of NP‐hard computational problems. Therefore, a greedy randomized adaptive search procedure (GRASP) heuristic is developed, enriched with a variable neighborhood descent (VND). The neighborhood structures include exact integer linear programming models to find the best paths and two‐node‐connected replacements, as well as a shaking operation in order to prevent being trapped in a local minima. The ring star problem (RSP) represents a relevant model in network optimization, where the core is a ring instead of an arbitrary two‐node‐connected graph. We contrast our GRASP/VND methodology with a previous reference work on the RSP in order to highlight the effectiveness of our heuristic. The heuristic is competitive, and the best results produced for several instances so far are under study. In this study, a discussion of the results and trends for future work are provided.     

Optimal and approximate approaches for selecting proxy agents in mobile IP based network backbones

In a mobile environment, each mobile host should have a home agent on its home network that maintains a registry of the current location of the mobile host. This registry is normally updated every time a mobile host moves from one subnet to another. We study the tradeoff between the cost of updating the registry and the cost of searching for a mobile host while it is away from home. Using a set of special agents, called proxy agents, which implement a two-tier update process, the cost of updates could be reduced; however, the search cost might increase. We study different approaches to identify a set of proxy agents that minimizes the cost of search. In this paper, we use mathematical programming to obtain optimal solutions to the problem. We consider two situations: the cost of search measured by the sum of all search message costs, and the cost of search measured by the maximum cost of such messages. For these two respective cases we formulate the minimization of the cost of search as Min-Sum and Min-Max problems. For large networks in which the optimization problem may be intractable, we study three different approximate approaches: (1) clustering, (2) genetic algorithms, and (3) simulated annealing. Results of a large set of experiments are presented.     

A hybrid TP+PLS algorithm for bi-objective flow-shop scheduling problems

This paper presents a new, carefully designed algorithm for five bi-objective permutation flow shop scheduling problems that arise from the pairwise combinations of the objectives (i) makespan, (ii) the sum of the completion times of the jobs, and (iii) both, the weighted and non-weighted total tardiness of all jobs. The proposed algorithm combines two search methods, two-phase local search and Pareto local search, which are representative of two different, but complementary, paradigms for multi-objective optimization in terms of Pareto-optimality. The design of the hybrid algorithm is based on a careful experimental analysis of crucial algorithmic components of these two search methods. We compared our algorithm to the two best algorithms identified, among a set of 23 candidate algorithms, in a recent review of the bi-objective permutation flow-shop scheduling problem. We have reimplemented carefully these two algorithms in order to assess the quality of our algorithm. The experimental comparison in this paper shows that the proposed algorithm obtains results that often dominate the output of the two best algorithms from the literature. Therefore, our analysis shows without ambiguity that the proposed algorithm is a new state-of-the-art algorithm for the bi-objective permutation flow-shop problems studied in this paper.     

Lateness minimization with Tabu search for job shop scheduling problem with sequence dependent setup times

We tackle the job shop scheduling problem with sequence dependent setup times and maximum lateness minimization by means of a tabu search algorithm. We start by defining a disjunctive model for this problem, which allows us to study some properties of the problem. Using these properties we define a new local search neighborhood structure, which is then incorporated into the proposed tabu search algorithm. To assess the performance of this algorithm, we present the results of an extensive experimental study, including an analysis of the tabu search algorithm under different running conditions and a comparison with the state-of-the-art algorithms. The experiments are performed across two sets of conventional benchmarks with 960 and 17 instances respectively. The results demonstrate that the proposed tabu search algorithm is superior to the state-of-the-art methods both in quality and stability. In particular, our algorithm establishes new best solutions for 817 of the 960 instances of the first set and reaches the best known solutions in 16 of the 17 instances of the second set.     

A bi-objective reverse logistics network analysis for post-sale service

Reverse logistics, induced by various forms of return, has received growing attention throughout this decade. Reverse logistics network design is a major strategic issue. This paper addresses the analysis of reverse logistic networks that deal with the returns requiring repair service. A problem involving a manufacturer outsourcing to a third-party logistics (3PLs) provider for its post-sale services is proposed. First, a bi-objective optimization model is developed. Two objectives, minimization of the overall costs and minimization of the total tardiness of cycle time, are addressed. The facility capacity option at each potential location is treated as a discrete parameter. The purpose is to find a set of non-dominated solutions to the facility capacity arrangement among the potential facility locations, as well as the associated transportation flows between customer areas and service facilities. Then, a solution approach is designed for solving this bi-objective optimization model. The solution approach consists of a combination of three algorithms: scatter search, the dual simplex method and the constraint method. Finally, computational analyses are performed on trial examples. Numerical results present the trade-off relationship between the two objectives. The numerical results also show that the optimization for the first objective function leads to a centralized network structure; the optimization for the second objective function results in a decentralized network structure.     

