A Smart Structural Algorithm (SSA) Based on Infeasible Region to Solve Mixed Integer Problems

2017 ◽  
Vol 8 (1) ◽  
pp. 24-44 ◽  
Author(s):  
Mohammad Hassan Salmani ◽  
Kourosh Eshghi
Keyword(s):  
Heuristic Algorithm ◽  
Feasible Solution ◽  
Heuristic Algorithms ◽  
Optimization Problems ◽  
Mixed Integer ◽  
Feasible Region ◽  
Limited Area ◽  
Objective Functions ◽  
Fields Of Study ◽  
Best Value

Optimization is an important fields of study in science where researchers seek to make the best and most practical decisions. Solving real optimization problems is an intractable issue which calls for generating an approximate using meta-heuristic algorithms. This study proposes a meta-heuristic algorithm which mainly searches the infeasible region. In this approach, the authors start from an infeasible solution, and while they try to get near to the feasible region, they ensure that the best value is kept for the objective function. The algorithm examines the space in such terms as Infeasibility and Objective Functions, Neighborhood Limited Area, Random Smart Points, and the calculation of new solutions. The algorithm can convert an infeasible solution to an appropriate corresponding feasible solution by applying a simple mathematical methodology. Finally, to test the efficiency of our algorithm, a sample random MIP problem and a hard benchmark TSP instance are solved and discussed in detail.

Using Chemotherapy Science Algorithm (CSA) to Solve the Knapsack Problem

2018 ◽  
Vol 7 (1) ◽  
pp. 86-103
Author(s):  
Mohammad Hassan Salmani ◽  
Kourosh Eshghi
Keyword(s):  
Cell Size ◽  
Knapsack Problem ◽  
Heuristic Algorithm ◽  
Heuristic Algorithms ◽  
Optimization Problems ◽  
Cell Area ◽  
Collateral Damage ◽  
Cell Position ◽  
Feasible Solutions

Optimization, which, by definition, can help one find the best solution from all feasible solutions, has sometimes been an interesting and important area for research in science. Solving real and hard optimization problems calls for developing approximate, heuristic, and meta-heuristic algorithms. In this article, a new meta-heuristic algorithm is proposed on the basis of the chemotherapy method to cure cancers – this algorithm mainly searches the infeasible region. As in chemotherapy, this algorithm tries to kill unsatisfactory (especially infeasible) solutions (cancers cells); however, collateral damage is sometimes inevitable – some healthy, innocuous, and good cells might be targeted as well. Also, different conceptual terms including Cell Size, Cell Position, Cell Area, and Random Cells are presented and defined in this article. Furthermore, Chemotherapy Science Algorithm (CSA) and its structure are tested based on benchmark Knapsack Problem. Reported results show the efficiency of the proposed algorithm.

scholarly journals Application of Heuristic and Metaheuristic Algorithms in Solving Constrained Weber Problem with Feasible Region Bounded by Arcs

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
Igor Stojanović ◽  
Ivona Brajević ◽  
Predrag S. Stanimirović ◽  
Lev A. Kazakovtsev ◽  
Zoran Zdravev
Keyword(s):  
Heuristic Algorithm ◽  
Optimization Problems ◽  
Continuous Optimization ◽  
Facility Location Problem ◽  
Metaheuristic Algorithms ◽  
Feasible Region ◽  
Weber Problem ◽  
Bee Colony ◽  
Feasible Solutions ◽  
Weiszfeld Procedure

The continuous planar facility location problem with the connected region of feasible solutions bounded by arcs is a particular case of the constrained Weber problem. This problem is a continuous optimization problem which has a nonconvex feasible set of constraints. This paper suggests appropriate modifications of four metaheuristic algorithms which are defined with the aim of solving this type of nonconvex optimization problems. Also, a comparison of these algorithms to each other as well as to the heuristic algorithm is presented. The artificial bee colony algorithm, firefly algorithm, and their recently proposed improved versions for constrained optimization are appropriately modified and applied to the case study. The heuristic algorithm based on modified Weiszfeld procedure is also implemented for the purpose of comparison with the metaheuristic approaches. Obtained numerical results show that metaheuristic algorithms can be successfully applied to solve the instances of this problem of up to 500 constraints. Among these four algorithms, the improved version of artificial bee algorithm is the most efficient with respect to the quality of the solution, robustness, and the computational efficiency.

scholarly journals Analysis of a constructive matheuristic for the traveling umpire problem

2019 ◽  
Vol 15 (1) ◽  
pp. 41-57 ◽  
Author(s):  
Reshma Chirayil Chandrasekharan ◽  
Túlio A.M. Toffolo ◽  
Tony Wauters
Keyword(s):  
Optimization Problem ◽  
Feasible Solution ◽  
Heuristic Algorithms ◽  
Major League Baseball ◽  
Design Parameters ◽  
Objective Functions ◽  
Hard Constraints ◽  
Benchmark Instances ◽  
Feasible Solutions ◽  
Single Objective

