Nondominated solution

2011 ◽  
Keyword(s):  
Nondominated Solution

scholarly journals Planning for Multiple Preferences versus Planning with No Preference

2012 ◽  
Vol 2012 ◽  
pp. 1-9
Author(s):  
Daniel Bryce
Keyword(s):  
Multiple Solutions ◽  
Search Algorithm ◽  
Resource Consumption ◽  
Decision Makers ◽  
Relative Performance ◽  
Empirical Comparison ◽  
Multiple Alternative ◽  
Nondominated Solution ◽  
Single Objective

Many planning applications must address conflicting plan objectives, such as cost, duration, and resource consumption, and decision makers want to know the possible tradeoffs. Traditionally, such problems are solved by invoking a single-objective algorithm (such as A*) on multiple, alternative preferences of the objectives to identify nondominated plans. The less-popular alternative is to delay such reasoning and directly optimize multiple plan objectives with a search algorithm like multiobjective A* (MOA*). The relative performance of these two approaches hinges upon the number of -values computed for individual search nodes. A* may revisit a node several times and compute a different -value each time. MOA* visits each node once and may compute some number of -values (each estimating the value of a different nondominated solution constructed from the node). While A* does not share -values between searches for different solutions, MOA* can sometimes find multiple solutions while computing a single -value per node. The results of extensive empirical comparison show that (i) the performance of multiple invocations of a single-objective A* versus a single invocation of MOA* is often worse in time and quality and (ii) that techniques for balancing per node cost and exploration are promising.

scholarly journals Modeling and Optimization of the Multiobjective Stochastic Joint Replenishment and Delivery Problem under Supply Chain Environment

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Lin Wang ◽  
Hui Qu ◽  
Shan Liu ◽  
Cai-xia Dun
Keyword(s):  
Optimization Problem ◽  
Differential Evolution Algorithm ◽  
Service Level ◽  
Joint Replenishment ◽  
Delivery Problem ◽  
Multi Objective ◽  
Intelligent Optimization Algorithms ◽  
Evolution Algorithm ◽  
Nondominated Solution ◽  
The One

As a practical inventory and transportation problem, it is important to synthesize several objectives for the joint replenishment and delivery (JRD) decision. In this paper, a new multiobjective stochastic JRD (MSJRD) of the one-warehouse andn-retailer systems considering the balance of service level and total cost simultaneously is proposed. The goal of this problem is to decide the reasonable replenishment interval, safety stock factor, and traveling routing. Secondly, two approaches are designed to handle this complex multi-objective optimization problem. Linear programming (LP) approach converts the multi-objective to single objective, while a multi-objective evolution algorithm (MOEA) solves a multi-objective problem directly. Thirdly, three intelligent optimization algorithms, differential evolution algorithm (DE), hybrid DE (HDE), and genetic algorithm (GA), are utilized in LP-based and MOEA-based approaches. Results of the MSJRD with LP-based and MOEA-based approaches are compared by a contrastive numerical example. To analyses the nondominated solution of MOEA, a metric is also used to measure the distribution of the last generation solution. Results show that HDE outperforms DE and GA whenever LP or MOEA is adopted.

scholarly journals Multiple Objective Fuzzy Sourcing Problem with Multiple Items in Discount Environments

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Feyzan Arikan
Keyword(s):  
Vital Role ◽  
Mixed Integer ◽  
Multiple Objective ◽  
Total Production ◽  
Integer Linear Programming Problem ◽  
Aspiration Levels ◽  
Multiple Item ◽  
Promising Solution ◽  
Nondominated Solution ◽  
Selection Of

The selection of proper supply sources plays a vital role to maintain companies’ competitiveness. In this study a multiple criteria fuzzy sourcing problem with multiple items in discount environment is considered as a multiple objective mixed integer linear programming problem. Fuzzy parameters are demand level and/or aspiration levels of objectives. Three objective functions are minimization of the total production and ordering costs, the total number of rejected units, and the total number of late delivered units, respectively. The model is developed for the all-units discount scheme. For the incremental discount and volume discount environment, modification requirements of the model are mentioned. The previously proposed interactive fuzzy approach combined with three fuzzy mathematical models is employed to obtain most satisfactory solution which is also a nondominated one. This study provides a realistic mathematical model and promising solution strategy to multiple item-single period sourcing problem in discount environment. Consideration of fuzziness makes the obtained nondominated solution implementable for the real cases.

