This paper studies the issue of well-posednessfor vector optimization. It is shown thatcoercivity implies well-posedness without any convexity assumptionson problem data.For convex vector optimization problems,solution sets of such problems are non-convex in general,but they are highly structured. By exploring such structures carefully via convex analysis,we are able to obtaina number of positive results, including a criterion for well-posedness in terms of that of associated scalar problems.In particularwe show that a well-known relative interiority conditioncan be used as a sufficient condition for well-posedness in convexvector optimization.

Given a graph G = (V,E) and a “cost function” $f: 2^V\rightarrow\mathbb{R}$ (provided by an oracle), the problem [PCliqW] consists in finding a partition into cliques of V(G) of minimum cost. Here, the cost of a partition is the sum of the costs of the cliques in the partition.We provide a polynomial time dynamic program for the case where G is an interval graph and f belongs to a subclass of submodular set functions, which we call “value-polymatroidal”.This provides a common solution for various generalizations of the coloringproblem in co-interval graphs such as max-coloring,“Greene-Kleitman's dual”, probabilist coloring and chromatic entropy. In the last two cases, this is the first polytime algorithm for co-interval graphs. In contrast, NP-hardness of related problems is discussed. We also describe an ILP formulation for [PCliqW] which gives a common polyhedral framework to express min-max relations such as ${\overline{\chi}}=\alpha$ for perfect graphs and the polymatroid intersection theorem. This approach allows to provide a min-max formula for [PCliqW] if G is the line-graph of a bipartite graph and f is submodular.However, this approach fails to provide a min-max relation for [PCliqW] if G is an interval graphs and f is value-polymatroidal.

Constructive heuristics for shop scheduling problems are often based onpriority (or dispatching) rules. However, recent work has demonstratedthat insertion algorithms that step by step insert operations or jobs into partial schedules usually clearly outperform priority rules.In this paper, we consider various job shop scheduling problems withsetup times. For each job a specific technological route and a releasedate are given. Moreover, the jobs are partitioned into groups. Asequence independent setup time S rj is required on machine j when a job of the r-th group is processed after a job of another group. We consider different types of job availability, namely item and batch availability. As objective function we use both regular and nonregular criteria. For such problems we apply insertion techniquescombined with beam search. Especially we consider different insertion orders of the operations or jobs. A refined variant of the insertion algorithmis presented, where several operations are inserted in parallel. The proposed variants have been tested on a large collection of test problems and compared with other constructive algorithms based onpriority rules.

In the course of globalization, many enterprises change theirstrategies and are coupled in partnerships with suppliers,subcontractors and customers. This coupling forms supply chainscomprising several geographically distributed productionfacilities. Production planning in a supply chain is a complicatedand difficult task, as it has to be optimal both for the localmanufacturing units and for the whole supply chain network. Inthis paper two analytical models are used to solve the productionplanning problem in supply chain involving several enterprises.Generally in practice, for competitive and/or practical reasons,frequently each enterprise prefers to optimize its production planwith little care about the other members of the supply chain. Thiscase is presented through a simple model of decentralizedoptimization. The aim of this study is to analyze and compare thetwo types of optimization: centralized and decentralized. Theinitial question is: what are the profit and the optimal policy ofglobal (centralized) optimization in contrast to local(decentralized)? We characterize this gain by comparing theoptimal profits obtained in both cases.

We consider the Airspace Sectorization Problem (ASP) in which airspacehas to be partitioned into a given number of sectors, each of whichbeing assigned to a team of air traffic controllers. The objective isto minimize the coordination workload between adjacent sectors whilebalancing the total workload of controllers. Many specificconstraints, including both geometrical and aircraft relatedconstraints are taken into account. The problem is solved in aconstraint programming framework. Experimental results show that ourapproach can be used on real life problems.

We analyze the convergence of the prox-regularization algorithmsintroduced in [1], to solve generalized fractional programs,without assuming that the optimal solutions set of the consideredproblem is nonempty, and since the objective functions arevariable with respect to the iterations in the auxiliary problemsgenerated by Dinkelbach-type algorithms DT1 and DT2, we considerthat the regularizing parameter is also variable. On the otherhand we study the convergence when the iterates are onlyηk -minimizers of the auxiliary problems. This situation ismore general than the one considered in [1]. We also give someresults concerning the rate of convergence of these algorithms,and show that it is linear and some times superlinear for someclasses of functions. Illustrations by numerical examples aregiven in [1].