Abstract The Traveling Umpire Problem (TUP) is a combinatorial optimization problem concerning the assignment of umpires to the games of a fixed double round-robin tournament. The TUP draws inspiration from the real world multi-objective Major League Baseball (MLB) umpire scheduling problem, but is, however, restricted to the single objective of minimizing total travel distance of the umpires. Several hard constraints are employed to enforce fairness when assigning umpires, making it a challenging optimization problem. The present work concerns a constructive matheuristic approach which focuses primarily on large benchmark instances. A decomposition-based approach is employed which sequentially solves Integer Programming (IP) formulations of the subproblems to arrive at a feasible solution for the entire problem. This constructive matheuristic efficiently generates feasible solutions and improves the best known solutions of large benchmark instances of 26, 28, 30 and 32 teams well within the benchmark time limit. In addition, the algorithm is capable of producing feasible solutions for various small and medium benchmark instances competitive with those produced by other heuristic algorithms. The paper also details experiments conducted to evaluate various algorithmic design parameters such as subproblem size, overlap and objective functions.

scholarly journals Anthropic Principle Algorithm:A new Heuristic Optimization Meth

2018 ◽  
Vol 1 (1) ◽  
Author(s):  
Elder Oroski ◽  
Pês S. Beatriz ◽  
Lopez H. Rafael ◽  
Bauchspiess Adolfo
Keyword(s):  
Genetic Algorithm ◽  
System Identification ◽  
Heuristic Algorithm ◽  
Heuristic Algorithms ◽  
Optimization Problems ◽  
Anthropic Principle ◽  
Optimization Process ◽  
Heuristic Optimization ◽  
The Universe ◽  
Made In

Heuristic optimization is an appealing method for solving some en- gineering problems, in which gradient information may not be available, or yet, when the problem presents many minima points. Thus, the goal of this paper is to present a new heuristic algorithm based on the Anthropic Prin- ciple, the Anthropic Principle Algorithm (APA). This algorithm is based on the following idea: the universe developed itself in the exact way to allow the existence of all current things, including life. This idea is very similar to the convergence in an optimization process. Arguing about the merit of the An- thropic Principle is not among the goals of this paper. This principle is treated only as an inspiration for heuristic optimization algorithms. In the final of the paper, some applications of the APA are presented. Classical problems such as Rosenbrock function minimization, system identification examples and min- imization of some benchmark functions are also presented. In order to vali- date the APA’s functionality, a comparison between the APA and the classic heuristic algorithms, Genetic Algorithm (GA) and Particle Swarm Optimiza- tion (PSO) is made. In this comparison, the APA presented better results in majority of tested cases, proving that it has a great potential for application in optimization problems.

scholarly journals Branch-and-Bound for Biobjective Mixed-Integer Linear Programming

2021 ◽  
Author(s):  
Nathan Adelgren ◽  
Akshay Gupte
Keyword(s):  
Branch And Bound ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Splitting Method ◽  
Mixed Integer ◽  
Feasible Region ◽  
Decision Space ◽  
Conflicting Objectives ◽  
Objective Space ◽  
Single Objective

We present a generic branch-and-bound algorithm for finding all the Pareto solutions of a biobjective mixed-integer linear program. The main contributions are new algorithms for obtaining dual bounds at a node, checking node fathoming, presolve, and duality gap measurement. Our branch-and-bound is predominantly a decision space search method because the branching is performed on the decision variables, akin to single objective problems, although we also sometimes split gaps and branch in the objective space. The various algorithms are implemented using a data structure for storing Pareto sets. Computational experiments are carried out on literature instances and on a new set of instances that we generate using a benchmark library (MIPLIB2017) for single objective problems. We also perform comparisons against the triangle splitting method from literature, which is an objective space search algorithm. Summary of Contribution: Biobjective mixed-integer optimization problems have two linear objectives and a mixed-integer feasible region. Such problems have many applications in operations research, because many real-world optimization problems naturally comprise two conflicting objectives to optimize or can be approximated in such a manner and are even harder than single objective mixed-integer programs. Solving them exactly requires the computation of all the nondominated solutions in the objective space, whereas some applications may also require finding at least one solution in the decision space corresponding to each nondominated solution. This paper provides an exact algorithm for solving these problems using the branch-and-bound method, which works predominantly in the decision space. Of the many ingredients of this algorithm, some parts are direct extensions of the single-objective version, but the main parts are newly designed algorithms to handle the distinct challenges of optimizing over two objectives. The goal of this study is to improve solution quality and speed and show that decision-space algorithms perform comparably to, and sometimes better than, algorithms that work mainly in the objective-space.

scholarly journals Heuristic Algorithms for Solving Multiobjective Transportation Problems

2016 ◽  
Vol 8 (3) ◽  
pp. 1
Author(s):  
Ali Musaddak Delphi
Keyword(s):  
Heuristic Algorithm ◽  
Heuristic Algorithms ◽  
Flow Time ◽  
Total Tardiness ◽  
Objective Functions ◽  
Total Flow ◽  
Late Work ◽  
Transportation Problems ◽  
Total Flow Time

