Analysis of Objectives Relationships in Multiobjective Problems Using Trade-Off Region Maps

Operations Research and Enterprise Systems

Laesanklang

et al. 2019

Self Cite

Many real-world applications require decision-makers to assess the quality of solutions while considering multiple conflicting objectives. Obtaining good approximation sets for highly constrained manyobjective problems is often a difficult task even for modern multiobjective algorithms. In some cases, multiple instances of the problem scenario present similarities in their fitness landscapes. That is, there are recurring features in the fitness landscapes when searching for solutions to different problem instances. We propose a methodology to exploit this characteristic by solving one instance of a given problem scenario using computationally expensive multiobjective algorithms to obtain a good approximation set and then using Goal Programming with efficient single-objective algorithms to solve other instances of the same problem scenario. We use three goal-based objective functions and show that on benchmark instances of the multiobjective vehicle routing problem with time windows, the methodology is able to produce good results in short computation time. The methodology allows to combine the effectiveness of state-of-the-art multiobjective algorithms with the efficiency of goal programming to find good compromise solutions in problem scenarios where instances have similar fitness landscapes.

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An Efficient Application of Goal Programming to Tackle Multiobjective Problems with Recurring Fitness Landscapes

Operations Research and Enterprise Systems

Laesanklang

et al. 2019

Self Cite

“…Hence, the technique proposed i this paper can be of practical use in that type of problems. In addition, the multiobjective analysis technique proposed by (Pinheiro et al, 2015(Pinheiro et al, , 2017 offers an effective tool to evaluate whether using goal programming to solve the problem is applicable or not.…”

Section: Resultsmentioning

confidence: 99%

“…As preliminary work, we applied the analysis technique proposed by Pinheiro et al (2015Pinheiro et al ( , 2017 on all instances considered here. The technique consists of performing four steps: first the global pairwise relationships are analysed using the Kendall correlation method; then the ranges of the values found on the given approximation front are estimated and assessed; next these ranges are used to plot a map using Gray code, similar to Karnaugh maps, that has the ability to highlight the trade-offs between multiple objectives; and finally local relationships are identified using scatter plots.…”

Section: The Workforce Scheduling and Routing Problemmentioning

confidence: 99%

“…This happens in other problems like vehicle routing and nurse scheduling where instances of the same problem scenario exhibit similar fitness landscapes (η-dimensional surface representing the Pareto front, where η is the number of objectives). This issue was investigated in Pinheiro et al (2015Pinheiro et al ( , 2017 which proposed a technique to analyse and visualise complex objective relationships and fitness landscapes in multiobjective problems. Thus, this paper proposes a methodology that exploits this similarity between instances of a multiobjetive optimisaton problem, in order to solve instances of the problem more efficiently.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Using Goal Programming on Estimated Pareto Fronts to Solve Multiobjective Problems

Proceedings of the 7th International Conference on Operations Research and Enterprise Systems

Laesanklang

et al. 2018

Self Cite

Abstract:Modern multiobjective algorithms can be computationally inefficient in producing good approximation sets for highly constrained many-objective problems. Such problems are common in real-world applications where decision-makers need to assess multiple conflicting objectives. Also, different instances of real-world problems often share similar fitness landscapes because key parts of the data are the same across these instances. We we propose a novel methodology that consists of solving one instance of a given problem scenario using computationally expensive multiobjective algorithms to obtain a good approximation set and then using Goal Programming with efficient single-objective algorithms to solve other instances of the same problem scenario. We propose three goal-based objective functions and show that on a real-world home healthcare planning problem the methodology can produce improved results in a shorter computation time.

A technique based on trade-off maps to visualise and analyse relationships between objectives in optimisation problems

J. Multi-Crit. Decis. Anal.

Atkin

2017

Self Cite

Understanding the relationships between objectives in a multiobjective optimisation problem is important for developing tailored and efficient solving techniques. In particular, when tackling combinatorial optimisation problems with many objectives, that arise in real-world logistic scenarios, better support for the decision maker can be achieved through better understanding of the often complex fitness landscape. This paper makes a contribution in this direction by presenting a technique that allows a visualisation and analysis of the local and global relationships between objectives in optimisation problems with many objectives. The proposed technique uses four steps: First, the global pairwise relationships are analysed using the Kendall correlation method; then, the ranges of the values found on the given Pareto front are estimated and assessed; next, these ranges are used to plot a map using Gray code, similar to Karnaugh maps, that has the ability to highlight the trade-offs between multiple objectives; and finally, local relationships are identified using scatter plots. Experiments are presented for three combinatorial optimisation problems: multiobjective multidimensional knapsack problem, multiobjective nurse scheduling problem, and multiobjective vehicle routing problem with time windows . Results show that the proposed technique helps in the gaining of insights into the problem difficulty arising from the relationships between objectives. KEYWORDS fitness landscape visualisation, multiobjective combinatorial problems, multiobjective fitness landscape analysis, trade-off region maps 1 throughout the majority of the search space and is often easy to identify. A local relationship exists in a restricted region of the search space and can be difficult to spot. Understanding local relationships is a useful tool to design tailored algorithms (Garrett & Dasgupta, 2008).