A Simple and Effective Methodology for Generating Bounded Solutions for the Set K-Covering and Set Variable K-Covering Problems: A Guide for or Practitioners

Abstract

As generalizations of the classic set covering problem (SCP), both the set K-covering problem (SKCP) and the set variable (K varies by constraint) K-covering problem (SVKCP) are easily shown to be NP-hard. Solution approaches in the literature for the SKCP typically provide no guarantees on solution quality. In this article, a simple methodology, called the simple sequential increasing tolerance (SSIT) matheuristic, that iteratively uses any general-purpose integer programming software (Gurobi and CPLEX in this case) is discussed. This approach is shown to quickly generate solutions that are guaranteed to be within a tight tolerance of the optimum for 135 SKCPs (average of 67 seconds on a standard PC and at most 0.13% from the optimums) from the literature and 65 newly created SVKCPs. This methodology generates solutions that are guaranteed to be within a specified percentage of the optimum in a short time (actual deviation from the optimums for the 135 SKCPs was 0.03%). Statistical analyses among the five best SKCP algorithms and SSIT demonstrates that SSIT performs as well as the best published algorithms designed specifically to solve SKCPs and SSIT requires no time-consuming effort of coding problem-specific algorithms-a real plus for OR practitioners.Contribution/Originality: This study documents a methodology that iteratively uses integer programming software to efficiently generate solutions that are guaranteed to be very close to the optimums for the set Kcovering problem. A significant benefit of this methodology is that no problem specific algorithm needs to be coded by the user.

Using general-purpose integer programming software to generate bounded solutions for the multiple knapsack problem: a guide for or practitioners

“…More benefits of SSIT are detailed in [19]. Successful applications of SSIT to solve several binary integer programs (BIP) have been documented in the literature [14][15][16][17][18][19]. For these applications, SSIT typically generates solutions guaranteed to be within 0.1% of the optimums in about 60 seconds on standard PCs.…”

“…The pseudo code below summarizes the SSIT algorithm for a generic COP. More details about SSIT can be found in McNally et al [14]. SSIT Algorithm [ It is important to note that there is no need to "optimize" either the number of tolerances used or their values as well as the execution times for each tolerance.…”

Simple strategies that generate bounded solutions for the multiple‐choice multi‐dimensional knapsack problem: a guide for OR practitioners

“…Successful applications of SSIT to solve several BIPs have been documented in the literature. McNally et al (2021) was able to solve 135 set K-covering problems (SKCP) from the literature on a standard PC in an average of 67 seconds and obtained an average guaranteed bound of 0.13% from the optimums using the Gurobi software package. Statistical analyses demonstrated that these SSIT results were as good as the best published results obtained from algorithms specifically designed to solve SKCPs.…”

“…The pseudocode and Fig. 1 (McNally et al., 2021) below summarize the SSIT methodology for a generic BIP.…”

Methods to Synchronize Data in a Microservice Architecture

“…This approach involves splitting the application into separate microservices, each of which fulfills its own separate business purpose. For each microservice, there are the following characteristic requirements [1][2][3][4][5][6].…”