Perturbed Decomposition Algorithm applied to the multi-objective Traveling Salesman Problem

Dealing with multi-objective combinatorial optimization, this article proposes a new multi-objective set-based meta-heuristic named Perturbed Decomposition Algorithm (PDA). Combining ideas from decomposition methods, local search and data perturbation, PDA provides a 2-phase modular framework for finding an approximation of the Pareto front. The first phase decomposes the search into a number of linearly aggregated problems of the original multi-objective problem. The second phase conducts an iterative process: aggregated problems are first perturbed then selected and optimized by an efficient single-objective local search solver. Resulting solutions will serve as a starting point of a multi-objective local search procedure, called Pareto Local Search. After presenting a literature review of meta-heuristics on the multi-objective symmetric Traveling Salesman Problem (TSP), we conduct experiments on several instances of the bi-objective and tri-objective TSP. The experiments show that our proposed algorithm outperforms the best current methods on this problem.     

A multi-objective model for facility location–allocation problem with immobile servers within queuing framework

This research investigates a practical bi-objective model for the facility location–allocation (BOFLA) problem with immobile servers and stochastic demand within the M/M/1/K queue system. The first goal of the research is to develop a mathematical model in which customers and service providers are considered as perspectives. The objectives of the developed model are minimization of the total cost of server provider and minimization of the total time of customers. This model has different real world applications, including locating bank automated teller machines (ATMs), different types of vendor machines, etc. For solving the model, two popular multi-objective evolutionary algorithms (MOEA) of the literature are implemented. The first algorithm is non-dominated sorted genetic algorithm (NSGA-II) and the second one is non-dominated ranked genetic algorithm (NRGA). Moreover, to illustrate the effectiveness of the proposed algorithms, some numerical examples are presented and analyzed statistically. The results indicate that the proposed algorithms provide an effective means to solve the problems.     

Bi-objective optimisation model for installation scheduling in offshore wind farms

A bi-objective optimisation using a compromise programming approach is proposed for installation scheduling of an offshore wind farm. As the installation cost and the completion period of the installation are important aspects in the construction of an offshore wind farm, the proposed method is used to deal with those conflicting objectives. We develop a mathematical model using integer linear programming (ILP) to determine the optimal installation schedule considering several constraints such as weather condition and the availability of vessels. We suggest two approaches to deal with the multi-objective installation scheduling problem, namely compromise programming with exact method and with metaheuristic techniques. In the exact method the problem is solved by CPLEX whereas in the metaheuristic approach we propose Variable Neighbourhood Search (VNS) and Simulated Annealing (SA). Moreover, greedy algorithms and a local search for solving the scheduling problem are introduced. Two generated datasets are used for testing our approaches. The computational experiments show that the proposed metaheuristic approaches produce interesting results as the optimal solution for some cases is obtained.     

A framework for the application of metaheuristics to?tasks-to-processors assignation problems

The optimization of the execution time of a parallel algorithm can be achieved through the use of an analytical cost model function representing the running time. Typically the cost function includes a set of parameters that model the behavior of the system and the algorithm. In order to reach an optimal execution, some of these parameters must be fitted according to the input problem and to the target architecture. An optimization problem can be stated where the modeled execution time for the algorithm is used to estimate the parameters. Due to the large number of variable parameters in the model, analytical minimization techniques are discarded. Exhaustive search techniques can be used to solve the optimization problem, but when the number of parameters or the size of the computational system increases, the method is impracticable due to time restrictions. The use of approximation methods to guide the search is also an alternative. However, the dependence on the algorithm modeled and the bad quality of the solutions as a result of the presence of many local optima values in the objective functions are also drawbacks to these techniques. The problem becomes particularly difficult in complex systems hosting a large number of heterogeneous processors solving non-trivial scientific applications. The use of metaheuristics allows for the development of valid approaches to solve general problems with a large number of parameters. A well-known advantage of metaheuristic methods is the ability to obtain high-quality solutions at low running times while maintaining generality. We propose combining the parameterized analytical cost model function and metaheuristic minimization methods, which contributes to a novel real alternative to minimize the parallel execution time in complex systems. The success of the proposed approach is shown with two different algorithmic schemes on parallel heterogeneous systems. Furthermore, the development of a general framework allows us to easily develop and experiment with different metaheuristics to adjust them to particular problems.     

On Equilibria for ADM Minimization Games

In the ADM minimization problem the input is a set of arcs along a directed ring. The input arcs need to be partitioned into non-overlapping chains and cycles so as to minimize the total number of endpoints, where a k-arc cycle contributes k endpoints and a k-arc chain contains k+1 endpoints. We study ADM minimization problem both as non-cooperative and cooperative games. In these games each arc corresponds to a player, and the players share the cost of the ADM switches. We consider two cost allocation models, a model which was considered by Flammini et al., and a new cost allocation model, which is inspired by congestion games. We compare the price of anarchy and price of stability in the two cost allocation models, as well as the strong price of anarchy and the strong price of stability.     

