scholarly journals Simulated Annealing Algorithm for the Multiple Choice Multidimensional Knapsack Problem

2021 ◽  
Author(s):  
Shalin Shah
Keyword(s):  
Simulated Annealing ◽  
Open Source ◽  
Knapsack Problem ◽  
Simulated Annealing Algorithm ◽  
Multiple Choice ◽  
Optimal Solutions ◽  
Multidimensional Knapsack Problem ◽  
Multidimensional Knapsack ◽  
Benchmark Instances ◽  
Annealing Algorithm

The multiple choice multidimensional knapsack problem (MCMK) is a harder version of the 0/1 knapsack problem, and is ever more complex than the 0/1 multidimensional knapsack problem. In MCMK, there are several groups of items. The objective is to maximize the value (profit) by choosing exactly 1 item from each group such that all the constraints are satisfied. It is difficult and NP-hard even to find a solution that does not violate all constraints. In this work, we present a simulated annealing based algorithm with open source C++ code to find good solutions to the multidimensional multiple choice knapsack problem. In all of the benchmark instances we used, the algorithm is able to find optimum (or close) solutions, thereby proving that the algorithm is suitable for solving larger instances for which optimal solutions are unknown.

scholarly journals Optimization Method to Address Psychosocial Risks through Adaptation of the Multidimensional Knapsack Problem

Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1126
Author(s):  
Marta Lilia Eraña-Díaz ◽  
Marco Antonio Cruz-Chávez ◽  
Fredy Juárez-Pérez ◽  
Juana Enriquez-Urbano ◽  
Rafael Rivera-López ◽  
...  
Keyword(s):  
Risk Factors ◽  
Simulated Annealing ◽  
Knapsack Problem ◽  
Simulated Annealing Algorithm ◽  
Psychosocial Risk Factors ◽  
Psychosocial Risk ◽  
Multidimensional Knapsack Problem ◽  
Optimal Subset ◽  
Multidimensional Knapsack ◽  
A Company

This paper presents a methodological scheme to obtain the maximum benefit in occupational health by attending to psychosocial risk factors in a company. This scheme is based on selecting an optimal subset of psychosocial risk factors, considering the departments’ budget in a company as problem constraints. This methodology can be summarized in three steps: First, psychosocial risk factors in the company are identified and weighted, applying several instruments recommended by business regulations. Next, a mathematical model is built using the identified psychosocial risk factors information and the company budget for risk factors attention. This model represents the psychosocial risk optimization problem as a Multidimensional Knapsack Problem (MKP). Finally, since Multidimensional Knapsack Problem is NP-hard, one simulated annealing algorithm is applied to find a near-optimal subset of factors maximizing the psychosocial risk care level. This subset is according to the budgets assigned for each of the company’s departments. The proposed methodology is detailed using a case of study, and thirty instances of the Multidimensional Knapsack Problem are tested, and the results are interpreted under psychosocial risk problems to evaluate the simulated annealing algorithm’s performance (efficiency and efficacy) in solving these optimization problems. This evaluation shows that the proposed methodology can be used for the attention of psychosocial risk factors in real companies’ cases.

scholarly journals A two-agent one-machine multitasking scheduling problem solving by exact and metaheuristics

2021 ◽  
Author(s):  
Chin-Chia Wu ◽  
Ameni Azzouz ◽  
Jia-Yang Chen ◽  
Jianyou Xu ◽  
Wei-Lun Shen ◽  
...  
Keyword(s):  
Simulated Annealing ◽  
Completion Time ◽  
Simulated Annealing Algorithm ◽  
Optimal Schedule ◽  
Computational Studies ◽  
Scheduling Problem ◽  
Optimal Solutions ◽  
Large Size ◽  
Annealing Algorithm ◽  
One Machine

AbstractThis paper studies a single-machine multitasking scheduling problem together with two-agent consideration. The objective is to look for an optimal schedule to minimize the total tardiness of one agent subject to the total completion time of another agent has an upper bound. For this problem, a branch-and-bound method equipped with several dominant properties and a lower bound is exploited to search optimal solutions for small size jobs. Three metaheuristics, cloud simulated annealing algorithm, genetic algorithm, and simulated annealing algorithm, each with three improvement ways, are proposed to find the near-optimal solutions for large size jobs. The computational studies, experiments, are provided to evaluate the capabilities for the proposed algorithms. Finally, statistical analysis methods are applied to compare the performances of these algorithms.

A multiproduct economic order quantity model with simulated annealing application

2017 ◽  
Vol 12 (1) ◽  
pp. 119-142 ◽  
Author(s):  
Valdecy Pereira ◽  
Helder Gomes Costa
Keyword(s):  
Simulated Annealing ◽  
Design Methodology ◽  
Simulated Annealing Algorithm ◽  
Economic Order Quantity ◽  
Economic Order ◽  
Optimal Solutions ◽  
Order Quantity ◽  
Single Product ◽  
Content Type ◽  
Annealing Algorithm

Purpose This paper aims to present a set of five models for the economic order quantity problem. Four models solve problems for a single product: incremental discounts with or without backorders and all-unit discounts with or without backorders, and the last model solves problems for the multiproduct case. Design/methodology/approach A basic integer non-linear model with binary variables is presented, and its flexible structure allows for all five models to be utilised with minor modifications for adaptation to individual situations. The multiproduct model takes into consideration the work of Chopra and Meindl (2012), who studied two types of product aggregations: full and adaptive. To find optimal or near-optimal solutions for the multiproduct case, the authors propose a simulated annealing metaheuristic application. Numerical examples are presented to improve the comprehension of each model, and the authors also present the efficiency of the simulated annealing algorithm through an example that aggregates 50 products, each one with different discount schemes and some allowing backorders. Findings Our model proved to be efficient at finding optimal or near optimal solutions even when confronted with mathematical complexities such as the allowance of backorders and incremental discounts. Originality/value Finally our model can process a mix of products with different discount schemes at the same time, and the simulated annealing metaheuristics could find optimal or near optimal solutions with very few iterations.

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