scholarly journals AI-Driven Multiobjective Scheduling Algorithm of Flood Control Materials Based on Pareto Artificial Bee Colony

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Banteng Liu ◽  
Junjie Lu ◽  
Yourong Chen ◽  
Ping Sun ◽  
Kehua Zhao ◽  
...  
Keyword(s):  
Flood Control ◽  
Artificial Bee Colony ◽  
Scheduling Algorithm ◽  
Optimal Solution ◽  
Scheduling Optimization ◽  
Satisfaction Rate ◽  
Bee Colony ◽  
Transportation Distance ◽  
Nondominated Solution ◽  
Nondominated Sorting

Considering the competition between rescue points, we use artificial intelligence (AI) driven Internet of Thing (IoT) and regional material storage data to propose a multiobjective scheduling algorithm of flood control materials based on Pareto artificial bee colony (MSA_PABC). To address the scheduling of flood control materials, the multiple types of flood control materials, the multiple disaster sites, and entertain both emergency and fairness of rescue need to be considered comprehensively. The MSA_PABC has the constraints such as storage quantity constraint of warehouse materials, material demand constraint, and maximum transportation distance of flood control materials. We establish the scheduling optimization model of flood control materials for each disaster rescue point and the total scheduling optimization model for all flood control materials. Then, MSA_PABC uses the modified Pareto artificial bee colony algorithm to solve the multiobjective models. Three types of initialization strategies are proposed to calculate the fitness of each rescue point and the overall evaluation value of the food source. We propose the employ bee operations such as niche technology and local search of the variable neighborhood, the onlooker bee operations such as Pareto nondominated sorting and crossover operation, the scout bee operations such as maximum evolutionary threshold, and end elimination mechanism. Finally, our proposed solution obtains the nondominated solution set and its optimal solution. The experimental results show that no matter how the number of rescue points changes, MSA_PABC can find the nondominated solution set and optimal solution quickly. It improves the convergence rate of MSA_PABC and material satisfaction rate. Our solution also reduces the average maximum transportation distance, the standard deviation of maximum transportation distance, and the standard deviation of material satisfaction rate. The evaluation also demonstrates MSA_PABC outperforms the state-of-arts such as ABC (artificial bee colony), NSGA2 (nondominated sorting genetic algorithm 2), and MOPSO (multiobjective particle swarm optimization).

scholarly journals Multiobjective Quantum Evolutionary Algorithm for the Vehicle Routing Problem with Customer Satisfaction

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Jingling Zhang ◽  
Wanliang Wang ◽  
Yanwei Zhao ◽  
Carlo Cattani
Keyword(s):  
Customer Satisfaction ◽  
Evolutionary Algorithm ◽  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Time Window ◽  
Adaptive Grid ◽  
Solution Set ◽  
Mixed Integer ◽  
Routing Problem ◽  
Nondominated Solution

The multiobjective vehicle routing problem considering customer satisfaction (MVRPCS) involves the distribution of orders from several depots to a set of customers over a time window. This paper presents a self-adaptive grid multi-objective quantum evolutionary algorithm (MOQEA) for the MVRPCS, which takes into account customer satisfaction as well as travel costs. The degree of customer satisfaction is represented by proposing an improved fuzzy due-time window, and the optimization problem is modeled as a mixed integer linear program. In the MOQEA, nondominated solution set is constructed by the Challenge Cup rules. Moreover, an adaptive grid is designed to achieve the diversity of solution sets; that is, the number of grids in each generation is not fixed but is automatically adjusted based on the distribution of the current generation of nondominated solution set. In the study, the MOQEA is evaluated by applying it to classical benchmark problems. Results of numerical simulation and comparison show that the established model is valid and the MOQEA is effective for MVRPCS.

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