The Robustness of Two Common Heuristics for the p-Median Problem

1979 ◽  
Vol 11 (4) ◽  
pp. 373-380 ◽  
Author(s):  
K E Rosing ◽  
E L Hillsman ◽  
Hester Rosing-Vogelaar
Keyword(s):  
Heuristic Algorithms ◽  
Test Problems ◽  
Optimal Solutions ◽  
Problem Size ◽  
Median Problem ◽  
Robust Tests

Optimal p-median solutions were computed for six test problems on a network of forty-nine demand nodes and compared with solutions from two heuristic algorithms. Comparison of the optimal solutions with those from the Teitz and Bart heuristic indicates that this heuristic is very robust. Tests of the Maranzana heuristic, however, indicate that it is efficient only for small values of p (numbers of facilities) and that its robustness decreases rapidly as problem size increases.

Solving Clique Partitioning Problems: A Comparison of Models and Commercial Solvers

2021 ◽  
pp. 1-23
Author(s):  
Yu Du ◽  
Gary Kochenberger ◽  
Fred Glover ◽  
Haibo Wang ◽  
Mark Lewis ◽  
...  
Keyword(s):  
Linear Model ◽  
Quadratic Model ◽  
Problem Instance ◽  
Test Problems ◽  
Optimal Solutions ◽  
Problem Size ◽  
Clique Partitioning ◽  
Huge Impact ◽  
Partitioning Problems ◽  
The Right

Finding good solutions to clique partitioning problems remains a computational challenge. With rare exceptions, finding optimal solutions for all but small instances is not practically possible. However, choosing the most appropriate modeling structure can have a huge impact on what is practical to obtain from exact solvers within a reasonable amount of run time. Commercial solvers have improved tremendously in recent years and the combination of the right solver and the right model can significantly increase our ability to compute acceptable solutions to modest-sized problems with solvers like CPLEX, GUROBI and XPRESS. In this paper, we explore and compare the use of three commercial solvers on modest sized test problems for clique partitioning. For each problem instance, a conventional linear model from the literature and a relatively new quadratic model are compared. Extensive computational experience indicates that the quadratic model outperforms the classic linear model as problem size grows.

Multi-objective integrated planning and scheduling model for operating rooms under uncertainty

2018 ◽  
Vol 232 (9) ◽  
pp. 930-948 ◽  
Author(s):  
Javad Ansarifar ◽  
Reza Tavakkoli-Moghaddam ◽  
Faezeh Akhavizadegan ◽  
Saman Hassanzadeh Amin
Keyword(s):  
Genetic Algorithm ◽  
Decision Making ◽  
Particle Swarm Optimization ◽  
Heuristic Algorithms ◽  
Particle Swarm ◽  
Operating Rooms ◽  
Programming Approach ◽  
Test Problems ◽  
Swarm Optimization ◽  
Multi Objective

This article formulates the operating rooms considering several constraints of the real world, such as decision-making styles, multiple stages for surgeries, time windows for resources, and specialty and complexity of surgery. Based on planning, surgeries are assigned to the working days. Then, the scheduling part determines the sequence of surgeries per day. Moreover, an integrated fuzzy possibilistic–stochastic mathematical programming approach is applied to consider some sources of uncertainty, simultaneously. Net revenues of operating rooms are maximized through the first objective function. Minimizing a decision-making style inconsistency among human resources and maximizing utilization of operating rooms are considered as the second and third objectives, respectively. Two popular multi-objective meta-heuristic algorithms including Non-dominated Sorting Genetic Algorithm and Multi-Objective Particle Swarm Optimization are utilized for solving the developed model. Moreover, different comparison metrics are applied to compare the two proposed meta-heuristics. Several test problems based on the data obtained from a public hospital located in Iran are used to display the performance of the model. According to the results, Non-dominated Sorting Genetic Algorithm-II outperforms the Multi-Objective Particle Swarm Optimization algorithm in most of the utilized metrics. Moreover, the results indicate that our proposed model is more effective and efficient to schedule and plan surgeries and assign resources than manual scheduling.

scholarly journals Layout optimization of simplified trusses using mixed integer linear programming with runtime generation of constraints

2020 ◽  
Vol 61 (5) ◽  
pp. 1977-1999
Author(s):  
H. Fairclough ◽  
M. Gilbert
Keyword(s):  
Linear Programming ◽  
Integer Linear Programming ◽  
Mixed Integer Linear Programming ◽  
Geometry Optimization ◽  
Layout Optimization ◽  
Mixed Integer ◽  
Optimal Solutions ◽  
Problem Size ◽  
Solution Quality ◽  
Starting Point

AbstractTraditional truss layout optimization employing the ground structure method will often generate layouts that are too complex to fabricate in practice. To address this, mixed integer linear programming can be used to enforce buildability constraints, leading to simplified truss forms. Limits on the number of joints in the structure and/or the minimum angle between connected members can be imposed, with the joints arising from crossover of pairs of members accounted for. However, in layout optimization, the number of constraints arising from ‘crossover joints’ increases rapidly with problem size, along with computational expense. To address this, crossover constraints are here dynamically generated and added at runtime only as required (so-called lazy constraints); speedups of more than 20 times are observed whilst ensuring that there is no loss of solution quality. Also, results from the layout optimization step are shown to provide a suitable starting point for a non-linear geometry optimization step, enabling results to be obtained that are in agreement with literature solutions. It is also shown that symmetric problems may not have symmetric optimal solutions, and that multiple distinct and equally optimal solutions may be found.

