Using Goal Programming on Estimated Pareto Fronts to Solve Multiobjective Problems

Abstract

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.

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

“…Figure 2 presents the results of the effectiveness analysis. As it was the case in Pinheiro et al (2018) for another problem, the overall effectiveness of the obtained weight vectors here surpassed 90%. Pilot instance 50-δ0-tw4 presented the best average value of 96% and 250-δ0-tw4 presented the worst with 91.3%.…”

“…In this work, we applied a methodology based on goal programming to use efficient single-objective algorithms to solve a multiobjective vehicle routing problem with time windows. The methodology was first presented in (Pinheiro et al, 2018) and it consists of: 1) solving a pilot instance of the problem using multiobjective algorithms (which are typically computationally expensive) to obtain a good approximation set, 2) having the decision-maker to choose preferred target compromise solutions, and then 3) employing goal programming to solve other instances of the same dataset using the selected solutions in 2) as the target. Three different objective functions were used to guide the search for the target solutions with goal programming.…”

“…While the WSRP datasets tackled in (Pinheiro et al, 2018) arise from realworld scenarios, the MOVRPTW datasets considered here were fabricated for benchmarking purposes. Also, even the largest MOVRPTW scenario is considerably smaller than a medium-sized WSRP.…”

“…For example, it has been applied to nurse scheduling (Azaiez and Al Sharif, 2005) (Musa and Saxena, 1984) and to a version of the vehicle routing problem with soft time-windows (Calvete et al, 2007). Figure 1 shows the overall concept of the methodology which was originally proposed in Pinheiro et al (2018). Each of the steps is explained below in reference to the MOVRPTW tackled in this paper.…”

“…Previous work proposed a technique to analyse and visualise complex objective relationships and fitness landscapes in multiobjective problems (Pinheiro et al, 2015(Pinheiro et al, , 2017. Later, Pinheiro et al (2018) introduced a methodology to exploit the recurring similarity between instances of a multiobjective workforce scheduling and routing optimisation problem, in order to solve instances of the same problem scenario more efficiently. In this methodology, a pilot problem instance is solved first using some effective (but not necessarily computationally efficient) multiobjective algorithm to produce an approximation to the Pareto optimal set.…”