Periodic Vehicle Routing Problem: classification and heuristic for tactical planning.The Periodic Vehicle Routing Problem (PVRP) consists in assigning customer visits to vehicle routes in some periods of a time horizon so as to satisfy some service level requirements that can take theform of frequency of visit, constraint on time lag between visits, or pre-defined visit patterns. We present different variants of this problem and propose a classification. Then, we consider a model for tactical planning for which we propose a heuristic: we optimise theplanning of customer visits to achieve both workload balancing andregionalisation of the routes. The objective of regionalisation reflects a desire to specializeroutes to restricted geographical area. The standard minimisation of distancetravelled is left for the underlying operational decision making model.Our heuristic achieves practical solutions for an industrialinstance with 16658 visits to schedule over a horizon of 20 days.

We consider a multiobjective optimization problem with a feasible setdefined by inequality and equality constraints such that all functionsare, at least, Dini differentiable (in some cases, Hadamard differentiableand sometimes, quasiconvex). Several constraint qualifications are givenin such a way that generalize both the qualifications introduced by Maedaand the classical ones, when the functions are differentiable. Therelationships between them are analyzed. Finally, we give severalKuhn-Tucker type necessary conditions for a point to be Pareto minimumunder the weaker constraint qualifications here proposed.

The NP-hard problem of car sequencing has received a lot of attention these last years. Whereas a directapproach based on integer programming or constraint programming is generally fruitless when the number of vehicles tosequence exceeds the hundred, several heuristics have shown their efficiency. In this paper, very large-scaleneighborhood improvement techniques based on integer programming and linear assignment are presented for solving carsequencing problems. The effectiveness of this approach is demonstrated through an experimental study made on seminalCSPlib's benchmarks.

Fractional programming consists in optimizing a ratio oftwo functions subject to some constraints. Different versions of thismodel, linear or nonlinear, have applications in various fields likecombinatorial optimization, stochastic programming, data bases, andeconomy. Three resolution methods are presented: direct solution,parametric approach and solution of an equivalent problem.

For a given partial solution,the partial inverse problem is to modify the coefficientssuch that there is a full solution containing the partial solution, while the full solution becomes optimal under new coefficients, and the total modification is minimum.In this paper, we show that the partial inverseassignment problem and the partial inverse minimum cut problem are NP-hard ifthere are bound constraints on the changes of coefficients.

Uncertainty in optimization is not a new ingredient. Diverse modelsconsidering uncertainty have been developed over the last 40 years.In our paper we essentially discuss a particular uncertainty modelassociated with combinatorial optimization problems, developed inthe 90's and broadly studied in the past years. This approach namedminmax regret (in particular our emphasis is on the robustdeviation criteria) is different from the classical approach for handlinguncertainty, stochastic approach, where uncertainty is modeledby assumed probability distributions over the space of all possiblescenarios and the objective is to find a solution with good probabilisticperformance. In the minmax regret (MMR) approach, the set of all possible scenariosis described deterministically, and the search is for a solution thatperforms reasonably well for all scenarios, i.e., that has the bestworst-case performance. In this paper we discuss the computational complexity of some classiccombinatorial optimization problems using MMR approach, analyze thedesign of several algorithms for these problems, suggest the studyof some specific research problems in this attractive area, and alsodiscuss some applications using this model.

An important task of knowledge discovery deals with discovering association rules. This very general model has been widely studied and efficient algorithms have been proposed. But most of the time, only frequent rules are seeked. Here we propose to consider this problem as a multi-objective combinatorial optimization problem in order to be able to also find non frequent but interesting rules. As the search space may be very large, a discussion about different approaches is proposed and a hybrid approach that combines a metaheuristic and an exact operator is presented.

A concept of an Orderly Colored Longest Path (OCLP) refers to the problem of finding the longest path in a graph whose edges are colored with a given number of colors, under the constraint that the path follows a predefined order of colors. The problem has not been widely studied in the previous literature, especially for more than two colors in the color arrangement sequence. The recent and relevant application of OCLP is related to the interpretation of Nuclear Magnetic Resonance experiments for RNA molecules. Besides, an employment of this specific graph model can be found in transportation, games, and grid graphs. OCLP models the relationships between consecutive edges of the path, thus it appears very useful in representing the real problems with specific ties between their components. In the paper, we show OCLP’s correlation with similar issues known in graph theory. We describe the applications, three alternative models and new integer programming algorithms to solve OCLP. They are formulated by means of max flow problems in a directed graph with packing constraints over certain partitions of nodes. The methods are compared in a computational experiment run for a set of randomly generated instances.

