We consider a general class of combinatorial optimization problems including among others allocation, multiple knapsack, matching or travelling salesman problems. The standard version of those problems is the maximum weight optimization problem where a sum of values is optimized. However, the sum is not a good aggregation function when the fairness of the distribution of those values (correspon...

Many Integer Linear Programming (ILP) problems contain significant subproblems exclusively composed of 0-1 (binary) variables. Much effort has gone in to special solvers for 0-1 ILP, as well as specialized versions of 0-1 ILP. The boolean satisfiability problem (SAT), is fundamental to many fields, including Artificial Intelligence, Formal Verification, and Computer Aided Design, and can be vie...

In industry, when flexible manufacturing systems are designed within a group technology approach, numerous decision-taking processes emerge requiring control of the multiple characteristics of the system. In this context, several grouping problems are identified within the scope of combinatorial optimisation. Such is the case of the part families with precedence constraints problem, which is de...

يتحدث البحث عن العلاقات السوفيتية – الباكستانية خلال عام 1980 الذي شهد تطورات مهمة على المستوى الإقليمي والدولي لاسيما بعد الاحتلال السوفيتي لأفغانستان في 27 كانون الاول 1979، الامر زاد من توتر ابان ذلك العام وخلق ازمة سياسية علاقات البلدين ظلت اثارها مستمرة لعدة سنوات ، وقد سلط طبيعة وما صاحبها مفاوضات جرت بينهما بشأن حل الازمة الأفغانية .
 قسم الى محورين تضمن المحور الاول: ردود الفعل عقب...

Construct, Merge, Solve & Adapt (CMSA) is a recently developed algorithm for solving combinatorial optimization problems. It combines heuristic elements, such as the probabilistic generation of solutions, with an exact solver that iteratively applied to sub-instances tackled problem instance. In this paper, we present application CMSA NP-hard from family dominating set problems in undirecte...

The cutwidth minimization problem consists of finding a linear layout of a graph so that the maximum linear cut of edges (i.e., the number of edges that cut a line between consecutive vertices) is minimized. This paper starts by reviewing previous exact approaches for special classes of graphs as well as a linear integer formulation for the general problem. We propose a branch and bound algorit...

The Prize Collecting Traveling Salesman Problem (PCTSP) can be associated to a salesman that collects a prize in each city visited and pays a penalty for each city not visited, with travel costs among the cities. The objective is to minimize the sum of travel costs and penalties, while including in the tour enough cities to collect a minimum prize. This paper presents one solution procedure for...

In this paper we consider the NP-hard problem of finding a feasible solution (if any exists) for a generic MIP problem of the form min{cT x : Ax ≥ b, xj integer ∀j ∈ I}. Trivially, a feasible solution can be defined as a point x∗ ∈ P := {x : Ax ≥ b} that is equal to its rounding x̃, where the rounded point x̃ is defined by x̃j := [xj ] if j ∈ I and x̃j := xj otherwise, and [·] represents scalar rou...