scholarly journals An optimal solution for the budgets assignment problem

2021 ◽  
Author(s):  
Mahdi Jemmali
Keyword(s):  
Experimental Study ◽  
Community Development ◽  
Lower Bounds ◽  
Branch And Bound ◽  
Optimal Solution ◽  
Service Organizations ◽  
Hard Problem ◽  
Branch And Bound Algorithms ◽  
Np Hard Problem ◽  
Developmental Role

Municipalities are service organizations that have a major role in strategic planning and community development that consider the future changes and society developments, by implementing set of projects with pre-allocated budgets. Projects have standards, budgets and constraints that differ from one community to another and from one city to another. Fair distributing of different projects to municipalities, while ensuring the provision of various capabilities to reach developmental role is NP-Hard problem. Assuming that all municipalities have the same strategic characteristics. The problem is as follows: given a set of projects with different budgets, how to distribute all projects to all municipalities with a minimum budget gap between municipalities. To derive equity distribution between municipalities, this paper developed lower bounds and eleven heuristics to be utilized in the branch-and-bound algorithms. The performance of the developed heuristics, lower bounds and the exact solutions are presented in the experimental study.

Is optimal solution of every NP-complete or NP-hard problem determined from its characteristic for DNA-based computing

Biosystems ◽  
2005 ◽  
Vol 80 (1) ◽  
pp. 71-82 ◽  
Author(s):  
Minyi Guo ◽  
Weng-Long Chang ◽  
Machael Ho ◽  
Jian Lu ◽  
Jiannong Cao
Keyword(s):  
Optimal Solution ◽  
Hard Problem ◽  
Np Hard ◽  
Np Hard Problem ◽  
Np Complete

A SIMPLE LOWER BOUND FOR TOTAL COMPLETION TIME MINIMIZATION IN A TWO-MACHINE FLOWSHOP

2005 ◽  
Vol 22 (03) ◽  
pp. 391-407 ◽  
Author(s):  
B. M. T. LIN ◽  
J. M. WU
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Branch And Bound ◽  
Completion Time ◽  
Computational Study ◽  
Total Completion Time ◽  
Optimal Solutions ◽  
Branch And Bound Algorithms ◽  
Time Minimization ◽  
Input Instance

The purpose of this study is to present a simple lower bound to facilitate the development of branch-and-bound algorithms for the minimization of total completion time in a two-machine flowshop. The studied problem is known to be strongly NP-hard. In the literature, several lower bounds have been proposed. The bounding technique addressed in this paper is based upon a concept about rearrangement of the parameters of the input instance. The technique is intrinsically simple for computer implementations. We conduct computational experiments for problems with 10–65 jobs. Numerical results from our computational study indicate that the new scheme is very effective in reducing the execution time needed for composing optimal solutions.

ON THE EFFECTIVENESS OF SYNCHRONOUS PARALLEL BRANCH-AND-BOUND ALGORITHMS

1995 ◽  
Vol 05 (03) ◽  
pp. 375-386 ◽  
Author(s):  
RICARDO CORRÊA ◽  
AFONSO FERREIRA
Keyword(s):  
Branch And Bound ◽  
Original Problem ◽  
Optimal Solution ◽  
Memory Model ◽  
Branch And Bound Algorithms ◽  
Parallel Version ◽  
Efficiency Measures ◽  
Parallel Branch And Bound ◽  
High Level ◽  
Work Done

We theoretically compare the efficiency of two versions, sequential and parallel (synchronous), of the method called branch-and-bound used for searching for an optimal solution in the scope of combinatorial optimization. The sequential version consists of successive decompositions of the original problem in smaller disjoint subproblems and its parallel version consists of a high level parallelization that assumes a shared memory model of parallel computation. Its principle consists of decomposing several subproblems in parallel at each iteration in a synchronous way, and its efficiency is usually defined with respect to its sequential counterpart. In this paper, we redefine the notion of efficiency in such a way that the usefulness of the work done by each processor will be taken into account. The knapsack problem is used as an application and some simulation results are presented to validate and illustrate the use of the new efficiency measures.

scholarly journals Interval Tests and Contractors Based on Optimality Conditions for Bound-Constrained Global Optimization

2020 ◽  
Vol 29 (03n04) ◽  
pp. 2060001
Author(s):  
Laurent Granvilliers
Keyword(s):  
Experimental Study ◽  
Optimality Conditions ◽  
Branch And Bound ◽  
Global Optimum ◽  
Constrained Global Optimization ◽  
First Order ◽  
Branch And Bound Algorithms ◽  
Complete Search ◽  
Monotonicity Test ◽  
Interval Branch And Bound

We study the problem of finding the global optimum of a nonlinear real function over an interval box by means of complete search techniques, namely interval branch-and-bound algorithms. Such an algorithm typically generates a tree of boxes from the initial box by alternating branching steps and contraction steps in order to remove non optimal sub-boxes. In this paper, we introduce a new contraction method that is designed to handle the boundary of the initial box where a minimizer may not be a stationary point. This method exploits the first-order optimality conditions and we show that it subsumes the classical monotonicity test based on interval arithmetic. A new branch-and-bound algorithm has been implemented in the interval solver Realpaver. An extensive experimental study based on a set of standard benchmarks is presented.

