A heuristic algorithm for the multi-criteria set-covering problems

AbstractA simple greedy heuristic algorithm for the multi-criteria set-covering problem is presented. This result is a multi-criteria generalization of the results established previously by Chvatal

Partitioning networks into cliques: a randomized heuristic approach

In the context of community detection in social networks, the term community can be grounded in the strict way that simply everybody should know each other within the community. We consider the corresponding community detection problem. We search for a partitioning of a network into the minimum number of non-overlapping cliques, such that the cliques cover all vertices. This problem is called the clique covering problem (CCP) and is one of the classical NP-hard problems. For CCP, we propose a randomized heuristic approach. To construct a high quality solution to CCP, we present an iterated greedy (IG) algorithm. IG can also be combined with a heuristic used to determine how far the algorithm is from the optimum in the worst case. Randomized local search (RLS) for maximum independent set was proposed to find such a bound. The experimental results of IG and the bounds obtained by RLS indicate that IG is a very suitable technique for solving CCP in real-world graphs. In addition, we summarize our basic rigorous results, which were developed for analysis of IG and understanding of its behavior on several relevant graph classes

Maximally Disjoint Solutions of the Set Covering Problem

This paper is concerned with finding two solutions of a set covering problem that have a minimum number of variables in common. We show that this problem is NP­ complete, even in the case where we are only interested in completely disjoint solutions. We describe three heuristic methods based on the standard greedy algorithm for set covering problems. Two of these algorithms find the solutions sequentially, while the third finds them simultaneously. A local search method for reducing the overlap of the two given solutions is then described. This method involves the solution of a reduced set covering problem. Finally, extensive computational tests are given demonstrating the nature of these algorithms. These tests are carried out both on randomly generated problems and on problems found in the literature

Models for the optimization of promotion campaigns: exact and heuristic algorithms.

This paper presents an optimization model for the selection of sets of clients that will receive an offer for one or more products during a promotion campaign. The complexity of the problem makes it very difficult to produce optimal solutions using standard optimization methods. We propose an alternative set covering formulation and develop a branch-and-price algorithm to solve it. We also describe five heuristics to approximate an optimal solution. Two of these heuristics are algorithms based on restricted versions of the basic formulation, the third is a successive exact k-item knapsack procedure. A heuristic inspired by the Next-Product-To-Buy model and a depth-first branch-and-price heuristic are also presented. Finally, we perform extensive computational experiments for the two formulations as well as for the five heuristics.Promotion campaign; Minimum quantity commitment; Integer programming; Branch-and-price algorithm; Non-approximability; Heuristics; Business-to-business; Business-to-consumer;

A linear programming based heuristic framework for min-max regret combinatorial optimization problems with interval costs

This work deals with a class of problems under interval data uncertainty, namely interval robust-hard problems, composed of interval data min-max regret generalizations of classical NP-hard combinatorial problems modeled as 0-1 integer linear programming problems. These problems are more challenging than other interval data min-max regret problems, as solely computing the cost of any feasible solution requires solving an instance of an NP-hard problem. The state-of-the-art exact algorithms in the literature are based on the generation of a possibly exponential number of cuts. As each cut separation involves the resolution of an NP-hard classical optimization problem, the size of the instances that can be solved efficiently is relatively small. To smooth this issue, we present a modeling technique for interval robust-hard problems in the context of a heuristic framework. The heuristic obtains feasible solutions by exploring dual information of a linearly relaxed model associated with the classical optimization problem counterpart. Computational experiments for interval data min-max regret versions of the restricted shortest path problem and the set covering problem show that our heuristic is able to find optimal or near-optimal solutions and also improves the primal bounds obtained by a state-of-the-art exact algorithm and a 2-approximation procedure for interval data min-max regret problems

A bi-objective model for emergency services location-allocation problem with maximum distance constraint

In this paper, a bi-objective mathematical model for emergency services location-allocation problem on a tree network considering maximum distance constraint is presented. The first objective function called centdian is a weighted mean of a minisum and a minimax criterion and the second one is a maximal covering criterion. For the solution of the bi-objective optimization problem, the problem is split in two sub problems: the selection of the best set of locations, and a demand assignment problem to evaluate each selection of locations. We propose a heuristic algorithm to characterize the efficient location point set on the network. Finally, some numerical examples are presented to illustrate the effectiveness of the proposed algorithms