<p>In this paper, we proposed three heuristic algorithms to solve multiobjective transportation problems, the first heuristic algorithm used to minimize two objective functions (total flow time and total late work), the second one used to minimize two objective functions (total flow time and total tardiness) and the last one used to minimize three objective functions (total flow time, total late work and total tardiness), where these heuristic algorithms which is different from to another existing algorithms and providing the support to decision markers for handing time oriented problems.</p>

scholarly journals A MILP Model for a Byzantine Fault Tolerant Blockchain Consensus

2020 ◽  
Vol 12 (11) ◽  
pp. 185
Author(s):  
Vitor Nazário Coelho ◽  
Rodolfo Pereira Araújo ◽  
Haroldo Gambini Santos ◽  
Wang Yong Qiang ◽  
Igor Machado Coelho
Keyword(s):  
Optimization Problems ◽  
Programming Model ◽  
Fault Tolerant ◽  
State Of The Art ◽  
Mixed Integer ◽  
Maximization Problem ◽  
Objective Functions ◽  
Objective Model ◽  
Adversarial Model ◽  
Algebraic Proofs

Mixed-integer mathematical programming has been widely used to model and solve challenging optimization problems. One interesting feature of this technique is the ability to prove the optimality of the achieved solution, for many practical scenarios where a linear programming model can be devised. This paper explores its use to model very strong Byzantine adversaries, in the context of distributed consensus systems. In particular, we apply the proposed technique to find challenging adversarial conditions on a state-of-the-art blockchain consensus: the Neo dBFT. Neo Blockchain has been using the dBFT algorithm since its foundation, but, due to the complexity of the algorithm, it is challenging to devise definitive algebraic proofs that guarantee safety/liveness of the system (and adjust for every change proposed by the community). Core developers have to manually devise and explore possible adversarial attacks scenarios as an exhaustive task. The proposed multi-objective model is intended to assist the search of possible faulty scenario, which includes three objective functions that can be combined as a maximization problem for testing one-block finality or a minimization problem for ensuring liveness. Automated graphics help developers to visually observe attack conditions and to quickly find a solution. This paper proposes an exact adversarial model that explores current limits for practical blockchain consensus applications such as dBFT, with ideas that can also be extended to other decentralized ledger technologies.

scholarly journals An Efficient Framework for Multi-Objective Risk-Informed Decision Support Systems for Drainage Rehabilitation

2020 ◽  
Vol 25 (4) ◽  
pp. 73
Author(s):  
Xiatong Cai ◽  
Abdolmajid Mohammadian ◽  
Hamidreza Shirkhani
Keyword(s):  
Optimization Problems ◽  
Drainage System ◽  
Mixed Integer ◽  
Engineering Optimization ◽  
Continuous Variables ◽  
Objective Functions ◽  
Multi Objective Optimization ◽  
Integer Optimization ◽  
Framework Structure ◽  
Multi Objective

Combining multiple modules into one framework is a key step in modelling a complex system. In this study, rather than focusing on modifying a specific model, we studied the performance of different calculation structures in a multi-objective optimization framework. The Hydraulic and Risk Combined Model (HRCM) combines hydraulic performance and pipe breaking risk in a drainage system to provide optimal rehabilitation strategies. We evaluated different framework structures for the HRCM model. The results showed that the conventional framework structure used in engineering optimization research, which includes (1) constraint functions; (2) objective functions; and (3) multi-objective optimization, is inefficient for drainage rehabilitation problem. It was shown that the conventional framework can be significantly improved in terms of calculation speed and cost-effectiveness by removing the constraint function and adding more objective functions. The results indicated that the model performance improved remarkably, while the calculation speed was not changed substantially. In addition, we found that the mixed-integer optimization can decrease the optimization performance compared to using continuous variables and adding a post-processing module at the last stage to remove the unsatisfying results. This study (i) highlights the importance of the framework structure inefficiently solving engineering problems, and (ii) provides a simplified efficient framework for engineering optimization problems.

Comparison of Meta-heuristic Algorithms on Benchmark Functions

2019 ◽  
Vol 2 (3) ◽  
pp. 508-517
Author(s):  
FerdaNur Arıcı ◽  
Ersin Kaya
Keyword(s):  
Heuristic Algorithms ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Optimization Algorithms ◽  
Gravitational Search Algorithm ◽  
Differential Evolution Algorithm ◽  
Population Based ◽  
Time Interval ◽  
Bee Colony ◽  
Different Characteristics

Optimization is a process to search the most suitable solution for a problem within an acceptable time interval. The algorithms that solve the optimization problems are called as optimization algorithms. In the literature, there are many optimization algorithms with different characteristics. The optimization algorithms can exhibit different behaviors depending on the size, characteristics and complexity of the optimization problem. In this study, six well-known population based optimization algorithms (artificial algae algorithm - AAA, artificial bee colony algorithm - ABC, differential evolution algorithm - DE, genetic algorithm - GA, gravitational search algorithm - GSA and particle swarm optimization - PSO) were used. These six algorithms were performed on the CEC&amp;rsquo;17 test functions. According to the experimental results, the algorithms were compared and performances of the algorithms were evaluated.

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