Operational research and solving of problems that have more affect the society can be solved in various ways depending on the complexity of the problems. Murat and Banu addressed the problem of finding the nadir point using integer programming in a multi-objective manner [3]. The addressed problem was not easy nor straight forward, more so when over three objectives are required. Apart from the need of more than three objectives, integer-programming problems increased causing difficulties to the expected solution. Among other developed algorithms, Murat and Banu developed the exact algorithm to help calculate the nadir point under multi-objective integer programs [3]. Due to many components within the problem, variations were developed to aid in finding bounds on every component to the major problem (the nadir point). The level of accuracy as determined by Murat and Banu depends on the quality of integer programming performed for a specific problem [8]. Some of the instances described by the authors include the shortest path and knapsack where algorithms work better. Duarte, Pantrigo, Pardo, et al. found out those solutions to real-life problems can be found using multiple conflicting objectives [2]. However, from previous research findings, such problems had their solutions found using evolutionary algorithms. The study done by Duarte explored the adaptation of the VS metaheuristic in solving multi-objective combinatorial challenges. The design can be described as a shake procedure for the improvement and acceptance of VNS schemas when dealing with more than one objective. Meng and Pan performed an optimization on fruit fly in creating an algorithm to solve the experienced multidimensional knapsack challenge (MKP) [7]. The exploitation and exploration of the search were balanced. To enable an enhanced and optimized mode of performing the research, a random and adjusted scheme selection rule was developed upon the consideration of certain features of FOA and MKP. Due to the complexity of the problem, extensive numerical simulations were conducted in association with the developed algorithms in verification of the proposed algorithms.

Using the multi-objective and multidimensional, Mansour and Pan used the method in solving a real estate problem in handling a problem related to the maintenance of the structure’s components within a limited budget in a limited time [5]. Under such few resources, it was expected that the multiple and conflicting objectives must be achieved. The main challenge that was experienced was the condition to achieve the set targets within a year of optimized different criteria that must be relative to the property’s maintenance objectives. The predetermined budget posed difficulties in achieving the set goals. However, innovative modeling multi-objective of REPMP [4]. In another research conducted by Bagherinejad & Dehghani [1], a knapsack problem (KP) together with its multidimensional version created the basic problems for optimization. The article (research) was considered a bi-objective integer of knapsack problem (BOMIKP) whose objective was to estimate the set of non-dimensional remedies with an evolutionary algorithm [6]. The results obtained using the method indicated the benefits and effectiveness of the applied procedures when reporting about the optimal problem. Human beings suffer from various challenges that need solutions derived using specific learning mechanisms. Human learning optimization (HLO) was applied by Wang, Yang, Ni, Ye, Fei, & Pardalos [9] in optimizing the algorithm and applying it to knapsack problems among the people. The study was conducted on individual people and learning about the manner the society operates. However, re-learning operations were developed that generated better solutions that brought out the target result of the human learning process.

1. Bagherinejad, J., & Dehghani, M. (2016). Optimizing the bi-objective multidimensional integer knapsack problem using non-dominated sorting particle swarm

optimization. International Journal of Industrial and Systems Engineering, 23(3), 263- 289.

2. Duarte, A., Pantrigo, J. J., Pardo, E. G., & Mladenovic, N. (2015). Multi-objective variable neighborhood search: an application to combinatorial optimization problems. Journal of Global Optimization, 63(3), 515-536.
3. Köksalan, M., & Lokman, B. (2015). Finding nadir points in multi-objective integer programs. Journal of Global Optimization, 62(1), 55-77.
4. Laabadi, S., Naimi, M., El Amri, H., & Achchab, B. (2018). The 0/1 Multidimensional Knapsack Problem and Its Variants: A Survey of Practical Models and Heuristic Approaches. American Journal of Operations Research, 8(05), 395.
5. Mansour, I. B., Alaya, I., & Tagina, M. (2017, July). Solving Multiobjective Knapsack Problem Using Scalarizing Function Based Local Search. In International Conference on Software Technologies (pp. 210-228). Springer, Cham.
6. Mavrotas, G., Florios, K., & Figueira, J. R. (2015). An improved version of a core based algorithm for the multi-objective multi-dimensional knapsack problem: A computational study and comparison with meta-heuristics. Applied Mathematics and Computation, 270, 25-43.