Determining Production Schedule with Resource Constraints Using Drum-Buffer-Rope (DBR) Approach

2012 ◽  
Vol 488-489 ◽  
pp. 1130-1133 ◽  
Author(s):  
Ping Yu Chang
Keyword(s):  
Mathematical Model ◽  
Production Scheduling ◽  
Feasible Solution ◽  
Resource Constraints ◽  
Optimal Solution ◽  
Hard Problem ◽  
Improve Quality ◽  
Production Schedule ◽  
Np Hard Problem ◽  
Wafer Manufacturing

In wafer plants, product will be manufactured through same process with different setups and specifications. This special manufacturing process is described as re-entrant flows. In photo process of wafer manufacturing, products is also restricted to be processed through same machine in each reentrance to improve quality. This phenomenon will cause scheduling in photo process being complicated and is proved to be a NP-hard problem. This research develops a mathematical model for photo process to minimize the makespan. A feasible solution is achieved using DBR (drum-buffer-rope) method. The results are compared to the optimal solution that is achieved using branch and bound algorithm. Our results show that DBR based method achieves a near optimal solution in shorter time. The results also indicate that DBR method can be useful in production scheduling with resource constraints.

Perspective Reformulations of Semicontinuous Quadratically Constrained Quadratic Programs

2020 ◽  
Author(s):  
Xiaojin Zheng ◽  
Yutong Pan ◽  
Zhaolin Hu
Keyword(s):  
Lower Bounds ◽  
Branch And Bound ◽  
Strong Duality ◽  
Computational Experiments ◽  
Quadratic Programs ◽  
Branch And Bound Algorithms ◽  
Study Perspective ◽  
Lifting Techniques ◽  
Quadratically Constrained

We study perspective reformulations (PRs) of semicontinuous quadratically constrained quadratic programs (SQCQPs) in this paper. Based on perspective functions, we first propose a class of PRs for SQCQPs and discuss how to find the best PR in this class via strong duality and lifting techniques. We then study the properties of the PR class and relate them to alternative formulations that are used to derive lower bounds for SQCQPs. Finally, we embed the PR bounds in branch-and-bound algorithms and conduct computational experiments to illustrate the effectiveness of the proposed approach.

scholarly journals Revisiting Traveling Salesman Problem (TSP): Analysis of GA and SA based Solutions

2021 ◽  
Vol 9 (2) ◽  
pp. 44
Author(s):  
Darius Bethel ◽  
Hakki Erhan Sevil
Keyword(s):  
Genetic Algorithm ◽  
Traveling Salesman Problem ◽  
Optimal Solution ◽  
Comprehensive Analysis ◽  
Traveling Salesman ◽  
Parameter Analysis ◽  
Hard Problem ◽  
Shortest Route ◽  
Original Contribution ◽  
Np Hard Problem

The purpose of this study to analyze genetic algorithm (GA) and simulated an-nealing (SA) based approaches applied to well-known Traveling Salesman Prob-lem (TSP). As a NP-Hard problem, the goal of TSP is to find the shortest route possible to travel all the cities, given a set of cities and distances between cities. In order to solve the problem and achieve the optimal solution, all permutations need to be checked, which gets exponentially large as more cities are added. Our aim in this study is to provide comprehensive analysis of TSP solutions based on two methods, GA and SA, in order to find a near optimal solution for TSP. The re-sults of the simulations show that although the SA executed with faster comple-tion times comparing to GA, it took more iterations to find a solution. Additional-ly, GA solutions are significantly more accurate than SA solutions, where GA found a solution in relatively less iterations. The original contribution of this study is that GA based solution as well as SA based solution are developed to perform comprehensive parameter analysis. Further, a quantifiable comparison is provided for the results from each parameter analysis of GA and SA in terms of performance of solving TSP.

scholarly journals Implementation of discrete particle swarm optimization algorithm in the capacitated vehicle routing problem

2020 ◽  
Vol 4 (2) ◽  
pp. 117-128
Author(s):  
Aisyahna Nurul Mauliddina ◽  
Faris Ahmad Saifuddin ◽  
Adesatya Lentera Nagari ◽  
Anak Agung Ngurah Perwira Redi ◽  
Adji Candra Kurniawan ◽  
...  
Keyword(s):  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Optimal Solution ◽  
Computational Time ◽  
Hard Problem ◽  
Np Hard ◽  
Routing Problem ◽  
Capacitated Vehicle Routing Problem ◽  
Np Hard Problem ◽  
Capacitated Vehicle

Capacitated Vehicle Routing Problem (CVRP) is known as an NP-hard problem. It is because CVRP problems are very hard for finding optimal solutions, especially in large instances. In general, the NP-hard problem is difficult to solve in the exact method, so the metaheuristic approach is implemented in the CVRP problem to find a near-optimal solution in reasonable computational time. This research uses the DPSO algorithm for solving CVRP with ten instances of benchmark datasets. DPSO implementation uses tuning parameters with the One Factor at Time (OFAT) method to select the best DPSO parameters. The outcome objective function will be compared with several PSO models proposed in previous studies. Statistical test using One Way Reputed Measure ANOVA is needed to compare algorithm performance. First, ANOVA uses for comparing’s results. Then, ANOVA is also used to test DPSO’s performance compared with DPSO-SA, SR-1, and SR-2 algorithm. The computational result shows that the basic DPSO algorithm not competitive enough with other methods for solving CVRP.

Sign in / Sign up

Export Citation Format

Share Document