Warm-Start Routines for Solving Augmented Weighted Tchebycheff Network Programs in Multiple-Objective Network Programming

Abstract

T hree warm-start routines are developed to find initial basic feasible solutions for augmented weighted Tchebycheff network programs, subproblems derived from multiple-objective network-programming problems. In an interactive solution procedure, a series of augmented weighted Tchebycheff network programs need to be solved sequentially to find representative nondominated solutions. To speed up the solution process using the network structure of the problem, these warm-start routines start the solution process of one augmented weighted Tchebycheff network program from the optimal solution of the previous one. All three warm-start routines use the same strategy but different ways of reducing the number of basic flow variables, or equivalently increasing the number of basic nonflow variables to construct a basic solution. These warm-start routines can be used by any interactive procedures to facilitate the solution process of multiple-objective network-programming problems. A detailed example is presented. A computational experiment is conducted to compare the performance of these warm-start routines. A cold-start routine and NETSIDE, specialized software for solving network problems with side constraints, are also used as references in the experiment. These warm-start routines can save substantial computation time.

Finding integer efficient solutions for multiple objective network programming problems

“…Sun [28] developed special warm-start routines to start the solution process of one AWTNP from the optimal solution of another. Sun [27] developed special procedures to speed up the solution process of AWTNPs by exploiting the problem structure.…”

“…However, the AWTNP is finally solved with the special simplex method for network problems with side constraints [3]. The warm start routines of Sun [28] and solution procedures of Sun [27] together with the special simplex method for network problems with side constraints [3] are employed in this study to solve AWTNPs.…”

“…Efficient solutions for MONP problems can be generated by solving augmented weighted Tchebycheff network programs (AWTNPs) [6,22,27,28,30]. However, efficient solutions generated this way are usually not integers.…”

“…The other is the integer issue, i.e., how to obtain integer efficient solutions from fractional efficient solutions. While Sun [28] addressed the warm-start issue and Sun [30] developed a branch-and-bound (BB) algorithm to find integer efficient solutions, the focus of this study is on finding integer efficient solutions quickly. Two algorithms are developed.…”

A branch‐and‐bound algorithm for representative integer efficient solutions in multiple objective network programming problems

“…In an interactive procedure, many integer efficient solutions need to be sampled and, therefore, many AWTINPs with different λ∈Λ need to be formed and solved. For each λ∈Λ, the warm start routine [42] is used to find an initial basic solution and the procedures in Sun [41] are then used to find the best basic solution of the MONP problem. The special simplex method for network problems with side constraints is then used to find an optimal efficient solution of the initial AWTNP.…”