Public inoculation centers are examples of facilities providing service to customers whose demand is elastic to travel and waiting time. That is, people will not travel too far, or stay in line for too long to obtain the service. The goal, when planning such services, is to maximize the demand they attract, by locating centers and staffing them so as to reduce customers' travel time and time spent in queue. In the case of inoculation centers, the goal is to maximize the people that travel to the centers and stay in line until inoculated. We propose a procedure for the allocation of multiple servers to centers, so that this goal is achieved. An integer programming model is formulated. Since demand is elastic, a supply-demand equilibrium equation must be explicitly included in the optimization model, which then becomes nonlinear. As there are no exact procedures to solve such problems, we propose a heuristic procedure, based on Heuristic Concentration, which finds a good solution to this problem. Numerical examples are presented.

The coupled tasks scheduling problem is a class of scheduling problems introduced forbeam steering software of sophisticated radar devices, called phased arrays. Due toincreasing popularity of such radars, the importance of coupled tasks scheduling isconstantly growing. Unfortunately, most of the coupled tasks problems are NP-hard, andonly a few practically usable algorithms for such problems were found. This paper providesa survey of already known complexity results of various variants of coupled tasksproblems. Then, it complements previous results by providing experimental results of twonew polynomial algorithms for coupled tasks scheduling, which are: an exact algorithm for1|(1,4,1),strictchains|Cmax problem,and a fast heuristic algorithm for more general1|(1,2k, 1), strictchains|Cmaxproblem, where k ∈ ℕ.

This paper addresses a Three-Dimensional Loading Capacitated Vehicle Routing Problem(3L-CVRP) which combines a three-dimensional loading problem and vehicle routing problemin distribution logistics. The problem requires the combinatorial optimization of afeasible loading solution and a successive routing of vehicles to satisfy client demands,where all vehicles must start and terminate at a central depot. In spite of its clearpractical significance in the real world of distribution management, 3L-CVRP in literatureis very limited for its high combinatorial complexity. We solve this problem by a hybridapproach which combines Genetic Algorithm and Tabu Search (GATS). Genetic algorithm isdeveloped for vehicle routing and tabu search for three-dimensional loading, while thesetwo algorithms are integrated for the combinatorial problem. We computationally evaluatethis hybrid genetic algorithm on all publicly available test instances, and obtain newbest solutions for several instances.

This paper considers two backup schemes for a database system: a database is updated at a nonhomogeneous Poisson process and an amount of updated files accumulates additively. To ensure the safety of data, full backups are performed at time NT or when the total updated files have exceeded a threshold level K, and between them, cumulative backups as one of incremental backups are made at periodic times iT(i = 1,2,...,N - 1). Using the theory of cumulative processes, the expected cost is obtained, and an optimal number N* of cumulative backup and an optimal level K* of updated files which minimize it are analytically discussed. It is shown as examples that optimal number and level are numerically computed when two costs of backup schemes are given.

Discrete-continuous project scheduling problems with positive discounted cash flows andthe maximization of the NPV are considered. We deal with a class of theseproblems with an arbitrary number of discrete resources and one continuous, renewableresource. Activities are nonpreemptable, and the processing rate of an activity is acontinuous, increasing function of the amount of the continuous resource allotted to theactivity at a time. Three common payment models – Lump Sum Payment, Payments at ActivityCompletion times, and payments in Equal Time Intervals are analyzed. Formulations ofmathematical programming problems for an optimal continuous resource allocation for eachpayment model are presented. Applications of two local search metaheuristics – Tabu Searchand Simulated Annealing are proposed. The algorithms are compared on a basis ofcomputational experiments. Some conclusions and directions for future research are pointedout.

In this paper, we consider a batch arrival MX/M/1 queue model with working breakdown. The server may be subject to a service breakdown when it is busy, rather than completely stoping service, it will decrease its service rate. For this model, we analyze a two-dimensional Markov chain and give its quasi upper triangle transition probability matrix. Under the system stability condition, we derive the probability generating function (PGF) of the stationary queue length, and then obtain its stochastic decomposition, which shows the relationship with that of the classical MX/M/ 1 queue without vacation or breakdown. Besides, we also give the Laplace-Stieltjes transform (LST) of the stationary waiting time distribution of an arbitrary customer in a batch. Finally, some numerical examples are given to illustrate the effect of the parameters on the system performance measures.