Maintenance costs and makespan minimization for assembly permutation flow shop scheduling by considering preventive and corrective maintenance

The joint optimization of production scheduling and maintenance planning has a significant influence on production continuity and machine reliability. However, limited research considers preventive maintenance (PM) and corrective maintenance (CM) in assembly permutation flow shop scheduling. This paper addresses the bi-objective joint optimization of both PM and CM costs in assembly permutation flow shop scheduling. We also propose a new mixed integer linear programming model for the minimization of the makespan and maintenance costs. Two lemmas are inferred to relax the expected number of failures and CM cost to make the model linear. A restarted iterated Pareto greedy (RIPG) algorithm is applied to solve the problem by including a new evaluation of the solutions, based on a PM strategy. The RIPG algorithm makes use of novel bi-objective-oriented greedy and referenced local search phases to find non-dominated solutions. Three types of experiments are conducted to evaluate the proposed MILP model and the performance of the RIPG algorithm. In the first experiment, the MILP model is solved with an epsilon-constraint method, showing the effectiveness of the MILP model in small-scale instances. In the remaining two experiments, the RIPG algorithm shows its superiority for all the instances with respect to four well-known multi-objective metaheuristics.     

Multi-directional local search

This paper introduces multi-directional local search, a metaheuristic for multi-objective optimization. We first motivate the method and present an algorithmic framework for it. We then apply it to several known multi-objective problems such as the multi-objective multi-dimensional knapsack problem, the bi-objective set packing problem and the bi-objective orienteering problem. Experimental results show that our method systematically provides solution sets of comparable quality with state-of-the-art methods applied to benchmark instances of these problems, within reasonable CPU effort. We conclude that the proposed algorithmic framework is a viable option when solving multi-objective optimization problems.     

Parallel partitioning method (PPM): A new exact method to solve bi-objective problems

In this paper, we propose a new exact method, called the parallel partitioning method (PPM), able to solve efficiently bi-objective problems. This method is based on the splitting of the search space into several areas leading to elementary exact searches. We compare this method with the well-known two-phase method (TPM). Experiments are carried out on a bi-objective permutation flowshop problem (BOFSP). During experiments the proposed PPM is compared with two versions of TPM: the basic TPM and an improved TPM dedicated to scheduling problems. Experiments show the efficiency of the new proposed method.     

Decomposition based hybrid VNS–TS algorithm for distributed parallel factories scheduling with virtual corporation

The main purpose of this paper is to develop a decomposition based hybrid variable neighborhood search/tabu search (DVT) algorithm for multi-factory production network scheduling problem where a number of different individual factories collaborate despite their different objectives. It is assumed some of the network's factories are interested in total processing cost minimization whereas the remaining factories are interested in the production profits maximization. It is also assumed that jobs can migrate from their original factory to other factories but a transportation time is incurred. Our proposed algorithm comprises of a tabu search and a variable neighborhood search with several local search algorithms. In this hybridization, to improve the search ability of the algorithm, we make use of guiding principles with ordering of neighborhood structures by mixed integer linear programming relaxation. In the proposed algorithm, the parallel search strategy is designed for a scalar bi-objective. Multiple objectives are combined with L₁-metric technique then each sub-search procedure evolves separately until a good approximation of the Pareto-front is obtained. The non-dominated sets obtained from our algorithm and original heuristic (algorithm without ordering concept) are compared using three different indices. Furthermore, the problem is modeled as a mixed integer linear programming and solved by improved ϵ-constraint approach (IEA) with CPLEX solver. The results of comparisons between IEA and DVT algorithm showed the proposed algorithm yielded most of the solutions in the net non-dominated front.     

Efficient meta-heuristics based on various dominance criteria for a single-machine bi-criteria scheduling problem with rejection

In this paper, we try to fill in the gap between theory and practice in production scheduling by defining a new term as “rejection” and treating the corresponding scheduling problem with multi-objective optimization approach. We study a bi-objective single machine scheduling problem with rejection. At the beginning of scheduling time horizon, scheduler needs to decide which job shall be rejected due to the resource constraints regarding two objective functions: minimization of total weighted completion time of accepted jobs and total rejection penalty of rejected jobs. We develop different algorithms to find the best estimation of Pareto-optimal front for this problem. In order to improve the quality of the solutions, on the one hand, and facilitate the process of selecting best solution for the final decision maker, on the other hand, we integrate various dominance criteria into our proposed algorithms. Finally we compare the performance of those methods by testing on a large set of instances and highlight the advantages and weak points of each one.     

星图互联网络上的并行路径算法

为了提高星图互联网络中任意两个结点之间传输大量数据信息的效率以及当星图网络中出现结点故障或链路故障的情况下保证数据信息的正常传输,从群论的角度出发,重点采用循环置换的相关性质,给出了一种新的寻找星图互联网络中任意两点之间的所有并行路径的方法。由于在寻找的过程中,该方法将条件细化成不同的情况讨论,从而保证了在每种情况下给出的所有并行路径的长度构成的集合的上界都是最短的,同时也保证了该算法的有效性和最优性。