DECOMPOSITION ALGORITHMS FOR THE INTERVAL SCHEDULING PROBLEM

2010 ◽  
Vol 27 (04) ◽  
pp. 517-537 ◽  
Author(s):  
SHIDONG WANG ◽  
LI ZHENG ◽  
ZHIHAI ZHANG
Keyword(s):  
Large Scale ◽  
Heuristic Algorithms ◽  
Integer Program ◽  
Computational Effort ◽  
Small Scale ◽  
Test Problems ◽  
Decomposition Algorithms ◽  
Scheduling Problem ◽  
Interval Scheduling ◽  
Average Percentage

Scheduling track lines at a marshalling station where the objective is to determine the maximal weighted number of trains on the track lines can be modeled as an interval scheduling problem: each job has a fixed starting and finishing time and can only be carried out by an arbitrarily given subset of machines. This scheduling problem is formulated as an integer program, which is NP-Complete when the number of machines and jobs are unfixed and the computational effort to solve large scale test problems is prohibitively large. Heuristic algorithms (HAs) based on the decomposition of original problem have been developed and the benefits lie in both conceptual simplicity and computational efficiency. Genetic algorithm (GA) to address the scheduling problem is also proposed. Computational experiments on low and high utilization rates of machines are carried out to compare the performance of the proposed algorithms with Cplex. Computational results show that the HAs and GA perform well in most condition, especially HA2 with the maximum of average percentage deviation on average 3.5% less than the optimal solutions found by Cplex in small-scale problem. Our methodologies are capable of producing improved solutions to large-scale problems with reasonable computing resources, too.

Computational Complexity Analysis of Selective Breeding Algorithm

2014 ◽  
Vol 591 ◽  
pp. 172-175
Author(s):  
M. Chandrasekaran ◽  
P. Sriramya ◽  
B. Parvathavarthini ◽  
M. Saravanamanikandan
Keyword(s):  
Computational Complexity ◽  
Selective Breeding ◽  
Heuristic Algorithms ◽  
Complexity Analysis ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Approximate Solutions ◽  
Problem Size ◽  
Combinatorial Optimization Problems ◽  
Complete Problems

In modern years, there has been growing importance in the design, analysis and to resolve extremely complex problems. Because of the complexity of problem variants and the difficult nature of the problems they deal with, it is arguably impracticable in the majority time to build appropriate guarantees about the number of fitness evaluations needed for an algorithm to and an optimal solution. In such situations, heuristic algorithms can solve approximate solutions; however suitable time and space complication take part an important role. In present, all recognized algorithms for NP-complete problems are requiring time that's exponential within the problem size. The acknowledged NP-hardness results imply that for several combinatorial optimization problems there are no efficient algorithms that realize a best resolution, or maybe a close to best resolution, on each instance. The study Computational Complexity Analysis of Selective Breeding algorithm involves both an algorithmic issue and a theoretical challenge and the excellence of a heuristic.

Evaluating the ε-Domination Based Multi-Objective Evolutionary Algorithm for a Quick Computation of Pareto-Optimal Solutions

2005 ◽  
Vol 13 (4) ◽  
pp. 501-525 ◽  
Author(s):  
Kalyanmoy Deb ◽  
Manikanth Mohan ◽  
Shikhar Mishra
Keyword(s):  
Steady State ◽  
Evolutionary Algorithm ◽  
Optimization Problems ◽  
Computational Time ◽  
Test Problems ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Nsga Ii ◽  
Multi Objective

