A heuristic approach to minimize three criteria using efficient solutions

Abstract

In <span>optimization, scheduling problems is concerning allocations of some resources which are usually limited. These allocations are done in order to fulfil some criterion by performing some tasks or jobs to optimize one or more objective functions. Simultaneous multi-criteria scheduling problem is known as np-hard optimization problem. Here, we consider three criteria for scheduling a number of jobs on a single machine. The problem is to minimize the sum of total completion time, maximum earliness and maximum tardiness. Every job is to be processed without interruption and becomes available for processing at time zero. The aim is to find a processing order of the jobs to minimize three-objective functions simultaneously. We present a new heuristic approach to find a best overall solution (accepted) of the problem using efficient solutions of one of the other related criteria. We establish a result to restrict the range of the optimal solution, and the lower bound depends on the decomposition of the problem into three subproblems. The approach is tested on a set of problems of different number of jobs. Computational results demonstrate the efficiency of the proposed approach.</span>

Solving Tri-criteria: Total Completion Time, Total Earliness, and Maximum Tardiness Using Exact and Heuristic Methods on Single-Machine Scheduling Problems

“…, 𝑛 cannot be found, considering that at least one of the aforementioned is a strict disparity. Another way is that 𝛼 * is dominated by 𝛼 [20].…”

“…Large and complex problems in the research community are often solved using contemporary heuristic optimization techniques [19]. Hassan et al [20] used a heuristic algorithm to minimize the (𝐸 𝑚𝑎𝑥 + 𝑇 𝑚𝑎𝑥 + ∑𝐶 𝑗 )in a SMSP. Neamah and Kalaf [21] proved that SPT and EDD rules give efficient (optimal) solutions for two problems 1//(∑𝐶 𝑗 , ∑𝑉 𝑗 , 𝐸 𝑚𝑎𝑥 ), and 1//∑𝐶 𝑗 + ∑𝑉 𝑗 + 𝐸 𝑚𝑎𝑥 , also, proven special cases, resulting in the most an efficient and optimal solution to these problems.…”

Solving Three Objectives Single-Machine Scheduling Problem Using Fuzzy Multi-Objective Linear Programming

“…The following notations are used in order to describe the multi-objective single-machine scheduling model [27]. N = number of jobs, p j = processing time for job j ∀j= (1, …, N), d j = due date for job j, M = a large positive integer value, MST: (minimum slack times) here, the jobs are sequenced in non-decreasing order of minimum slack time s j , where s j = d j -p j , SPT: (shortest processing time) jobs are sequenced in non-decreasing order of p j , EDD: (Early due date) jobs are sequenced in nondecreasing order of d j .…”

“…The following model has three criteria namely, 𝑍 1 : total completion time, 𝑍 2 : maximum earliness, 𝑍 3 : maximum tardiness [27], the aim is finding the best possible (optimal) schedule that minimizes these criteria. We should note that at least two of these objectives are in conflict with each other [4].…”

Solving the multi-criteria: Total completion time, total late work, and maximum earliness problem

“…Ahmed in 2022 [7] studied the multicriteria(∑ 𝑪 𝒋 , 𝑻 𝒎𝒂𝒙 , 𝑹 𝑳 )and multi-objective function (∑ 𝑪 𝒋 + 𝑻 𝒎𝒂𝒙 + 𝑹 𝑳 )and found the optimal solution by using BAB method with and without DR then use some heuristic methods. Hassan et al in 2022 [8] introduced a heuristic algorithm to reduce the (∑ 𝑪 𝒋 + 𝑬 𝒎𝒂𝒙 + 𝑻 𝒎𝒂𝒙 ) in just one machine scheduling.…”