Since the suggestion of a computing procedure of multiple Pareto-optimal solutions in multi-objective optimization problems in the early Nineties, researchers have been on the look out for a procedure which is computationally fast and simultaneously capable of finding a well-converged and well-distributed set of solutions. Most multi-objective evolutionary algorithms (MOEAs) developed in the past decade are either good for achieving a well-distributed solutions at the expense of a large computational effort or computationally fast at the expense of achieving a not-so-good distribution of solutions. For example, although the Strength Pareto Evolutionary Algorithm or SPEA (Zitzler and Thiele, 1999) produces a much better distribution compared to the elitist non-dominated sorting GA or NSGA-II (Deb et al., 2002a), the computational time needed to run SPEA is much greater. In this paper, we evaluate a recently-proposed steady-state MOEA (Deb et al., 2003) which was developed based on the ε-dominance concept introduced earlier (Laumanns et al., 2002) and using efficient parent and archive update strategies for achieving a well-distributed and well-converged set of solutions quickly. Based on an extensive comparative study with four other state-of-the-art MOEAs on a number of two, three, and four objective test problems, it is observed that the steady-state MOEA is a good compromise in terms of convergence near to the Pareto-optimal front, diversity of solutions, and computational time. Moreover, the ε-MOEA is a step closer towards making MOEAs pragmatic, particularly allowing a decision-maker to control the achievable accuracy in the obtained Pareto-optimal solutions.

scholarly journals Multi-Objective Location-Allocation-Routing Problem of Perishable Multi-Product Supply Chain With Direct Shipment and Open Routing Possibilities Under Sustainability

2021 ◽  
Author(s):  
Ali Mahmoodirad ◽  
Behzad Aghaei Fishani ◽  
Sadegh Niroomand ◽  
Mohammad Fallah
Keyword(s):  
Supply Chain ◽  
Social Impact ◽  
Heuristic Algorithms ◽  
Supply Chain Design ◽  
Grey Wolf Optimizer ◽  
Test Problems ◽  
Perishable Products ◽  
Heuristic Solution ◽  
Routing Problem ◽  
Multi Objective

Abstract In this study a multi-objective formulation is proposed for designing a supply chain of perishable products including suppliers, plants, distributors, and customers under sustainable development. In addition to the studies of the literature, direct shipment between producers and customers and also alternative products possibility are allowed. In this problem the objectives like facilities establishment costs, transportation costs, negative environmental impacts, and social impact (fixed and variable employment rates) are optimized simultaneously. As in real situations, most of the transportation activities of such supply chain are performed by hiring transportation devices, the open routing logic is applied to form the travelling path of each hired transportation device. Furthermore, the possibility of direct shipment from the plants to the customers is considered in order to increase profitability of the plants. Because of the NP-hard nature of the supply chain design problems, some meta-heuristic solution approaches of the literature are modified to multi-objective form and applied to solve the problem. Several test problems from small to large sizes are generated randomly to evaluate the meta-heuristic algorithms. As a result, among the proposed algorithms, the multi-objective grey wolf optimizer (MGWO) perform better than others by considering four well-known evaluation metrics. At the end, a case study from perishable products supply chain of Iran is solved and analyzed to show the applicability of the proposed problem.

A Preference-Based Multiobjective Evolutioary Algorithm for Finding Knee Solutions

2015 ◽  
Vol 781 ◽  
pp. 559-563 ◽  
Author(s):  
Sufian Sudeng ◽  
Naruemon Wattanapongsakorn
Keyword(s):  
Evolutionary Algorithm ◽  
Decision Maker ◽  
Test Problems ◽  
Optimal Solutions ◽  
View Point ◽  
Controller Parameter ◽  
Multi Objective

The aim of this paper is to develop a knee-based Multi-Objective Evolutionary Algorithm (MOEA) which is a method to find optimal solutions focusing on knee regions. The knee solutions are very interesting to the decision maker (DM) when he/she does not have an explicit preference. The proposed approach uses the extended angle-based dominance concept to guide the search towards knee regions. The extent of the obtained solutions can be controlled by the means of user-supplied density controller parameter. The approach is demonstrated with two and three-objective knee-based test problems. The results have shown that our approach is competitive to well-known knee-based MOEAs in convergence view point.

Meta-Heuristic Structure for Multiobjective Optimization Case Study

2014 ◽  
pp. 38-58
Author(s):  
T. Ganesan ◽  
I. Elamvazuthi ◽  
K. Z. KuShaari ◽  
P. Vasant
Keyword(s):  
Performance Metrics ◽  
Heuristic Algorithms ◽  
Weighted Sum ◽  
Optimal Solutions ◽  
Green Sand ◽  
Weighted Sum Method ◽  
Real World Problem ◽  
Green Sand Mould System

In engineering optimization, one often encounters scenarios that are multiobjective (MO) where each of the objectives covers different aspects of the problem. It is hence critical for the engineer to have multiple solution choices before selecting of the best solution. In this chapter, an approach that merges meta-heuristic algorithms with the weighted sum method is introduced. Analysis on the solution set produced by these algorithms is carried out using performance metrics. By these procedures, a novel chaos-based metaheuristic algorithm, the Chaotic Particle Swarm (Ch-PSO) is developed. This method is then used generate highly diverse and optimal solutions to the green sand mould system which is a real-world problem. Some comparative analyses are then carried out with the algorithms developed and employed in this work. Analysis on the performance as well as the quality of the solutions produced by the algorithms is presented in this chapter.

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